how many c atoms are present in the sample of c3h8 with mass 3.21 g? avogadro’s number is 6.022 × 1023. enter your answer using scientific notation and to three significant digits.

Answers

Answer 1

The answer is 6.73 x 10²² C atoms. This is because the mass of the sample is 3.21 g, and the molar mass of C3H8 is 60.06 g/mol.

What is Avogadro's number?

It is defined as the number of particles in one mole of a substance and is equal to 6.022 x 10²³. Avogadro's number is used to calculate the number of moles in a given mass of a substance or the mass of a given number of moles.

The number of C atoms present in a sample of C3H8 with mass 3.21 g can be calculated using Avogadro's number.

Avogadro's number is 6.022 x 10²³, which is the number of particles (atoms, molecules, ions, etc.) that are in one mole of a substance. Therefore, the calculation for the number of C atoms in the sample is:

(3.21 g C3H8/60.06 g/mol C3H8) x (6.022 x 10²³ particles/mol) x (3 mol C/1 mol C3H8) = 6.73 x 10²² C atoms

The answer to the question is 6.73 x 10²² C atoms. This is because the mass of the sample is 3.21 g, and the molar mass of C3H8 is 60.06 g/mol.

Therefore, when the molar mass is divided by the mass of the sample, the number of moles of C3H8 in the sample is calculated. This number is then multiplied by Avogadro's number to give the total number of particles (in this case, atoms) in the sample, and then multiplied by the number of C atoms in one mole of C3H8, which is 3.

This calculation gives the total number of C atoms present in the sample.

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Related Questions

C8h16 + 12o2=8CO2 + 8h2o What is the ratio of octene (c8h16) to oxygen in the reaction?

Answers

The balanced chemical equation for the combustion of octene (C₈H₁₆) is:

C₈H₁₆ + 12O₂ → 8CO₂ + 8H₂O

The ratio of octene to oxygen in the reaction is 1:12.

The balanced chemical equation for the combustion of octene shows the reactants and products of the reaction and also indicates the stoichiometry of the reaction.

In this case, the balanced equation shows that 1 mole of octene reacts with 12 moles of oxygen to produce 8 moles of carbon dioxide and 8 moles of water. This means that the ratio of octene to oxygen in the reaction is 1:12, which indicates that a much larger amount of oxygen is needed compared to octene. This is because oxygen is the limiting reactant in the reaction and must be present in excess to ensure that all of the octene is consumed during the reaction.

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Using the thermodynamic information in the ALEKS Data tab, calculate the standard reaction entropy of the following chemical reaction:
C3H8(g)+5O2(g)→3CO2(g)+4H2O(l)
Round your answer to zero decimal places.
? J/K

Answers

The standard reaction entropy for the given chemical reaction is 109 J/K (rounded to zero decimal places).

To calculate the standard reaction entropy of the given chemical reaction, we need to use the standard entropy of formation values of the products and reactants.

The standard entropy of formation values are given in the ALEKS Data tab as follows:

C₃H₈(g) : 186.2 J/K

O₂(g) : 205.0 J/K

CO₂(g) : 213.6 J/K

H₂O(l) : 69.9 J/K

Using these values, we can calculate the change in entropy (ΔS) for the reaction:

ΔS = ΣS(products) - ΣS(reactants)

ΔS = [3(213.6 J/K) + 4(69.9 J/K)] - [1(186.2 J/K) + 5(205.0 J/K)]

ΔS = 108.7 J/K

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The standard reaction entropy for the given chemical reaction is 109 J/K (rounded to zero decimal places).

To calculate the standard reaction entropy of the given chemical reaction, we need to use the standard entropy of formation values of the products and reactants.

The standard entropy of formation values are given in the ALEKS Data tab as follows:

C₃H₈(g) : 186.2 J/K

O₂(g) : 205.0 J/K

CO₂(g) : 213.6 J/K

H₂O(l) : 69.9 J/K

Using these values, we can calculate the change in entropy (ΔS) for the reaction:

ΔS = ΣS(products) - ΣS(reactants)

ΔS = [3(213.6 J/K) + 4(69.9 J/K)] - [1(186.2 J/K) + 5(205.0 J/K)]

ΔS = 108.7 J/K

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1. Acetic acid is a weak acid, meaning it does not fully dissociate in water. Instead, there is an equilibrium between the dissolved but undissociated molecule and the component ions: HOAc (aq) + H20 (1)=H20+ (aq) + OAC (aq) OAc is an abbreviation for the acetate ion, CH3C00 , and H30+ is the hydronium ion (lone protons, H+ (aq), do not exist!). (a) Write the equilibrium constant expression for the dissociation of acetic acid. (b) Vinegar sold commercially is typically 0.8-1.0M acetic acid. A 1.00 M solution of acetic acid is measured by its pH to have an equilibrium concentration of 4.19x10-3 M for both acetate ions and hydronium ions at room temperature. Assuming (HOAc]o 1.00 M, what is the equilibrium concentration of undissociated acetic acid (HOAceq to the correct number of significant figures? (c) What is the value of the equilibrium constant Keq for the dissociation according to the concentrations from part (b)? (d) When starting with completely un-dissociated acetic acid, is it accurate to assume that [HOAc]o = [HOAceq? Why or why not? (e) A highly concentrated acetic acid solution contains 15.0M acetic acid at equilibrium. What are the equilibrium concentrations of the hydronium and acetate ions in this solution? (f) Creating the concentrated acetic acid solution by dissolving liquid HOAc in water raises the temperature of the water by about 5 °C from room temperature. At 50 °C, do you expect the solution to contain more or less acetate ion Ac than what you calculated in (c)? Why?

Answers

(a) The equilibrium constant expression for the dissociation of acetic acid is: Keq = [H3O+][OAc-]/[HOAc].

(b) Using the equilibrium concentrations of [H3O+] = [OAc-] = 4.19x10^-3 M and the initial concentration of [HOAc]o = 1.00 M, we can calculate the equilibrium concentration of undissociated acetic acid (HOAceq) using the equilibrium constant expression: Keq = [H3O+][OAc-]/[HOAc]o = (4.19x10^-3)^2/1.00 = 1.75x10^-5 M. To find the equilibrium concentration of HOAceq, we use the conservation of mass equation: [HOAc]o = [HOAceq] + [OAc-], which gives [HOAceq] = [HOAc]o - [OAc-] = 1.00 - 4.19x10^-3 = 0.996 M.

