Faculty of Science
Department of Chemistry
8/2019 SECOND SEMESTER EXAMINATIONS
351 STATISTICAL MECHANICS AND THERMODYNAMICS
INSTRUCTIONS: Answer any FOUR questions.
Pluck's constant, h: 6.26 x 1034 J.S
zmann constant, k: 1.38 x 10 JK
nic mass Unit, amu: 1.661 x 10-kg
Nag
3Higi
C₂ (N₂) = 27.9 +0.00418T JK mol
C₂ (H₂) = 29.6+0.00231T JK 'mol
C₂ (NH) 29.9+0.00261T JK 'mol"¹
Gas constant, R: 8.314 JK mol
Avogadro constant, L: 6.022 x 10 mol
Speed of light, C: 2.998 x 10" ms¹¹
1. (a) Deduce the translational, rotational and vibrational mode of motion for the following
molecules: (i) NHs (ii) CO₂ (iii) CH.
(b) Calculate the enthalpy change at 800 °C for the reaction:
2NH
اله
November, 2019
UNIT: 4
Time allowed: 3hrs
All 92.2 kJ/mol
=
2. (a) Sate the equipartition law of energy.
(b) Apply the classical theory in calculating the expected heat capacity at constant pressure
for H₂ and Cl2 molecule given that the experimental value for H₂ is 28.86 JK 'mol and that
of Cle is 34.51 JK 'mol Explain the variation in these values.
(b) What will be the C₂ for a monoatomic gas?

NaOH is a base through all 3 definitions of base: Arrhenius, Bronsted-Lowry, and Lewis.

Arrhenius

An Arrhenius base is defined as a compound that increases the OH⁻ concentration in an aqueous solution. In other words, Arrhenius bases are compounds that have an OH⁻ ion. NaOH does dissolve into Na⁺ + OH⁻, so it will increase the OH⁻ of a solution. This means the compound is an Arrhenius base.

Bronsted-Lowry

Bronsted-Lowry bases are defined as a species that can accept a proton. Remember that a proton can be shown as H⁺. As stated above, NaOH dissolves into Na⁺ + OH⁻. In this form, the OH⁻ can accept the H⁺ to create H₂O. Thus, NaOH is a Bronsted-Lowry base.

Lewis Base

Lewis bases are compounds that can donate an electron pair. The O in dissolved NaOH has 3 electron pairs, which is what causes the negative charge on OH⁻. The O is able to donate one of the electron pairs to another species during a reaction. So, NaOH is a Lewis base.

The concentration of NaOH in the resulting solution is 1.80 mol/L.To determine the concentration of NaOH in the resulting solution, we need to use the equation:

What is concentration ?

concentration (in units of mol/L) = moles of solute / volume of solution (in units of L)

First, we need to calculate the moles of NaOH added to the flask:

moles of NaOH = mass of NaOH / molar mass of NaOH

moles of NaOH = 36.0 g / 40.00 g/mol

moles of NaOH = 0.900 mol

Next, we need to determine the volume of the solution. We know that 36.0 g of NaOH were added to a 500.0 mL volumetric flask, but the final volume of the solution is not given. We can assume that the volume of the solution is 500.0 mL, since that is the volume of the flask. However, we also need to take into account the fact that the addition of NaOH may cause the volume of the solution to increase slightly due to the dissolution of the solute.

Assuming that the volume of the solution is 500.0 mL, we can convert this to units of liters:

volume of solution = 500.0 mL / 1000 mL/L

volume of solution = 0.500 L

Now we can use the equation above to calculate the concentration of NaOH in the resulting solution:

concentration = 0.900 mol / 0.500 L

concentration = 1.80 mol/L

Therefore, the concentration of NaOH in the resulting solution is 1.80 mol/L.

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Complete question is: If 36.0 g of NaOH (MM = 40.00 g/mol) are added to a 500.0 mL volumetric flask, and water is added to fill the flask, 1.80 mol/L concentration of NaOH in the resulting solution.

