Why was extraction by both acid AND base necessary to arrive at highly purified benzoic acid?

The correct answer to the question of which type of molecule contains -[tex]NH_{2}[/tex](amino) groups is B. Protein.

Proteins are made up of long chains of amino acids, which are the building blocks of protein molecules. Amino acids are characterized by their -[tex]NH_{2}[/tex] (amino) group, which is what makes them unique from other types of molecules like carbohydrates, lipids, and nucleic acids. Carbohydrates, on the other hand, are made up of simple sugars like glucose, fructose, and galactose. They do not contain amino groups in their molecular structure. Lipids are fats, oils, and waxes that are made up of fatty acids and glycerol. They also do not contain amino groups in their molecular structure. Nucleic acids like DNA and RNA are composed of nucleotides, which do not contain amino groups. Therefore, it can be concluded that proteins are the only type of molecule that contains -[tex]NH_{2}[/tex] (amino) groups. These groups play an important role in the structure and function of proteins, as they help to form the peptide bonds that link amino acids together in a protein chain.

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Answer:

12.09528g [tex]H_{2}[/tex]

68.12208g [tex]NH_{3}[/tex]

Explanation:

[tex]n = \frac{V}{V_{m} } \\ = \frac{134.4}{22.4} \\ = 6 mol H_{2}[/tex]

[tex]n=\frac{m}{M} \\m= nM\\=(6)(2.051588)\\=12.09528g H_{2}[/tex]

[tex]N_{2} : NH_{3} \\ 1 : 2\\2:x\\x= 4mol NH_{3} \\\\n = \frac{m}{M} \\m=nM\\=(4)(17.03052)\\=68.12208g NH_{3}[/tex]

The molarity of the solution containing 16.4 g of KCl in 254 ml of solution is 0.866 M. Molarity is defined as the number of moles of solute per liter of solution.

Number of moles = Mass / Molar mass
Number of moles = 16.4 g / 74.55 g/mol = 0.22 mol

Volume = 254 ml / 1000 ml/L = 0.254 L

Molarity = Number of moles / Volume

Molarity = 0.22 mol / 0.254 L = 0.866 M

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The mass of Cr₃⁺ ion in the original solution is 14.2 g and the mass of Mg²⁺ ion in the original solution is 10.8 g.

To calculate the mass of Cr₃⁺ and Mg²⁺ ions in the original solution, we can use the given information about the addition of NaF solution and the mass of precipitate formed.

The first step is to calculate the moles of NaF added to the solution. We can use the formula:

moles = concentration × volume

Substituting the values, we get:

moles of NaF added = 1.55 mol/L × 1.00 L = 1.55 moles

Since NaF reacts with both Cr₃⁺ and Mg²⁺ ions, we need to find the limiting reagent between the two ions to determine the maximum amount of precipitate that can form. The balanced chemical equations for the precipitation reactions are:

2 Cr³⁺(aq) + 3 F⁻(aq) → CrF₃(s)

Mg²⁺(aq) + 2 F⁻(aq) → MgF₂(s)

From these equations, we can see that the stoichiometric ratio of Cr³⁺:F⁻ is 2:3, while that of Mg²⁺:F⁻ is 1:2. Therefore, the limiting reagent will be the one that forms the least amount of precipitate.

To calculate the mass of precipitate formed, we can use the formula:

mass = moles × molar mass

The molar mass of CrF₃ is 157.99 g/mol, while that of MgF₂ is 62.30 g/mol. The mass of the precipitate is given as 50 g, so we can calculate the moles of precipitate formed for each ion:

moles of CrF₃ = 50 g / 157.99 g/mol ≈ 0.316 moles

moles of MgF₂ = 50 g / 62.30 g/mol ≈ 0.803 moles

Since Cr³⁺ forms two moles of precipitate for every three moles of NaF, the moles of Cr³⁺ can be calculated as:

moles of Cr³⁺ = (2/3) × moles of NaF added = (2/3) × 1.55 moles ≈ 1.03 moles

Similarly, the moles of Mg²⁺ can be calculated as:

moles of Mg²⁺ = 1/2 × moles of NaF added = 1/2 × 1.55 moles ≈ 0.775 moles

Now, we can use the moles of Cr³⁺ and Mg²⁺ to calculate their respective masses in the original solution:

mass of Cr³⁺ = moles of Cr³⁺ × molar mass of Cr³⁺ = 1.03 moles × 106.16 g/mol ≈ 14.2 g

mass of Mg²⁺ = moles of Mg²⁺ × molar mass of Mg²⁺ = 0.775 moles × 24.31 g/mol ≈ 10.8 g

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The role of the modification seen on Fucose could be to fine-tune its chemical properties and interactions with other molecules, particularly proteins, through the addition or removal of functional groups. This would, in turn, influence the function of the glycoproteins and glycolipids containing the modified Fucose.