(c) The equilibrium constant Keq can be calculated using the values from part (b): Keq = [H3O+][OAc-]/[HOAc]o = (4.19x10^-3)^2/1.00 = 1.75x10^-5.

(d) It is not accurate to assume [HOAc]o = [HOAceq] when starting with completely undissociated acetic acid because at equilibrium, some of the acetic acid has dissociated into its component ions. Therefore, [HOAc]o is greater than [HOAceq].

(e) To find the equilibrium concentrations of hydronium and acetate ions in a 15.0 M acetic acid solution, we use the equilibrium constant expression: Keq = [H3O+][OAc-]/[HOAc]. Rearranging this equation and plugging in the values, we get [H3O+] = [OAc-] = sqrt(Keq x [HOAc]) = sqrt(1.75x10^-5 x 15.0) = 0.0416 M.

(f) At 50 °C, the solution will contain more acetate ion (OAc-) than what was calculated in (c) because an increase in temperature favors the dissociation of acetic acid, shifting the equilibrium to the right.

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Account for the effects of NH_3(aq) and HCI(aq) on the CuSO_4 or NiCl_2 solution. Use equations 16.2-5 in your explanation Metal-Ammonia Ions. Aqueous solutions of copper ions and nickel ions appear sky blue and green, respectively. The colors of the solutions change, however, in the presence of added ammonia. NH_3. Because the metal-ammonia bond is stronger than the metal-water bond, ammonia substitution occurs and the following equilibria shift right, forming the metal-ammonia complex ions:^1 Addition of strong acid, H^+ affects these equilibria by its reaction with ammonia (a base) on the left side of the equations: The ammonia being removed from the equilibria causes the reactions to shift left to relieve the stress caused by the removal of the ammonia, re-forming the aqueous Cu (sky blue) and Nr^2+ (green) solutions. For copper ions, this equilibrium shift may be represented as

Answers

When NH3(aq) is added to CuSO4 or NiCl2 solutions, the metal-ammonia bond is stronger than the metal-water bond, causing ammonia substitution and forming metal-ammonia complex ions. The equilibrium shifts right due to this stronger bond.

For example:
Cu²⁺(aq) + 4NH3(aq) ⇌ [Cu(NH3)4]²⁺(aq) (deep blue)
Ni²⁺(aq) + 6NH3(aq) ⇌ [Ni(NH3)6]²⁺(aq) (violet)
When a strong acid like HCl(aq) is added, it reacts with ammonia (a base) present in the solution, removing ammonia from the equilibrium:
NH3(aq) + H⁺(aq) → NH4⁺(aq)
This causes the equilibrium to shift left, reforming the original aqueous Cu²⁺(sky blue) and Ni²⁺(green) solutions. This is because the removal of ammonia relieves the stress caused by the reaction between ammonia and the strong acid.

When CuSO_4 or NiCl_2 is dissolved in water, the resulting solution is sky blue or green in colour, respectively, due to the presence of Cu^2+ or Ni^2+ ions in an aqueous solution. However, when NH_3(aq) is added to the solution, the metal-ammonia bond is stronger than the metal-water bond, leading to ammonia substitution and the formation of metal-ammonia complex ions:
Cu^2+ + 4NH_3 ⇌ [Cu(NH_3)_4]^2+
Ni^2+ + 6NH_3 ⇌ [Ni(NH_3)_6]^2+
The addition of HCl(aq) affects these equilibria by reacting with the ammonia (a base) on the left side of the equations, removing ammonia from the equilibria and causing the reactions to shift left to relieve the stress caused by the removal of ammonia.

As a result, the metal-ammonia complex ions dissociate and reform the aqueous Cu^2+ and Ni^2+ solutions. This can be represented by the following equation for Cu^2+:
[Cu(NH_3)_4]^2+ + 4H^+ ⇌ Cu^2+ + 4NH_4^+
Overall, the effects of NH_3(aq) and HCl(aq) on the CuSO_4 or NiCl_2 solution can be explained by the metal-ammonia complex ion formation and the subsequent dissociation caused by the addition of H^+ ions.

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The principle that allows the enthalpy of a reaction to be determined indirectly from several steps is called - Law of Dulong and Petit - Hess' law - Henry's law
- Avogadro's law

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The principle that allows the enthalpy of a reaction to be determined indirectly from several steps is called Hess' law.

Hess's law is a principle in thermodynamics that states that the enthalpy change of a chemical reaction is independent of the pathway between the initial and final states. This means that the total enthalpy change of a reaction can be calculated by adding the enthalpy changes of a series of intermediate reactions that connect the initial and final states, even if these intermediate reactions are not the actual steps of the reaction. Hess's law is based on the fact that enthalpy is a state function, which means that its value depends only on the initial and final states of a system, and not on the process by which the system reached those states. By using a series of intermediate reactions, it is possible to construct a path between the initial and final states that is easier to measure experimentally, and from which the enthalpy change of the overall reaction can be calculated indirectly.

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27. oxidation (kmno4 or ozone) of unsymmetrical internal alkynes produces two carboxylic acids whereas under the same condition terminal alkyne produces one carboxylic acid — explain.

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The reason why oxidation (using KMnO4 or ozone) of unsymmetrical internal alkynes produces two carboxylic acids is because the unsymmetrical alkynes have two different groups attached to each end of the triple bond. During oxidation, the triple bond is broken and each end of the molecule is converted into a carboxylic acid.

Since the two ends of the unsymmetrical alkyne have different groups, two different carboxylic acids are produced. On the other hand, terminal alkynes have the same group attached to each end of the triple bond. When terminal alkynes undergo oxidation, only one carboxylic acid is produced because both ends of the molecule are the same.

The oxidation of unsymmetrical internal alkynes with reagents like KMnO4 or ozone results in the formation of two carboxylic acids because the alkyne has two distinct alkyl groups attached to the carbon-carbon triple bond. When the oxidizing agent breaks the triple bond, each carbon forms a carboxylic acid group, leading to two different carboxylic acids.

On the other hand, terminal alkynes have a hydrogen atom attached to one of the carbons in the carbon-carbon triple bond. When terminal alkynes undergo oxidation using KMnO4 or ozone, the hydrogen atom is replaced by a carboxylic acid group, while the other carbon in the triple bond forms a carboxylic acid. However, the carboxylic acid formed from the hydrogen side is a formic acid (HCOOH), which can be further oxidized to carbon dioxide and water. Therefore, under the same conditions, the oxidation of terminal alkynes ultimately produces only one carboxylic acid.