When heated, ammonium nitrate decomposes explosively according to the balancing equation: 2 NH₄NO₃(s) + 2 N₂(g) + 4 H₂O(g) Calculate the total volume of gas generated by the full breakdown of 1.55 kg of ammonium nitrate (at 125 °C and 748 mmHg).

When ammonium nitrate is heated, it produces nitrous oxide and water molecules. When ammonium nitrate (NH₄NO₃) is heated, it produces nitrous oxide (N₂O) and water (H₂O).

Endothermic dissolution of ammonium nitrate in water occurs because more energy is consumed to separate the ions in the solid than is created when the ions establish new connections with water molecules.

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Answer:  the mass percentage of C in codeine is 72.21%.

Explanation: Molar mass of C = 12.011 g/mol

Molar mass of CisHziNO = 299.368 g/mol (whole of molar masses of all molecules within the compound)

Number of C molecules in codeine = 18

Mass of C in codeine = 12.011 g/mol x 18 = 216.198 g/mol

Mass rate of C in codeine = (216.198 g/mol ÷ 299.368 g/mol) x 100% = 72.21%

Explanation:

41.3 × (6.022 × 10²³)

248.7 × 10²³

2.487 × 10²⁵

Although, a part of your question is missing, you might be referring to this full question "How does crushing a candy to smaller pieces affect its digestion?"

Crushing the candy into smaller pieces increases the surface area of the solvent which will result in the reduction of digestion or dissolution.

Digestion is the process in which food taken is broken down into smaller components that can be absorbed into the bloodstream. Digestion helps in converting food into molecules, like glucose so that the body can utilize that energy for its growth and development.

While Crushing the candy into smaller pieces, we are increasing the surface area of the solvent which will result in the reduction of digestion or dissolution of the candy. Thus, the larger the size of the pieces, the slower will be the process of digestion. This physical process in which large pieces of food are cut and crushed into smaller pieces is known as mechanical digestion.

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The word equation for the given skeleton equation is: Solid aluminum + gaseous oxygen → Solid aluminum oxide.

Chemical equations are a way of representing chemical reactions using chemical formulas and symbols. They provide a concise and standardized way of describing chemical reactions and are an important tool for chemists to communicate and understand chemical changes.

In any chemical equation, reactants are written on left side of an arrow, whereas the products are written on right side. The arrow indicates the direction of reaction, from the reactants to products.

Chemical equations use chemical formulas to represent the elements and compounds involved in a reaction.

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Answer:

D. something's that's produced during a chemical reaction

Answer:

Explanation:

The answer is Option D.

A substance that is produced during a chemical reaction.

for example in a chemical reaction A+B -----> C

here, reactants A and B react together to produce product C.

Answer 1:

During the summer months in the northern hemisphere (where the United States is located), Earth is in position C, which is when the northern hemisphere is tilted towards the sun.

Answer 2:

The highest tide occurs during the full moon phase, which is represented by position C in the diagram.

Answer 3:

A star that has a luminosity of 10^-2 is likely a red dwarf.

Answer 4:

Telescopes that observe short-wavelength radiation, such as X-rays and gamma rays, do not need to be placed in orbit around Earth because these wavelengths are absorbed by the atmosphere. Therefore, telescopes that observe these wavelengths are typically placed in space, outside of Earth's atmosphere.

Answer 5:

The student is likely demonstrating the relationship between the Earth and the Sun's gravitational pull. The ball represents the Sun, and the string represents the gravitational force pulling the Earth towards the Sun. The demonstration shows how the Earth orbits the Sun due to this gravitational force.

Gravitational force is described as a force that exists between any two objects in the universe that have mass.

It is the force that causes objects with mass to be attracted to each other. The magnitude of the gravitational force between two objects depends on their masses and the distance between them.

Along with the electromagnetic force, the strong nuclear force, and the weak nuclear force, gravity is one of the four fundamental forces of the universe.

Sir Isaac Newton initially introduced it in his law of universal gravitation, and Albert Einstein later elaborated on it in his theory of general relativity.

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The pH of a solution that has a hydronium concentration of 4.8 x 10⁻¹² is 11.32.