Fucose is a monosaccharide, specifically a deoxyhexose sugar, which is often found as a component of glycoproteins and glycolipids in eukaryotes. It can be modified through the addition or removal of functional groups, such as sulfation or acetylation, which can alter its properties and interactions with other molecules.

A possible role of the modification seen on Fucose could be to modulate its interactions with proteins, such as lectins or enzymes, that recognize and bind to Fucose-containing structures. By altering the chemical properties of Fucose, the modification may enhance or weaken the binding affinity between Fucose and its binding partners.

For instance, the addition of a sulfate group to Fucose (creating sulfated Fucose) could increase its overall negative charge, potentially improving its interaction with positively charged protein domains. Conversely, acetylation of Fucose, which adds an acetyl group, might reduce the overall negative charge, leading to weaker binding or altered selectivity.

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To calculate the A GPxn, we can use the formula A GPxn = ΣA G°f(products) - ΣA G°f(reactants), where A G°f is the standard free energy of formation.

Plugging in the values from the table, we get:
A GPxn = (-603.3 kJ/mol + (-394.4 kJ/mol)) - (-1129.1 kJ/mol)
A GPxn = -8.6 kJ/mol

Since A Grxn is negative, the reaction would be spontaneous under standard conditions. However, since A GPxn is only slightly negative (-8.6 kJ/mol), the reaction would not proceed to completion without some external driving force.

If CaCO3 is placed in an evacuated flask, the partial pressure of CO2 at equilibrium can be calculated using the equilibrium constant, Kp. The equilibrium constant can be expressed as:

Kp = (P CO2)^x, where x is the coefficient of CO2 in the balanced equation (1 in this case)

We can then use the formula A Grxn = -RT ln Kp to solve for P CO2:

A GPxn = -RT ln Kp
-8.6 kJ/mol = -(8.314 J/mol·K)(298 K) ln(P CO2)
ln(P CO2) = 3.307
P CO2 = e^3.307 = 27.3 atm

Therefore, the partial pressure of CO2 at equilibrium would be 27.3 atm.

The spontaneity of the reaction can be affected by a change in temperature. We can use the equation A GPxn = A Hrxn - TΔSrxn to see how the free energy change varies with temperature. If we increase the temperature, the TΔSPxn term becomes more favorable (i.e. more positive), which can offset the positive A Hrxn term, resulting in a more negative A GPxn and a more spontaneous reaction.

Therefore, increasing the temperature can make the reaction more spontaneous. On the other hand, decreasing the temperature can make the reaction less spontaneous.

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The correct answer is (d) 5.61 g.

To calculate the grams of KOH in a 400 mL of 0.250 M KOH solution, we can follow the given steps:

Convert the volume from milliliters (mL) to liters (L): 400 mL = 0.4 L.

Use the molarity formula:

moles of solute = molarity × volume in liters.

Here, the molarity of the solution is given as 0.250 M, and the volume is 0.4 L.

moles of KOH = 0.250 M × 0.4 L = 0.1 moles.

Convert moles to grams using the molar mass of KOH (39.1 g/mol for K, 15.999 g/mol for O, and 1.008 g/mol for H):

The molar mass of KOH is (39.1 + 15.999 + 1.008) g/mol = 56.107 g/mol.

grams of KOH = 0.1 moles × 56.107 g/mol = 5.61 g.

Therefore, the grams of KOH in 400 mL of 0.250 M KOH solution is 5.61 g.

So, the correct answer is (d) 5.61 g.

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When hydrogen chloride gas is added to water, the products are hydronium ions and chloride ions and as the hydrogen ion is an acceptor, water is described as a Bronsted-Lowry base.