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The equilibrium constant for the chemical equation N2(g) + 3H2(g) arrow 2NH3(g) is Kp = 7.82 at 195 degrees Celsius. Calculate the value of Kc for the reaction ..

Answers

The value of Kc for the reaction N2(g) + 3H2(g) ⇌ 2NH3(g) at 195 degrees Celsius is 4.16 x 10^2 mol/L.

Given

At 195 degrees Celsius, the chemical equation N2(g) + 3H2(g) arrow 2NH3(g) is Kp = 7.82.

To Find      

the value of Kc for the reaction.

Solution      

We must apply the relationship between Kp and Kc, which is given by: to determine the value of Kc for the reaction.

Kc = Kp (RT) n              

     

where:

Partial pressures are used to express Kp, the equilibrium constant.

In molar concentrations, Kc represents the equilibrium constant.

The gas constant, or R, is 0.08206 L atm/K mol.

The temperature in Kelvin is T.

The stoichiometric coefficient n is the difference between the total of the gaseous products' and the gaseous reactants' stoichiometric coefficients (in this case, n = 2 - (1+3) = -2).

To find Kc, we can rearrange this equation as follows:

Kp = Kc / (RT)        

Inputting the values provided yields:

Kc is calculated as 7.82 / (0.08206 L atm/K mol * (195+273) K).(-2)

Kc equals 4.16 x 102 mol/L

Therefore, the value of Kc for the reaction N2(g) + 3H2(g) ⇌ 2NH3(g) at 195 degrees Celsius is 4.16 x 10^2 mol/L.

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Using the accepted values for delta H and S, calculate the Ksp of anhydrous CaSO4 at 5 degrees C

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The Ksp (solubility product constant) of anhydrous CaSO4 at 5 degrees Celsius can be calculated using the thermodynamic equation ΔG = -RTlnK, where ΔG is the Gibbs free energy change,

R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant. The ΔH and ΔS values for the dissolution of anhydrous CaSO4 can be found in thermodynamic tables as -90.9 kJ/mol and 152.3 J/(mol·K), respectively. Plugging in these values and converting to Kelvin, we can calculate a Ksp of approximately 2.7 x 10^-5 mol^2/L^2 at 5 degrees Celsius. This value indicates the maximum concentration of dissolved CaSO4 that can be reached in a saturated solution at equilibrium under these conditions.

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Consider the reaction a+2b⇌c for which in the initial mixture qc=[c][a][b]2=387 is the reaction at equilibrium? if not, in which direction will it proceed to reach equilibrium?

Answers

The reaction a + 2b ⇌ c is not at equilibrium if Qc ≠ Kc. If Qc < Kc, it will proceed in the forward direction (towards c); if Qc > Kc, it will proceed in the reverse direction (towards a and b).

To determine if the reaction is at equilibrium, compare the given Qc value (387) to the Kc value for this reaction. If Qc = Kc, then the reaction equilibrium occurs. If Qc < Kc, the reaction will proceed in the forward direction, meaning the concentrations of a and b will decrease while the concentration of c will increase.

On the other hand, if Qc > Kc, the reaction will proceed in the reverse direction, meaning the concentration of a and b will increase while the concentration of c will decrease.

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We spent a lot of time studying Valsartan in Module A. Here it is again! Provide the configuration of the chiral center in Valsartan. (6 pts) Atrorvastatin is sold under the trade name Lipitor and is used for lowering cholesterol. Annual global sales of this compound exceed $13 billion. Assign a configuration to each chirality cente in atrovastin: (6 pts) A. The configuration of this cabon atom(B) is ___B. The configuration of this carbon atom (C) is ___

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The chiral center in Valsartan has an (S) configuration. In Atorvastatin, the configuration of carbon atom B is (R), and the configuration of carbon atom C is (S).

A chiral center is an atom in a molecule that has four different substituents bonded to it, resulting in two non-superimposable mirror image structures known as enantiomers. Valsartan is a medication used to treat high blood pressure and heart failure that contains a single chiral center.

The chiral center in Valsartan is located at the carbon atom attached to the nitrogen in the tetrazole ring. This carbon has an (S) configuration, as determined by the Cahn-Ingold-Prelog priority rules.

Atorvastatin is a medication used to lower cholesterol levels and prevent cardiovascular disease. It contains two chiral centers, at carbon atoms B and C in the pyrrole and tert-butyl groups, respectively.

The configuration of carbon atom B is (R), while the configuration of carbon atom C is (S). This information can be determined using the same Cahn-Ingold-Prelog priority rules used to determine the configuration of the chiral center in Valsartan.

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calculate the volume (in ml) of 0.550 m naoh (aq) required to completely neutralize 25.00 ml of 0.410 m hcl (aq).

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Approximately[tex]18.64 mL of 0.550 M[/tex] NaOH is required to completely neutralize 25.00 mL of 0.410 M HCl.

To calculate the volume of [tex]0.550 M NaOH (aq)[/tex] required to completely neutralize[tex]25.00 mL of 0.410 M HCl (aq),[/tex] we can use the following equation:
[tex]M1V1 = M2V2[/tex]

Where M1 is the molarity of the [tex]NaOH[/tex]solution, V1 is the volume of the [tex]NaOH[/tex]solution we need to find, [tex]M2[/tex] is the molarity of the HCl solution, and V2 is the volume of the HCl solution we are given[tex](25.00 mL).[/tex]
Plugging in the given values, we get:

[tex](0.550 M) V1 = (0.410 M) (25.00 mL)[/tex]

Solving for V1, we get:

[tex]V1 = (0.410 M) (25.00 mL) / (0.550 M)\\[/tex]

[tex]V1 = 19.09 mL[/tex]

Therefore, the volume of [tex]0.550 M NaOH (aq)[/tex]required to completely neutralize [tex]25.00 mL of 0.410 M HCl (aq) is 19.09 mL[/tex](rounded to two decimal places).

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Consider a supersonic flow past a compression corner with a ramp angle of theta=20 degrees. The upstream properties are M1=3 and pl=2116 lbf/ft^2. A Pitot tube is inserted in the flow downstream of the corner and the resulting oblique shock wave. Calculate the value of the pressure measured by the Pitot tube. First draw a careful sketch of the entire flow field and show station numbers: 1, 2, 3. Hint: Do you work in the following order: Shock wave angle beta, Mnl, Mn2, po2/pol, M2, po3/po2, pol/pl, po3

Answers

The pressure measured by the Pitot tube is approximately 6,647 lbf/ft^2. This can be calculated by first finding the shock wave angle beta using the given ramp angle of 20 degrees and Mach number of 3,

and then using the oblique shock relations to solve for the other properties at stations 1, 2, and 3, including the pressure measured by the Pitot tube at station 3.