The term "potential of hydrogen" (sometimes known as "power of hydrogen") has historically been used to describe this property in chemistry. It is a scale used to describe how basic or how acidic an aqueous solution is. Lower pH values are recorded for acidic solutions (solutions with higher H+ ion concentrations) than for basic or alkaline solutions.The set of standard solutions whose pH has been defined by international agreement can be used to trace the pH scale.[4] Using a concentration cell with transference, the potential difference between a hydrogen electrode and a standard electrode, such as the silver chloride electrode, is measured to get the primary pH standard values. With the use of a glass electrode, a pH meter, or a color-changing indicator, the pH of aqueous solutions can be determined.

The pH of a solution is the negative log of its hydronium ion concentration. To calculate the pH of a solution, we can use the following equation:

pH = -log[H⁺]

Therefore, the pH of a solution with a hydronium ion concentration of 4.8 x 10⁻¹² is -log(4.8 x 10⁻¹²) = 11.32.

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The combined gas law, which links a gas's pressure, volume, and temperature, can be used to solve this issue. When the balloon reaches an altitude with a pressure of 0.65 atm and a temperature of -150 C, its capacity will fall to 4.9 L.

The Centigrade scale, Celsius size, and Kelvin scale are the three scales that are most frequently used to measure temperature.Any item contains molecules that move or vibrate. Its temperature will rise when it is heated because the molecules are moving more quickly.A tool called a thermometer is used to measure it. the three units used to measure temperature.

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The experiment employing these pipettes would most likely have a 5% error rate.

When your estimate aims at a known, accurate figure, percent error is a useful metric. Use it to measure how near an estimate is to the actual value, in general. When an approximation value is near to the true value, there are fewer mistakes.

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.

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4 moles of AgBr is produced

2 moles of Calcium nitrate is produced

Stoichiometry is used in calculating the quantities of the reactants and products in a chemical reaction as well as identifying the limiting reactant are all part of this process.

The reaction equation is;

[tex]CaBr_{2} (aq) + 2 AgNO_{3} (aq) ---- > 2 AgBr (s) + Ca(NO_{3} )_{2} (aq)[/tex]

If 2 moles of [tex]AgNO_{3}[/tex] produces 2 moles of AgBr

4 moles of [tex]AgNO_{3}[/tex] will produce 4 * 2/2 = 4 moles of AgBr

If 2 moles of [tex]AgNO_{3}[/tex] produces 1 mole of  Calcium nitrate

4 moles of [tex]AgNO_{3}[/tex] will produce 4 * 1/2
2 moles of  Calcium nitrate

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The answers are:

A rock is a naturally occurring collection of minerals, and the kind and quantity of minerals it contains influence its hardness. Quartz, feldspar, mica, and calcite are just a few of the minerals that are present in all rocks. Additionally, rocks may include mineraloids and organic byproducts. Rocks are categorised based on their texture, mineral makeup, and additional features including colour, streak, lustre, and cleavage.

The three rocks are sedimentary, igneous, and metamorphic rocks. Rocks can be utilised in a variety of applications, including building, landscaping, and industrial activities.

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Answer:

20 valence electrons

Explanation:

The number of valence electrons in carbon (C), hydrogen (H), and chlorine (Cl) are 4, 1, and 7, respectively. The number of total valence electrons (TVE) in CH₂Cl₂ is calculated as follows-

TVE in CH₂Cl₂ = valence electrons in C + 2(valence electrons in H) + 2(valence electrons in Cl)

= 4 + 2(1) + 2(7)

= 20

Sugar cane plantation owners needed cheap labor after the enslaved were freed.

We know that in the nineteenth century the era of slave trade was actually coming to a close and the concern of many of the slave owners both in Europe and America was the future of their agricultural businesses.

The slave owners mostly used the slaves to do the work on the farm and in the absence of the slaves, the work could not be done. This is why the owners of the slaves sought for cheap labor after the slaves were freed.

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Sugar was important in the late nineteenth century for both dietary and economic reasons. It was consumed by all social classes and significantly influenced the labor practices in agriculture.