Generally according to concept of Bronsted-Lowry theory," acid is defined as a substance which donates an H⁺ ion or a proton and forms its conjugate base and the base is defined as a substance which accepts an H⁺ ion or a proton and forms its conjugate acid".

And now we can see that a hydrogen ion usually gets transferred from the HCl molecule to the H₂O molecule to give chloride ions and hydronium ions. And it is also clear that the hydrogen ion donor, HCl acts as a Bronsted-Lowry acid and also as a hydrogen ion acceptor, H₂O is a Bronsted-Lowry base.

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In the modified ballistic pendulum experiment you described, the energy transferred from the ball to the pendulum would be lesser than in your earlier trials.

This is because when the ball bounces off the pendulum, it is an elastic collision, where some kinetic energy is retained by the ball after the collision, unlike the inelastic collision when the pendulum catches the ball.

a. If we reverse the pendulum such that it cannot catch the ball, the collision between the ball and the pendulum would be an elastic collision. In an elastic collision, the total kinetic energy of the system is conserved. Therefore, the energy transferred from the ball to the pendulum would be the same as in the earlier trials.

b. The angle that the pendulum swings would be greater than the angle from earlier trials. This is because in an elastic collision, the momentum of the system is conserved. Since the ball would bounce off the pendulum with the same speed at which it hit the pendulum, it would transfer more momentum to the pendulum. As a result, the pendulum would swing to a greater angle.

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In questions 6 and 7, we are comparing two different molecules that have the same molecular formula but different structures. Specifically, we are comparing cis-2-butene and trans-2-butene.

The difference between these two molecules lies in the geometry around the carbon-carbon double bond. In cis-2-butene, the two methyl groups (CH3) are on the same side of the double bond, while in trans-2-butene, the two methyl groups are on opposite sides of the double bond.

This difference in geometry leads to different physical and chemical properties of the two molecules, including differences in boiling point, melting point, reactivity, and stereochemistry. For example, cis-2-butene has a higher boiling point than trans-2-butene due to its greater polarity caused by the proximity of the two methyl groups on the same side. Additionally, the two isomers may react differently in certain chemical reactions due to differences in steric hindrance and orientation of functional groups relative to the double bond.

Therefore, the differences in the geometries of the carbon atoms in cis-2-butene and trans-2-butene are what provide a difference in the properties and reactivity of these molecules.

Amount of heat involved is: 311KJ

To calculate the heat involved in this reaction, we can use the following equation:

ΔH = n × ΔH°

where ΔH is the heat involved in the reaction, n is the number of moles of N₂ reacted, and ΔH° is the standard enthalpy change for the reaction.

First, we need to calculate the number of moles of N₂ reacted. We can do this by dividing the mass of N₂ by its molar mass:

n(N₂) = m(N₂) / M(N₂) = 68.0 g / 28.014 g/mol = 2.427 mol N₂

Given equation:

2N₂(g)+ 5O₂(g) + 2H₂O(l) → 4HNO₃(aq)

so, 2mols of N₂ produces -256kj heat

2.427 moles N₂ produces = 256*2.427/2 = -311KJ heat

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The concentration of vinegar in the mixture after n steps can be found using the formula

Cn = (0.86)^n, where Cn is the concentration of vinegar after n steps.

To find the number of steps required to reach a concentration of less than 14%,

we need to solve the equation (0.86)^n = 0.14.

Taking the logarithm of both sides gives n = log(0.14)/log(0.86), which is approximately 14.1 steps.

Therefore, after 15 steps, the mixture will contain less than 14% vinegar.

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The value of ΔG for the reaction at 25°C is (b) -1784 kJ/mole.

To find the value of ΔG, we can use the equation:

ΔG = ΔH - TΔS

where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

Plugging in the values given:

ΔH = -1854 kJ/mol
ΔS = -236 J/(K mol) = -0.236 kJ/(K mol)
T = 25°C + 273 = 298 K

ΔG = -1854 kJ/mol - 298 K * (-0.236 kJ/(K mol))
ΔG = -1854 kJ/mol + 70.328 kJ/mol
ΔG = -1783.672 kJ/mol

Therefore, the answer is b) -1784 kJ/mole.