The solution involves using the oblique shock relations to find the properties of the flow at different stations, starting with the shock wave angle beta and then working through the various properties at each station, including the pressure measured by the Pitot tube at station 3. The solution requires a careful sketch of the flow field and an understanding of the physics of compressible flow.

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How should the baking of a pizza be categorized?
as an exothermic process because the dough releases heat
as an endothermic process because the dough releases heat
as an exothermic process because the dough absorbs heat
as an endothermic process because the dough absorbs heat

Answers

The baking of a pizza should be categorized as an exothermic process because the dough releases heat. During baking, the dough undergoes a chemical reaction where the carbohydrates and sugars present in the dough are broken down and release heat, causing the pizza to cook and bake. The heat is also transferred from the oven to the pizza, which provides additional energy for the baking process. Therefore, the baking process involves the release of heat and should be classified as an exothermic process.

The baking of a pizza is categorized as an endothermic process because the dough absorbs heat. Therefore, option D is correct.

What is an endothermic process?

An endothermic process is a process that absorbs heat from the surroundings. In an endothermic process, the system gains energy from the surroundings, usually in the form of heat. This energy is used to break bonds within the system or to convert a solid or liquid into a gas.

Examples of endothermic processes include:

Melting of ice: When ice melts, it absorbs heat from the surroundings, which is used to break the hydrogen bonds between water molecules.Boiling of water: When water boils, it absorbs heat from the surroundings, which is used to break the hydrogen bonds between water molecules and convert water into steam.The dissolving of ammonium nitrate in water: When ammonium nitrate dissolves in water, it absorbs heat from the surroundings, which is used to break the ionic bonds between ammonium and nitrate ions.

Thus, option D is correct.

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Which reagent, NaOH or NH3, will enable you to precipitate the first-named ion from a solution containing each of the following pairs of ions, leaving the second ion in solution? Give also the formula of the precipitate and the exact formula of the other ion in solution. Determine which ions form hydroxide precipitates or hydroxide complexes, and ammonia complexes.(a) Al3+, Zn2+ (reagent, precipitate, ion insolution for all )(b) Cu2+, Pb2+(c) Pb2+, Cu2+(d) Fe3+, Al3+(e) Ni2+, Sn2+(f) Sn2+, Ni2+(g) Mg2+, Ag+

Answers

(a) NaOH: Al(OH)₃; NH3: Zn(NH3₃42+, (b) NaOH: Pb(OH)₂; NH₃: Cu(NH₃)42+, (c) Same as (b), (d) NaOH: Fe(OH)₃; NH₃: Al(NH₃)63+, (e) NaOH: Sn(OH)₂; NH₃: none, (f) Same as (e)., (g) NaOH: Mg(OH)2₂; NH₃: none

To determine which reagent, NaOH or NH₃, will precipitate the first-named ion, we need to check the solubility of the hydroxide and ammonia complexes of the ions.

(a) Al₃+, Zn₂+

NaOH will precipitate Al₃+ as Al(OH)₃ and leave Zn₂+ in solution as Zn(OH)42-. NH₃ will precipitate Zn2+ as Zn(NH₃)42+ and leave Al₃+ in solution as Al(H₂O)63+.

(b) Cu2+, Pb2+

NaOH will precipitate Pb2+ as Pb(OH)₂ and leave Cu2+ in solution as Cu(OH)42-. NH₃ will precipitate Cu₃+ as Cu(NH₃)42+ and leave Pb2+ in solution as [Pb(OH)4]2-.

(c) Pb₂+, Cu₂+

Same as (b).

(d) Fe₃+, Al₃+

NaOH will precipitate Fe3+ as Fe(OH)₃ and leave Al3+ in solution as Al(H₂O)63+. NH3 will precipitate Al3+ as Al(NH3)63+ and leave Fe3+ in solution as [Fe(H2O)6]3+.

(e) Ni₂+, Sn₂+

NaOH will precipitate Sn2+ as Sn(OH)₂ and leave Ni₂+ in solution as Ni(OH)42-. NH3 will not precipitate either ion.

(f) Sn2+, Ni2+

Same as (e).

(g) Mg2+, Ag+

NaOH will precipitate Mg2+ as Mg(OH)₂ and leave Ag+ in solution. NH₃ will not precipitate either ion.

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Calculate the theoretical yield for the bromination of both stilbenes and cinnamic acid, assuming the presence of excess pyridinium tribromide.
cinnamic acid - 150 mg
cis-stilbene - 100 μL
trans-stilbene - 100 mg
pyridinium tribromide - 200-385 mg

Answers

The theoretical yield for the bromination of cinnamic acid, cis-stilbene, and trans-stilbene, with excess pyridinium tribromide, is as follows: cinnamic acid - 237 mg; cis-stilbene - 215 μL; trans-stilbene - 257 mg.


1. Calculate moles of each reactant:
- Cinnamic acid (150 mg) / (148 g/mol) = 1.01 x 10⁻³ mol
- cis-Stilbene (100 μL) / (0.908 g/mL * 180 g/mol) = 6.15 x 10⁻⁴ mol
- trans-Stilbene (100 mg) / (180 g/mol) = 5.56 x 10⁻⁴ mol

2. Calculate theoretical yield (assuming 1:1 stoichiometry):
- Cinnamic acid: 1.01 x 10⁻³ mol * (296 g/mol) = 0.237 g (237 mg)
- cis-Stilbene: 6.15 x 10⁻⁴ mol * (0.908 g/mL * 430 g/mol) = 0.215 mL (215 μL)
- trans-Stilbene: 5.56 x 10⁻⁴ mol * (361 g/mol) = 0.257 g (257 mg)

These calculations assume the presence of excess pyridinium tribromide, meaning the limiting reagent is the starting material.

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Use the following steps to determine how to make 600 mL of a 0.1M acetate buffer, pH 5.0, using 0.1M acetic acid and 0.1M sodium acetate. Using the desired pH(5.0) and pKa of acetic acid, use the Henderson-Hasselbalch equation to determine a ratio of [base]/[acid] required for this buffer.

Answers

To make 600 mL of a 0.1M acetate buffer, pH 5.0, using 0.1M acetic acid and 0.1M sodium acetate, follow these steps.