Based on the information provided, one can infer that sugar was of significant importance in the late nineteenth century. It served as a staple in people's daily diets and was enjoyed by all social classes, from shopgirls to kings. In the economic sphere, sugar cane farming was a notable industry. Sugar canes were labor-intensive to grow and harvest, which required plantation owners to seek cheap labor. This implies that the sugar industry had a substantial influence on labor practices during this era. It is therefore clear that sugar was not only a dietary necessity but also a crucial factor in the broader economic and social structure of the community.

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Answer:

Please mark brainlist

Explanation:

The equilibrium expression for this reaction is Kw = [H₃O⁺][OH⁻], where Kw is the autoionization constant for water. At 25°C, the value of Kw is 1.0 x 10⁻¹⁴.

Each oxygen atom in peroxide compounds like hydrogen peroxide (H2O2) has an additional electron that it shares with the other oxygen atom in the compound, giving the oxygen a charge of -1.

Any substance comprised of two or more elements that are chemically linked together is known as a compound. A compound's constituent parts are always present in a specific ratio. As an illustration, the substance water (H2O) consists of two hydrogen atoms that are chemically bound to one oxygen atom.

Actually, oxygen belongs to the second period of the periodic table. It can create two covalent bonds with other elements to complete its octet and has six valence electrons.

Each oxygen atom in peroxide molecules like hydrogen peroxide (H2O2) has a charge of -1. This is due to the fact that each oxygen atom in the molecule has an additional electron that it shares with another oxygen atom.

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7.10 grams of C₈H₁₈ will react with 24.78 g of O₂ in this unbalanced combustion reaction.

Type of chemical reaction that occurs when substance reacts with oxygen gas to produce energy in the form of heat and light is called combustion reaction .

To balance the combustion reaction: C₈H₁₈ + 12.5 O₂ -> 8 CO₂ + 9 H₂O

The coefficients show that 12.5 moles of  O₂ are needed to react with 1 mole of C₈H₁₈.

1 mole of  O₂ has a mass of 32 g, so 24.78 g of  O₂ is:

24.78 g / 32 g/mol = 0.774 mol of O₂

0.774 mol of  O₂ / 12.5 mol of  O₂/mol of C₈H₁₈ = 0.06192 moles of C₈H₁₈

0.06192 moles of C8H18 x 114.23 g/mol of C₈H₁₈ = 7.10 g of C₈H₁₈

Therefore, 7.10 grams of C₈H₁₈ will react with 24.78 g of  O₂ in this unbalanced combustion reaction.

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0.0318 moles of acetic anhydride was used in the experiment.

To determine the number of moles of acetic anhydride (C4H6O3) used, we need to use the formula:

moles = mass / molar mass

First, we need to find the mass of 3.00 mL of acetic anhydride using its density:

mass = volume x density = 3.00 mL x 1.08 g/mL = 3.24 g

Next, we need to find the molar mass of acetic anhydride:

molar mass of C4H6O3 = 4(12.01 g/mol) + 6(1.01 g/mol) + 3(16.00 g/mol) = 102.08 g/mol

Now, we can use the formula to find the number of moles:

moles = mass / molar mass = 3.24 g / 102.08 g/mol = 0.0318 mol

Therefore, 0.0318 moles of acetic anhydride was used in the experiment.

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The mass in grams of BaCl₂ (formula mass = 208.23 amu) that will be required to produce 41.5 grams of Ba (PO₄)₂ is 18.48 g. This is using the stoichiometric ratio.

The relationship between the quantities of reactants and products prior to, during, and after chemical reactions is known as stoichiometry.

Stoichiometry is based on the law of conservation of mass, which states that the sum of the masses of the reactants and products must equal one another. This realization led scientists to conclude that the ratio of positive integers is typically formed by the relationships between the quantities of the reactants and products. This means that the amount of the product may be determined if the amounts of the individual reactants are known. On the other hand, if the amount of one reactant is known and the amount of the products can be computed using empirical data, the amount of the other reactants can likewise be calculated.