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So, the sorted alkyl halides based on their substitution pattern are: 1-bromobutane (primary), 2-bromobutane (secondary), and 2-bromo-2-methylbutane (tertiary).

The given alkyl halides are 1-bromobutane (primary), 2-bromobutane (secondary), and 2-bromo-2-methylbutane (tertiary). Here's the sorting process:

1. Primary alkyl halide: 1-bromobutane
- This is a primary alkyl halide because the carbon atom bonded to the halogen (bromine) is attached to only one other carbon atom.

2. Secondary alkyl halide: 2-bromobutane
- This is a secondary alkyl halide because the carbon atom bonded to the halogen (bromine) is attached to two other carbon atoms.

3. Tertiary alkyl halide: 2-bromo-2-methylbutane
- This is a tertiary alkyl halide because the carbon atom bonded to the halogen (bromine) is attached to three other carbon atoms.

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The correct answer is "physical change because even though gas formation was observed, the water was undergoing a state change, which means that its original properties are preserved".

When water boils, it undergoes a physical change from a liquid state to a gas state, but the water molecules remain the same and its chemical properties do not change. The boiling of water is a result of an increase in temperature and does not involve a chemical reaction.

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Answer:

The Holocaust was a tragic event that took place during World War II. Many people were persecuted and killed because of their race, religion, or ethnicity. Despite the atrocities that took place, there were survivors who managed to escape and rebuild their lives.

One of the most important characters in the story of the Holocaust survivors is Anne Frank, who kept a diary of her experiences while in hiding from the Nazis. Other important characters include Oskar Schindler, a German businessman who saved the lives of many Jews by employing them in his factory, and Raoul Wallenberg, a Swedish diplomat who saved thousands of Hungarian Jews from deportation to concentration camps.

The story of the survivors is filled with conflict and resolution. Many faced immense danger and struggled to stay alive, while others risked their own lives to help them. The end of the war brought a resolution to the conflict, but the survivors still faced many challenges as they tried to rebuild their lives.

Overall, the story of the survivors in the Holocaust is a testament to the human spirit and the ability to persevere in the face of unimaginable hardship.

Explanation:

Answer: Potassium (K) has the lowest electronegativity among the given elements.

Explanation:

Electronegativity is a measure of an element's ability to attract electrons towards itself when it is involved in a chemical bond with another element. Potassium has the lowest electronegativity because it has only one valence electron that is located far from the nucleus, making it easier to lose that electron and become a positively charged ion. In contrast, nitrogen, lithium, and bromine have higher electronegativities because they have more valence electrons or the valence electrons are closer to the nucleus, making it more difficult to remove or share electrons.

The element with the lowest electronegativity among the given options is potassium (K). Potassium has an electronegativity value of approximately 0.82 on the Pauling scale, which is the lowest value among the four elements listed. In contrast, nitrogen (N) has an electronegativity of approximately 3.04, bromine (Br) has an electronegativity of approximately 2.96, and lithium (Li) has an electronegativity of approximately 0.98. Electronegativity is a measure of an atom's ability to attract electrons towards itself in a chemical bond. The lower the electronegativity value, the less the atom attracts electrons towards itself.

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Digoxin is used in systolic heart failure because it helps to increase the strength and efficiency of the heart's contractions, particularly in cases where the systolic function of the heart is impaired.

Digoxin works by inhibiting the sodium-potassium ATPase pump, which leads to an increase in intracellular calcium concentrations and subsequently improves the contractility of the heart. This makes it an effective treatment option for patients with systolic heart failure, as it can help to improve cardiac output and reduce symptoms such as shortness of breath and fatigue.

However, due to its narrow therapeutic index, careful monitoring is necessary to ensure that digoxin levels remain within a safe and effective range.

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Part A: E°cell = 0.80 V - (-0.26 V) = 1.06 V, The standard potential for the given galvanic cell is 1.06 V.
Part B: Anode: a) Ni, e) negative electrode, d) loses mass, h) stronger reducing agent and Cathode: b) Ag, f) positive electrode, c) gain mass, g) attracts electrons.