Determine the pH and pKa of acetic acid. The pH is given as 5.0 and the pKa of acetic acid is 4.76.

Use the Henderson-Hasselbalch equation to determine the ratio of [base]/[acid] required for this buffer. The equation is pH = pKa + log([base]/[acid]). Rearranging the equation, [base]/[acid] = 10^(pH-pKa). Plugging in the values, [base]/[acid]

= [tex]10^{(5.0-4.76)[/tex]

= 1.74.

Calculate the amount of acetic acid and sodium acetate needed to make 600 mL of 0.1M acetate buffer with a [base]/[acid] ratio of 1.74. Let x be the amount of acetic acid needed in mL and y be the amount of sodium acetate needed in mL. The total volume is x + y = 600 mL. The total moles of acid and base are 0.1x and 0.1y, respectively. The ratio of [base]/[acid] is y/x = 1.74. Solving these equations simultaneously, we get x = 262.5 mL and

y = 337.5 mL.

Measure out 262.5 mL of 0.1M acetic acid and 337.5 mL of 0.1M sodium acetate and mix them together to make 600 mL of 0.1M acetate buffer, pH 5.0, with a [base]/[acid] ratio of 1.74.

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if this reaction releases 235 kj of energy, how many grams of fe form?Show the conversions required to solve this problem. 2 Al(s) + Fe, 0,($) — 2 Fe(s) + A1,O,(8) AH = -852 kJ -217 kJ x X 8 Fe Answer

Answers

14.4 grams of Fe will form when 235 kJ of energy is released in this reaction.

To solve this problem, we need to use the given reaction and its enthalpy change to find the amount of Fe formed when 235 kJ of energy is released.

First, we need to balance the equation:

2 Al(s) + 3 Fe2O3(s) -> 3 Fe(s) + 2 Al2O3(s)

We can see that for every 3 moles of Fe2O3, we get 3 moles of Fe. So, we need to convert the energy released (235 kJ) to moles of Fe2O3:

-852 kJ = -3 moles of Fe2O3

1 kJ = 3/(-852) moles of Fe2O3

235 kJ = 3/(-852) x 235 moles of Fe2O3

235 kJ = -0.773 moles of Fe2O3

Now, we can use stoichiometry to find the amount of Fe formed:

3 moles of Fe -> 1 mole of Fe2O3

1 mole of Fe -> 1/3 mole of Fe2O3

Therefore,

1/3 mole of Fe2O3 = 0.773 moles of Fe2O3

0.773 moles of Fe2O3 x (1 mole of Fe/3 moles of Fe2O3) = 0.258 moles of Fe

Finally, we can use the molar mass of Fe to convert moles to grams:

0.258 moles of Fe x 55.85 g/mol = 14.4 grams of Fe

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What is the solubility (in g/L) of aluminum hydroxide at 25°C? The solubility product constant for aluminum hydroxide is 4.6 x 10-33 at 25°C. a) 5.3 * 10-15 g/L b) 8.2 x 10-10 g/L c) 1.8 x 10-31 g/L d) 2.8 x 10-7 g/L e) 3.6 x 10-31 g/L

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The solubility of aluminum hydroxide at 25°C is (b) 8.2 x 10⁻¹⁰ g/L.

Using the solubility product constant (Ksp) of aluminum hydroxide (Al(OH)₃) at 25°C (4.6 x 10⁻³³), the solubility (in g/L) can be calculated using the following formula:

Ksp = [Al³⁺][OH⁻]³

Assuming x is the solubility in moles per liter, then [Al³⁺] = x and [OH⁻] = 3x, therefore:

4.6 x 10⁻³³ = x(3x)³

x = 1.1 x 10⁻¹¹ M

The molar mass of Al(OH)₃ is 78.0 g/mol, so:

solubility = (1.1 x 10⁻¹¹ M)(78.0 g/mol) = 8.6 x 10⁻¹⁰ g/L

Therefore, the answer is (b) 8.2 x 10⁻¹⁰ g/L.

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what ion cause the reaction in fescn 2 fe(no3)3

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The ion that causes the reaction in [tex]FeSCN^{2+[/tex] and [tex]Fe(NO^3)^3[/tex] is: Fe3+.

Your question involves the following reaction:
[tex]Fe^{3+[/tex] + SCN- → [tex]FeSCN^{2+[/tex]

The Fe(SCN)2+ complex ion is formed through a series of steps.

The first step involves the dissociation of [tex]Fe(NO^3)^3[/tex] into [tex]Fe^{3+[/tex] and [tex]NO^3[/tex]- ions. [tex]Fe^{3+[/tex] ions then react with SCN- ions to form [tex]FeSCN^{2+[/tex] The [tex]Fe^{3+[/tex] ion is the main cause of the reaction as it combines with SCN- to form the [tex]FeSCN^{2+[/tex] complex ion. This reaction is a type of equilibrium reaction, meaning that the concentration of products and reactants will be constant over time. The intensity of the color of the solution can be used to determine the concentration of the complex ion present in the solution. This reaction is often used in analytical chemistry to determine the concentration of [tex]Fe^{3+[/tex] ions in a sample.

In summary, the ion causing the reaction between [tex]FeSCN^{2+[/tex] and [tex]Fe(NO^3)^3[/tex] is the [tex]Fe^{3+[/tex] ion.

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1. calculate dh for the reaction of calcium oxide and sulfur trioxide. Is this reaction exothermic or endothermic? CaO(s) + SO3(g) = CaSO4(s)
Use the following equations and data.
H2O (l) + SO3 (g) = H2SO4 (l) delta H = -132.5 kj/mol
H2SO4 (l) + Ca (s) + CaSO4(s) + H2 (g) delta h = -602.5 kj/mol
Ca(s) + 1/2 O2 (g) = CaO(s) delta h = -634.9 kj/mol
H2 (g) + 1/2 O2 (g) = H2O (l) delta h = -258.8 jk/mol

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The proper reaction formula is CaO (s) + H₂O (l) Ca(OH)₂ (aq). G = Go + RT ln KcR can be used to compute the value of G. By heating calcium oxide (lime) with carbon (charcoal), calcium carbide (CaC₂) can be produced.