Using the stoichiometric ratio of the equation and the molar masses of the reactants, we can calculate the mass of BaCl₂ required to produce 41.5 grams of Ba (PO₄)₂.

Molar mass of BaCl₂ = 208.23 g/mol

Molar mass of Ba (PO₄)₂ = 601.92 g/mol

According to the equation, the stoichiometric ratio between BaCl₂ and the product (Ba (PO₄)₂ is 1 : 3.

Therefore, we will need 1 mol of BaCl₂ to produce 3 moles of Ba (PO₄)₂

Therefore, the mass of BaCl2 required to produce 41.5 grams of Ba (PO₄)₂ is:

Mass of BaCl₂ = 41.5 g/601.92 g/mol x 208.23 g/mol

Mass of BaCl₂ = 18.48 g

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we can estimate that approximately 1.54 grams of water will be produced when 4.95 grams of Fe3O4 react completely with hydrogen.

The balanced chemical equation for the reaction between Fe₃O₄  and hydrogen is:

Fe₃O₄ + 4H₂ → 3Fe + 4H₂O

we can see that 4 moles of hydrogen react with 1 mole of Fe₃O₄  to produce 4 moles of water.

To find the number of moles of Fe₃O₄  in 4.95g, we need to divide the mass by the molar mass of Fe₃O₄ :

4.95 g Fe₃O₄  / (231.53 g/mol Fe₃O₄ ) = 0.0214 mol Fe₃O₄

According to the mole ratio in the balanced equation, 4 moles of hydrogen produce 4 moles of water. Therefore, we can calculate the number of moles of hydrogen required to react with 0.0214 mol Fe₃O₄ :

0.0214 mol Fe₃O₄ × (4 mol H2 / 1 mol Fe₃O₄ ) = 0.0855 mol H2

Finally, we can use the molar mass of water to calculate the mass of water produced:

0.0855 mol H₂O × (18.02 g/mol H2O) = 1.54 g H₂O

Therefore, we can estimate that approximately 1.54 grams of water will be produced when 4.95 grams of Fe₃O₄  react completely with hydrogen.

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The first quarter is the point in the lunar cycle where the moon is one (1) week after the new moon has risen. At first quarter, the moon will also be in its "waning gibbous" phase.

The moon is called a "new moon" when it lies between the sun and the Earth, as opposed to a "full moon," which occurs when the moon is directly above. Furthermore, because we cannot even see the new moon from Earth, unlike full moons, it appears as though it doesn't exist at all.

A half (1/2) or 50% of the moon is lighted during the waning gibbous phase, which occurs once per new moon.

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The half‑life of Ga67 is 3.67 days.

The half-life of a chemical reaction can be defined as the time taken for the concentration of a given reactant to reach 50% of its initial concentration (i.e. the time taken for the reactant concentration to reach half of its initial value). It is usually expressed in seconds.

Half-lives are characteristic properties of the various unstable atomic nuclei and the particular way in which they decay.

Given,

Let the initial amount be 100, so final amount will be 100 - 64 = 36

time = 2.33 days

= 2.33 × 24 × 60 × 60

= 201312 seconds

k = ( 1÷ t) log ( initial ÷ final)

k = 0.189 s⁻¹

half life = 0.693 ÷ k

= 315286.62 seconds

= 3.67 days

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a. The rate law for this reaction is: Rate = k[Cl] [H₂]. This means that the rate of the reaction is directly proportional to the concentrations of both Cl and H₂ molecules.

Rate law is an equation that describes the rate of a chemical reaction as a function of the concentrations of reactants. The rate law allows us to describe how the rate of a reaction changes when the concentrations of reactants are changed. It is derived from the rate equation, which is a mathematical expression that can be used to calculate the rate of a reaction from the concentrations of the reactants and the rate constant.

b. The rate law for this reaction is: Rate = k[O] [Os]. This means that the rate of the reaction is directly proportional to the concentrations of both O and Os molecules.
c. The rate law for this reaction is: Rate = k[NO₂]₂. This means that the rate of the reaction is directly proportional to the square of the concentration of NO₂ molecules.