Part A:

To calculate the standard potential for the given galvanic cell, we use the formula first, we need to identify the cathode and anode in the cell. The cathode is where reduction occurs, and the anode is where oxidation occurs.
From the given half-reactions:
E°cell = E°red(cathode) - E°red(anode)
From the table of standard reduction potentials, we have:
E°red(Ni2+(aq) + 2e⁻ → Ni(s)) = -0.26 V
E°red(Ag+(aq) + e⁻ → Ag(s)) = 0.80 V
Since Ag has a higher reduction potential, it will act as the cathode and Ni will act as the anode. Now, we can plug the values into the formula:
E°cell = 0.80 V - (-0.26 V) = 1.06 V
Therefore, the standard potential for the given galvanic cell is 1.06 V.

Part B:
a) Ni - anode
b) Ag - cathode
c) gain mass - cathode
d) losses mass - anode
e) positive electrode - cathode
f) negative electrode - anode
g) attracts electrons - cathode
h) stronger reducing agent - cathode

So we can say that :

Anode: a) Ni, e) negative electrode, d) loses mass, h) stronger reducing agent

Cathode: b) Ag, f) positive electrode, c) gain mass, g) attracts electrons

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Scandium (Sc) has the highest first ionization energy among the given atoms.

To determine this, we should understand that ionization energy is the energy required to remove an electron from an atom. Generally, ionization energy increases across a period (from left to right) and decreases down a group (from top to bottom) in the periodic table. The reason is that as we move across a period, the nuclear charge increases, holding the electrons more tightly, and as we move down a group, the electrons are farther away from the nucleus, making them easier to remove.

Sc has the highest ionization energy because of the poor shielding of the d-orbital, which causes the Zeff of Sc to increase. Hence, increasing the ionization energy.

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Scandium (Sc) has the highest first ionization energy among the given atoms.

To determine this, we should understand that ionization energy is the energy required to remove an electron from an atom. Generally, ionization energy increases across a period (from left to right) and decreases down a group (from top to bottom) in the periodic table. The reason is that as we move across a period, the nuclear charge increases, holding the electrons more tightly, and as we move down a group, the electrons are farther away from the nucleus, making them easier to remove.

Sc has the highest ionization energy because of the poor shielding of the d-orbital, which causes the Zeff of Sc to increase. Hence, increasing the ionization energy.

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The ratio of effusion rate of O₂ to SO₂ is 2.526

Effusion rate refers to the speed at which a gas passes through a small opening and enters a vacuum or an area of lower pressure.. It depends on the size of the hole, the pressure of the gas, and the molecular weight of the gas. Lighter gases effuse faster than heavier gases. The effusion rate is directly proportional to the velocity of the gas molecules, which is in turn proportional to the square root of the temperature of the gas.

Effusion rate of a gas is inversely proportional to the square root of its molar mass.

The molar mass of O₂ is 2 × 15.999 g/mol = 31.998 g/mol.

The molar mass of SO₂ is 32.066 g/mol + 2 × 15.999 g/mol = 64.064 g/mol.

The ratio of their effusion rates is:

√(64.064 g/mol) / √(31.998 g/mol) = 2.526

Rounded to four significant figures, the ratio is 2.526.

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The percent yield for this experiment is approximately 75%. The percent yield is the actual yield of a reaction divided by the theoretical yield, multiplied by 100. In this case, we need to first find the theoretical yield of NH3 that should have been produced based on the amount of N2 and H2 that were reacted.

The balanced chemical equation for the reaction is:
N2 + 3H2 → 2NH3
From the given information, you have reacted 0.5 mol N₂ with 0.5 mol H₂. To find the limiting reactant, compare the mole ratios:
For N₂: 0.5 mol N₂ × (2 mol NH₃ / 1 mol N₂) = 1 mol NH₃ (theoretical yield)
For H₂: 0.5 mol H₂ × (2 mol NH₃ / 3 mol H₂) ≈ 0.333 mol NH₃ (theoretical yield)
Since the theoretical yield for H₂ is smaller, H₂ is the limiting reactant. The maximum amount of NH₃ that can be formed is 0.333 mol. The actual yield is given as 0.25 mol NH₃. Now, calculate the percent yield:
Percent Yield = (Actual Yield / Theoretical Yield) × 100
Percent Yield = (0.25 mol / 0.333 mol) × 100 ≈ 75%

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Answer:

Yes

Explanation:

A fine chemical is defined as "Single, pure, and complex chemicals that are only produced in small amounts by multi-purpose plants".