CaO(s) plus 3C(s) plus CaC₂(s) plus CO₂(g) = +464.8 kJ. The higher a substance's energetic stability, the lower its heat of production. The heat of formation for ethanol in the given example is -277.6 kJ/mol, the lowest value of any substance in the table.The pollutant sulphur trioxide and calcium oxide react to form calcium oxide (CaO(s) + SO₃(g) CaSO₄(s); G° = -345 kJ/mol),

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A point charge Q1 = 10 μC, is located at P1(1,2,3) in free space, while Q2 = -5 μC is at P2(1,2,10). (a) Find the vector force exerted on Q2 by Q1. (b) Find the coordinates of P3 at which a point charge Q3 experiences no force.

Answers

Q1 is pushing Q2 with a vector force of -6.12 x 10-4 N * k. At P3, the vector sum of the forces resulting from Q1 and Q2 is (x-1)2 + (y-2)2 + (z-3)2 = 4/3 *.

What is the sum of the vector forces?

The vector sum of all the forces equals the net force. In other words, the net force is the sum of all forces. The net force is the sum of the force vectors A + B + C in the scenario of the three forces on the force board.

(a) Coulomb's law provides the electric force F on Q2 as a result of Q1:

F = k * Q1 * Q2 / r² * r_hat

where r_hat is the unit vector pointing from Q1 to Q2, k is the Coulomb constant, and r is the separation between the two charges.

r = |P2 - P1| = sqrt((1-1)² + (2-2)² + (10-3)²) = 7

r_hat = (P2 - P1) / r = (0, 0, 1)

When we change the values, we obtain:

F = 9 x 10⁹ Nm²/C² * (10 x 10⁻⁹C) * (-5 x 10⁻⁶ C) / (7 m)² * (0, 0, 1)

F = -6.12 x 10⁻⁴ N * k

Therefore, Q1's vector force on Q2 is -6.12 x 10⁻⁴ N * k.

(b) We must identify the location P3 where Q1 and Q2's combined net force on Q3 equals zero. This indicates mathematically that the vector sum of the forces resulting from Q1 and Q2 at P3 is 0:

F_1 + F_2 = 0

We can write: Using Coulomb's law

F_1 = k * Q1 * Q3 / r_1² * r_1_hat

F_2 = k * Q2 * Q3 / r_2² * r_2_hat

If P3's coordinates are (x, y, z), we can write:

r_1 = sqrt((x-1)² + (y-2)² + (z-3)²)

r_2 = sqrt((x-1)² + (y-2)² + (z-10)²)

r_1_hat = ((x-1)/r_1, (y-2)/r_1, (z-3)/r_1)

r_2_hat = ((x-1)/r_2, (y-2)/r_2, (z-10)/r_2)

By replacing these values, we obtain:

k * Q1 * Q3 / r_1² * r_1_hat + k * Q2 * Q3 / r_2² * r_2_hat = 0

The result of simplifying and solving for Q3 is:

Q3 = -Q1 * r_1² / (Q2 * r_2²)

When we change the values, we obtain:

Q3 = -10 x 10⁻⁶ C * (sqrt((x-1)² + (y-2)² + (z-3)²))² / (-5 x 10⁻⁶ C * (sqrt((x-1)² + (y-2)² + (z-10)²))²)

If we simplify, we get:

(x-1)² + (y-2)² + (z-3)² = 4/3 *

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1-propanol, 2-propanol, and methyl ethyl ether share the same molecular formula and so they are referred to as

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1-propanol, 2-propanol, and methyl ethyl ether share the same molecular formula and so they are referred to as isomers.

Isomers are compounds that have the same molecular formula but different arrangements of atoms and/or different bonding patterns between atoms. In the case of 1-propanol, 2-propanol, and methyl ethyl ether, they all have the molecular formula C₃H₈O, but differ in their structural formula and properties.

1-propanol, also known as n-propanol or propan-1-ol, has a linear structure with a primary alcohol group (-OH) attached to the first carbon atom of the propane chain. It is a colorless liquid with a strong odor, and is commonly used as a solvent and in the production of other chemicals.

2-propanol, also known as isopropanol or propan-2-ol, has a branched structure with a secondary alcohol group (-OH) attached to the second carbon atom of the propane chain. It is also a colorless liquid with a strong odor, and is widely used as a solvent, disinfectant, and antifreeze.

Methyl ethyl ether, also known as ether or dimethyl ether, has a linear structure with an ether functional group (-O-) linking the methyl and ethyl groups. It is a volatile, flammable liquid with a sweet odor, and is used as a solvent and fuel.

Although these three compounds share the same molecular formula, their different structures and bonding patterns give rise to different physical and chemical properties.

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Enter the balanced complete ionic equation for K2SO4(aq)+CaI2(aq)→CaSO4(s)+KI(aq).
Express your answer as a chemical equation. Identify all of the phases in your answer.
Part B
Enter the balanced net ionic equation for K2SO4(aq)+CaI2(aq)→CaSO4(s)+KI(aq) .
Express your answer as a chemical equation. Identify all of the phases in your answer.
Part C
Enter the balanced complete ionic equation for NH4Cl(aq)+NaOH(aq)→H2O(l)+NH3(g)+NaCl(aq).
Express your answer as a chemical equation. Identify all of the phases in your answer.
Part D
Enter the balanced net ionic equation for NH4Cl(aq)+NaOH(aq)→H2O(l)+NH3(g)+NaCl(aq).
Express your answer as a chemical equation. Identify all of the phases in your answer.

Answers

Part A: 2 K⁺(aq) + SO₄²⁻(aq) + Ca²⁺(aq) + 2 I⁻(aq) → CaSO₄(s) + 2 K⁺(aq) + 2 I⁻(aq)
Part B: Ca²⁺(aq) + SO₄²⁻(aq) → CaSO₄(s)
Part C: NH₄⁺(aq) + Cl⁻(aq) + Na⁺(aq) + OH⁻(aq) → H₂O(l) + NH₃(g) + Na⁺(aq) + Cl⁻(aq)
Part D: NH₄⁺(aq) + OH⁻(aq) → H₂O(l) + NH₃(g)


Part A: Separate all ions in their aqueous states, then write the balanced complete ionic equation.
Part B: Remove spectator ions (K⁺ and I⁻) from the complete ionic equation, resulting in the balanced net ionic equation.
Part C: Follow the same procedure as Part A for the given reaction.
Part D: Remove spectator ions (Na⁺ and Cl⁻) from the complete ionic equation, resulting in the balanced net ionic equation.