The Kb of the acid is approximately 1.28 x 10^-12.

When determining the Kb of an acid with a given Ka value of 7.8 x 10^-3, the ion product of water (Kw) can be utilized.

At a temperature of 25°C, Kw is known to be 1 x 10^-14. The relationship between Ka, Kb, and Kw is given by the equation:

Kw = Ka * Kb.

By rearranging this equation, we can find the value of Kb, which is the desired quantity.

Substituting the given values into the rearranged equation, we obtain

Kb = (1 x 10^-14) / (7.8 x 10^-3),

which simplifies to

Kb ≈ 1.28 x 10^-12

This result indicates that the Kb of the acid is approximately 1.28 x 10^-12.

This calculation is useful in determining the basicity of the acid and its reactivity in basic solutions. Additionally, the relationship between Ka, Kb, and Kw is an important concept in acid-base chemistry, and it is essential for understanding the behavior of acids and bases in various chemical reactions. Overall, this calculation is a simple yet essential example of how to determine the Kb of an acid using known values of Ka and Kw.

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There are approximately 0.34 firkins in 825 in³.

To find how many firkins are in 825 in³, we need to follow these steps:
1. Convert 825 in³ to gallons using the conversion factor 1 gallon = 231.0 in³.
2. Convert the gallons to barrels using the conversion factor 1 barrel = 42.0 gallons.
3. Convert the barrels to firkins using the conversion factor 1 barrel = 4 firkins.

Step 1: Convert 825 in³ to gallons:
825 in³ * (1 gallon / 231.0 in³) = 3.57 gallons (approximately)

Step 2: Convert 3.57 gallons to barrels:
3.57 gallons * (1 barrel / 42.0 gallons) = 0.085 barrels (approximately)

Step 3: Convert 0.085 barrels to firkins:
0.085 barrels * (4 firkins / 1 barrel) = 0.34 firkins (approximately)

So, there are approximately 0.34 firkins in 825 in³.

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The incorrect statement for red blood cells is A. They prefer CO2 at pH 7.35. Red blood cells have a higher affinity for CO2 compared to O2. Hence, they bind CO2 at the tissues where the partial pressure of CO2 is higher due to metabolic activity.

Similarly, they bind O2 at the lungs where the partial pressure of O2 is higher due to respiration. Therefore, options D and E are correct.

Moreover, the oxygen dissociation curve of hemoglobin is shifted to the right at lower pH, which means that at pH 7.35, the affinity of hemoglobin for oxygen is decreased, and it is more likely to release oxygen to the tissues. On the other hand, at pH 7.45, the affinity of hemoglobin for oxygen is increased, and it is more likely to bind oxygen in the lungs. Therefore, option C is also correct.

However, option A is incorrect because red blood cells actually prefer CO2 at lower pH (i.e., acidic conditions), not at pH 7.35, which is closer to neutral pH. At lower pH, the affinity of hemoglobin for CO2 is increased, which helps in the transport of CO2 from the tissues to the lungs for elimination.

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The combining of the fragments which remain after the loss of -OH from the alcohol and H from the carboxylic acid represents the overall transformation when a carboxylic acid is converted to an ester. This process is called esterification. Therefor the option B is correct.

The combination of the parts left over after the loss of -OH from the alcohol and H from the carboxylic acid represents the complete transformation when a carboxylic acid is transformed into an ester.

Esterification is a typical reaction in organic chemistry that describes this process. A carboxylic acid and an alcohol react with the help of an acid catalyst to produce an ester and water during esterification.

The creation of a new C-O bond between the oxygen of the alcohol and the carbonyl carbon of the carboxylic acid drives the reaction. The -OH group of the carboxylic acid and the -H group of the alcohol are removed and the remaining pieces are joined to create the ester.

The production of many different chemicals, including plasticizers, perfumes and flavors, depends on this interaction. In general, esterification is a fundamental organic chemical reaction with several industrial and commercial uses.

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The solubility of [tex]Au(OH)_{3}[/tex] in water and 1.0 M nitric acid can be calculated using the solubility product constant (Ksp) expression: the solubility of [tex]Au(OH)_{3}[/tex]  in 1.0 M nitric acid solution is 5.5 x [tex]10^{-18}[/tex] M.