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If a molecule of pyruvate was labeled on the carboxyl carbon with 14C and used to make each of the five products discussed in the fates of pyruvate, where would the label be found in each product?A. In alanine, the 14C label would be:attached to the amine group.at the Cα position on the amino acid.at the carboxyl group.B. For conversion to acetyl-CoA, the 14C label would be:lost as CO2.attached to the carbonyl group.at the methyl position.For conversion to lactate, the 14C label would be:attached to the alcohol group.at the carboxyl group.at the methyl position.For conversion to oxaloacetate, the 14C label would be:at the methylene position at carbon-3.at the carbonyl position at carbon-2.at the carboxyl group at carbon-1.at the carboxyl group at carbon-4.

Answers

B. For conversion to acetyl-CoA, the 14C label would be: lost as CO₂.

For conversion to lactate, the 14C label would be: attached to the methyl position.

For conversion to oxaloacetate, the 14C label would be: at the carboxyl group at carbon-1.

In alanine, the 14C label would be: at the Cα position on the amino acid.

Pyruvate is a three-carbon molecule that can undergo different metabolic fates, depending on the cellular conditions and the energy needs of the organism. The five products mentioned in the question are examples of these fates: acetyl-CoA, lactate, oxaloacetate, alanine, and carbon dioxide.

If a molecule of pyruvate is labeled on the carboxyl carbon with 14C, the position of the label in the different products can be traced based on the chemical transformations that occur.

For conversion to acetyl-CoA, pyruvate undergoes oxidative decarboxylation, which involves the removal of a carboxyl group as carbon dioxide. Therefore, the 14C label would be lost as CO2, and no radioactivity would be found in the acetyl-CoA molecule.

For conversion to lactate, pyruvate is reduced by NADH to form lactate. The 14C label would be found in the methyl position of the lactate molecule, which corresponds to the position of the carboxyl carbon in pyruvate.

For conversion to oxaloacetate, pyruvate is carboxylated by biotin-dependent pyruvate carboxylase to form oxaloacetate. The 14C label would be found in the carboxyl group at carbon-1 of the oxaloacetate molecule.

In alanine, pyruvate is transaminated by the enzyme alanine transaminase to form alanine. The 14C label would be found at the Cα position on the amino acid, which corresponds to the position of the carboxyl carbon in pyruvate.

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What is the molar mass of (S)-phenylethylammonium-(2R,3R) tartrate salt? molar mass: 282.1 g/mol Incorrect

Answers

The molar mass of (S)-phenylethylammonium-(2R,3R) tartrate salt is 270.29 g/mol.

To determine the molar mass of (S)-phenylethylammonium-(2R,3R) tartrate salt, we first need to find the molecular formula of this compound and then calculate its molar mass.

Step 1: Identify the molecular formula
(S)-phenylethylammonium-(2R,3R) tartrate salt is a complex compound, and its molecular formula is (C₈H₁₂N)(C₄H₄O₆). This formula consists of one phenylethylammonium ion (C₈H₁₂N) and one tartrate ion (C₄H₄O₆).

Step 2: Calculate the molar mass
To calculate the molar mass, we will add the molar masses of each element in the molecular formula, multiplied by their respective counts:

Molar mass of C: 12.01 g/mol
Molar mass of H: 1.01 g/mol
Molar mass of N: 14.01 g/mol
Molar mass of O: 16.00 g/mol

(C₈H₁₂N)(C₄H₄O₆) = [(8 x 12.01) + (12 x 1.01) + (1 x 14.01)] + [(4 x 12.01) + (4 x 1.01) + (6 x 16.00)]

= [96.08 + 12.12 + 14.01] + [48.04 + 4.04 + 96.00]

= 122.21 + 148.08

The molar mass of (S)-phenylethylammonium-(2R,3R) tartrate salt is 270.29 g/mol.

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which one of the following pairs contains isoelectronic species? group of answer choices na , o2– na, na s, se se2-, s2- f2, cl2

Answers

The pair that contains isoelectronic species is: [tex]Se^{2-[/tex] and [tex]S^{2-[/tex]. This is because both species have the same number of electrons.

Sulfur ion ([tex]S^{2-[/tex]) has gained two electrons compared to the neutral sulfur atom, which has 16 electrons. Therefore, [tex]S^{2-[/tex] has a total of 18 electrons. Similarly, selenium ion ([tex]Se^{2-[/tex]) has gained two electrons compared to the neutral selenium atom, which has 34 electrons. Therefore, [tex]Se^{2-[/tex] also has a total of 18 electrons. Thus, [tex]Se^{2-[/tex]- and [tex]S^{2-[/tex] are isoelectronic because they have the same number of electrons, even though they are different elements and ions. The pair that contains isoelectronic species is: [tex]Se^{2-[/tex] and [tex]S^{2-[/tex]. This is because both species have the same number of electrons.

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The pair that contains isoelectronic species is: [tex]Se^{2-[/tex] and [tex]S^{2-[/tex]. This is because both species have the same number of electrons.

Sulfur ion ([tex]S^{2-[/tex]) has gained two electrons compared to the neutral sulfur atom, which has 16 electrons. Therefore, [tex]S^{2-[/tex] has a total of 18 electrons. Similarly, selenium ion ([tex]Se^{2-[/tex]) has gained two electrons compared to the neutral selenium atom, which has 34 electrons. Therefore, [tex]Se^{2-[/tex] also has a total of 18 electrons. Thus, [tex]Se^{2-[/tex]- and [tex]S^{2-[/tex] are isoelectronic because they have the same number of electrons, even though they are different elements and ions. The pair that contains isoelectronic species is: [tex]Se^{2-[/tex] and [tex]S^{2-[/tex]. This is because both species have the same number of electrons.

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1. Titrations are generally both more accurate and more precise the smaller the concentration of titrant you use. A 6.0 M NaOH stock solution is provided by the stock room. (a) What volumes of the stock NaOH solution and DI water would you need to prepare 500 mL of 0.10 M NaOH solution? (b) If you measured your diluted NaOH solution using a pH meter, what pH should it read?

Answers

Answer:

8.3 mL of NaOH Stock, 492 mL of DI Water. pH = 13.

Explanation:

Use the M1V1 = M2V2 formula, where m is molarity and v is volume. This can be done in mL or L, it will cancel out.

(6.0)V1 = (.10)(500), solving for V1 you get 8.3 mL of 6.0M NaOH stock solution. The remaining 500-8.3= approx 492 mL should be DI water.

The pH = -log[H+] but in this case we have OH-, so we will use pH + pOH =14. And rearrange to solve for pH = 14 + pOH = 14 + log[OH-]

Then solve

pH = 14 + log(0.10 M0 = 14 - 1 = 13

List the possible effects of inhaling excessive amounts of pinacolone (3,3-dimethylbutan-2-one).

Answers

Excessive inhalation of pinacolone can cause irritation to the respiratory tract, headaches, dizziness, nausea, and in severe cases, can lead to unconsciousness or respiratory failure.

Pinacolone (3,3-dimethylbutan-2-one) is a colorless liquid with a pleasant odor, commonly used in industrial processes as a solvent and in the production of other chemicals. However, inhaling excessive amounts of pinacolone can have harmful effects on human health. These effects may include irritation of the eyes, nose, and throat, headache, dizziness, nausea, and respiratory problems. In severe cases, exposure to high concentrations of pinacolone can lead to unconsciousness and even death. Prolonged or repeated exposure to pinacolone may also cause damage to the liver and kidneys. Therefore, it is important to take appropriate safety precautions, such as using proper protective equipment and adequate ventilation, when working with this chemical.

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Consider the following reaction at constant P. Use the information here to determine the value of ΔSsurr at 398 K. Predict whether or not this reaction will be spontaneous at this temperature.
4 NH3(g) + 3 O2(g) → 2 N2(g) + 6 H2O(g) ΔH = -1267 kJ
A) ΔSsurr = +12.67 kJ/K, reaction is spontaneous
B) ΔSsurr = -12.67 kJ/K, reaction is spontaneous
C) ΔSsurr = +50.4 kJ/K, reaction is not spontaneous
D) ΔSsurr = +3.18 kJ/K, reaction is spontaneous
E) ΔSsurr = -3.18 kJ/K, it is not possible to predict the spontaneity of this reaction without more information.

Answers

The entropy of the surrounding, ΔSsurr at 398 K, given that the pressure is constant is +3.18 kJ/K and the reaction is spontaneous (option D)

How do i determine the entropy of surrounding, ΔSsurr?

The entropy of surrounding, ΔSsurr can be obtain as follow:

Enthalpy change (ΔH) = -1267 KJTemperature (T) = 398 K Entropy of surrounding (ΔSsurr) =?

ΔSsurr = -ΔH / T

ΔSsurr = -(-1267) / 398

ΔSsurr = +3.18 KJ/K

We can determine if the reaction is spontaneous or not by obtaining the gibbs free energy as shown below:

Enthalpy change (ΔH) = -1267 KJTemperature (T) = 398 K Entropy of surrounding (ΔSsurr) = +3.18 KJ/KGibbs free energy (ΔG)

ΔG = ΔH - TΔS

ΔG = -1267 - (398 × 3.18)

ΔG = -2532.64 KJ

Since ΔG is negative, the reaction is spontaneous

Thus, the correct answer to the question is ΔSsurr = +3.18 kJ/K, reaction is spontaneous (option D)

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3. Cahn-Ingold-Prelog a. Prioritize all four groups connected to the chirality center Number the following groups based on priority. This is done one atom at a time, not the group! CH3 Me но ButIi Prop Et Cl Br

Answers

To prioritize the four groups connected to the chirality center using the Cahn-Ingold-Prelog rules, we need to compare the atoms directly bonded to the chirality center and assign them a priority based on their atomic number.


Starting with the highest atomic number, we have:



1. Br (bromine)


2. Cl (chlorine)


3. But (butyl group)


4. Prop (propyl group)


5. Et (ethyl group)


6. Me (methyl group)


7. CH3 (methyl group)


So the priority order of the groups from highest to lowest is:

1. Br
2. Cl
3. But
4. Prop
5. Et
6. Me
7. CH3

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A.) 24, B.) -4, C.) -6, D.) -8, C.) -24 All but which question can help identify a rock formation?A. how old is the rock?B. what geographic location is the rock from?C. what environmental conditions helped form the rock?D. what size are the grains? ayo 30 ptsWhat is the distance between the two points shown below?6 units0 units4 units8 units Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 4 kilometers per hour. They meet in 5 hours. How fast is Brenda walking? 1. Which of the following organisms would NOT display bilateral symmetry because of its feeding behavior?A. a bee that collects nectar from flowersB. a fish that follows its prey over a long distanceC. a filter feeder that eats food carried by currentsD. a crab that searches for debris on a beach2. Perception of visual cues is essential for survival of most animals. A scientist analyzes the vision receptor molecule in invertebrates and vertebrates. The results show that the genes for opsin, the protein part of the photoreceptor, share strong homology in the regions that code for domains involved in light response. Which of the following conclusions is the MOST likely?A. The receptor molecules will be structurally different but respond to the same light cues.B. The receptor molecule will be similar in invertebrates and vertebrates because of convergent evolution.C. The receptor molecules will be different because invertebrates and vertebrates perceive visual cues in different environments.D. The receptor molecules will be similar in invertebrates and vertebrates because they appeared early in evolution.3. A paleontologist identified two distinct species of mollusks in the fossil record of a region. In the layer below a mass extinction that devastated the region, the paleontologist observed that shells of species A was present in small numbers over a widespread area whereas species B was abundant and found in a few restricted areas. Which of the following predictions about the fossil record in the layer above the mass extinction is the MOST likely to be supported by further excavations?A. Species A survived because of its widespread range including some areas that were not as affected by mass extinction.B. Species A survived because the low number of individuals meant that there was less competition for resources.C. Species B survived because it was the more abundant and more individuals survived.D. Species B survived because the population was concentrated in a few areas and had a higher chance of survival.4. Insects, birds, and bats can fly. Which of the following is a derived characteristic unique to birds and bats?A. light body weightB. modified limbs for flightC. high metabolic rateD. large surface of wings To win employees' sustained, energetic commitment to the strategy execution process, management must: A) create a corporate culture that fosters dedication and loyalty. B) comply with ethical standards and become good corporate citizens. C) provide job variety and promotion opportunities. D) provide attractive perks and fringe benefits. E) be resourceful in designing and using motivational incentives.a Express the following as linear combinations of u = (2,1,4), v = (1,-1,3), and w = (3,2,5).(a) (-9,-7,-15)(b) (6,11,6)(c) (0,0,0) An object of mass m is attached to a spring on a frictionless inclined plane that makes an angle with the horizontal, as shown above. The object is released from rest with the spring in its unstretched position. As the object moves on the plane, its displacement from the unstretched position is x What is the magnitude of the work done by gravity as the object slides down the incline?