Ksp = [tex][Au_{3} ^{+} ][OH^{-} ]^3[/tex]

where [[tex][Au_{3} ^{+} ][/tex]] is the concentration of the [tex][Au_{3} ^{+} ][/tex] ions and [tex][OH^{-} ]^3[/tex] is the concentration of hydroxide ions.

(a) Solubility of [tex]Au(OH)_{3}[/tex] in water:

Ksp = [tex][Au_{3} ^{+} ][OH^{-} ]^3[/tex]

Ksp = x * [tex](x)^3[/tex] = [tex]x^4[/tex]

x = [tex](Ksp)^(1/4)[/tex] = [tex](5.510^{-46} )^(1/4)[/tex] = [tex]1.110^{-12}[/tex] M

Solubility of [tex]Au(OH)_{3}[/tex] in water is [tex]1.110^{-12}[/tex] M.

(b) Solubility of [tex]Au(OH)_{3}[/tex] in 1.0 M nitric acid solution:

[[tex][Au_{3} ^{+} ][/tex]] = [tex](Ksp / [OH^{-} ]^3)^1/4[/tex]

[[tex]OH^{-}[/tex]] = 1.0 x [tex]10^{-14}[/tex] M (from Kw expression)

[[tex][Au_{3} ^{+} ][/tex]] = (5.5 x [tex]10^{-46}[/tex] / [tex](1.0 x 10^{-14} M)^3)^1/4[/tex]

[[tex][Au_{3} ^{+} ][/tex]] = [tex]5.5 x 10^{-18} M[/tex]

Therefore, the solubility of [tex]Au(OH)_{3}[/tex]  in 1.0 M nitric acid solution is 5.5 x [tex]10^{-18}[/tex] M.

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Sodium borohydride is a highly selective reagent that can reduce ketones, aldehydes, and esters, but cannot reduce carboxylic acids. Sodium borohydride (NaBH4) is a highly selective reagent that is commonly used as a reducing agent in organic chemistry. It is used to reduce various functional groups to their corresponding alcohols.

The functional groups that can be reduced by sodium borohydride include ketones, aldehydes, and esters. However, carboxylic acids cannot be reduced by sodium borohydride.

The reduction of ketones and aldehydes by sodium borohydride is a well-known reaction that is often used in synthetic organic chemistry. The reduction of these functional groups involves the transfer of a hydride ion (H-) from sodium borohydride to the carbonyl carbon, resulting in the formation of a new alcohol group.

Similarly, esters can also be reduced by sodium borohydride to form alcohols. However, the reduction of esters is slower than that of ketones and aldehydes due to the presence of the bulky ester group.

On the other hand, carboxylic acids cannot be reduced by sodium borohydride because they are already at their lowest oxidation state. Instead, carboxylic acids can be converted to their corresponding esters or amides, which can then be reduced by sodium borohydride.

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The colour of the gas mixture in the vessel will darken if more N₂O₄ is added to the vessel, if the volume of the vessel is increased, and if the system is cooled down.

The given reaction is an endothermic reaction as indicated by the positive enthalpy change. When N₂O₄ is heated, it decomposes into NO₂ gas which is red/brown in colour. On the other hand, when NO₂ gas is cooled down or the pressure is increased, it forms N₂O₄ which is a colourless gas. Therefore, when the equilibrium shifts towards the reactants, the gas mixture in the vessel will lighten, and when the equilibrium shifts towards the products, the gas mixture will darken.

(a) If more N₂O₄ is added to the vessel, the concentration of N₂O₄ will increase, causing the equilibrium to shift towards the products to maintain equilibrium. Thus, the gas mixture in the vessel will darken due to the increased concentration of NO₂ gas.

(b) If the volume of the vessel is increased, the equilibrium will shift towards the side with more moles of gas to maintain equilibrium. In this case, the volume is increased on the reactant side, where there is only one mole of gas, while there are two moles of gas on the product side. Thus, the equilibrium will shift towards the products, resulting in the gas mixture in the vessel darkening.

(c) If the system is cooled down, the equilibrium will shift towards the side that produces heat. In this case, since the reaction is endothermic, the equilibrium will shift towards the reactants, resulting in the gas mixture in the vessel lightening as the concentration of NO₂ gas decreases.

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