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Complete Question:

The set of structures that includes only analogous organs is the wings of a butterfly, housefly, and bat, option A is correct.

Analogous organs perform similar functions in different organisms, but have different anatomical structures and evolved independently. In this case, butterflies, houseflies, and bats have wings that allow them to fly, but their wings have different structures and evolved independently.

The hind legs of horses, grasshoppers, and bats are not analogous, as each organism has different functions. The hands of man, monkey, and kangaroo are not analogous, as they have similar structures and evolved from a common ancestor. The mandibles of cockroach, mosquito, and honey bee are not analogous, as they have different structures and perform different functions in each organism, option A is correct.

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The complete question is:

Which one of the following is a set of structures that includes only analogous organs?

A) Wings of butterfly, housefly, and bat.

B) Hind legs of horse, grasshopper, and bat.

C) Hands of man, monkey, and kangaroo.

D) Mandibles of cockroaches, mosquitoes, and honey bees.

The polar ice caps are large areas of ice that cover the Earth's polar regions, specifically the North Pole (Arctic) and the South Pole (Antarctica). These ice caps consist mainly of ice sheets, glaciers, icebergs, and sea ice, which have significant impacts on the global climate, ecosystems, and sea levels. Here's how they help the world:

1. Climate regulation: The polar ice caps play a crucial role in maintaining the Earth's temperature by reflecting sunlight back into space. The bright, reflective surface of the ice (called albedo) helps to cool the planet and counteract the greenhouse effect. When the ice caps melt, the darker ocean or land underneath absorbs more sunlight, leading to higher temperatures and further ice melting – a process known as the ice-albedo feedback loop.

2. Ocean circulation: The polar ice caps influence global ocean circulation patterns. Cold, dense water sinks near the polar regions, driving the thermohaline circulation (also known as the global ocean conveyor belt). This circulation helps to distribute heat and nutrients around the world, impacting weather patterns and supporting marine ecosystems.

3. Sea level regulation: The ice caps store a vast amount of freshwater in the form of ice. If all the ice in Antarctica and Greenland were to melt, global sea levels would rise by around 65 meters (213 feet), with devastating consequences for coastal communities and ecosystems. By keeping this water locked in ice, the polar ice caps help to regulate sea levels and protect coastal areas from flooding.

4. Ecosystem support: The polar ice caps support unique and fragile ecosystems that are home to a wide variety of plants and animals. Some of these species, such as Arctic foxes, polar bears, and emperor penguins, are specifically adapted to life in the harsh polar environments. The ice caps are also critical to the survival of many marine species, including fish, seals, and whales, which rely on the ice for breeding grounds, shelter, and hunting.

5. Scientific research: The polar regions offer valuable opportunities for scientific research, particularly in the fields of climate science, glaciology, and paleoclimatology. Ice cores taken from the ice caps provide a historical record of Earth's climate, allowing scientists to understand past climate changes and make more informed predictions about the future.

This reaction has an activation energy of about 81.6 kJ/mol.

At 30 °C, the value of k is roughly 1.10 × 10¹³ s⁻¹.

a) To calculate the activation energy, use the Arrhenius equation:

k = A × e^(-Ea/RT)

where k = rate constant, A = pre-exponential factor, Ea = activation energy, R = gas constant, and T = temperature in Kelvin.

Use the given half-lives to calculate the rate constants at each temperature:

k₁ = 0.693 / t₁/2 = 0.693 / 22.5 = 0.0308 h⁻¹ at 20°C

k₂ = 0.693 / t₁/2 = 0.693 / 1.5 = 0.462 h⁻¹ at 40°C

Converting the temperatures to Kelvin:

T1 = 20°C + 273.15 = 293.15 K

T2 = 40°C + 273.15 = 313.15 K

Now use the Arrhenius equation to calculate the activation energy:

ln(k1/k2) = (Ea/R) × (1/T₂ - 1/T₁)

ln(0.0308/0.462) = (Ea/8.314) × (1/313.15 - 1/293.15)

-3.31 = (Ea/8.314) × (0.003386)

Ea = -3.31 × 8.314 / 0.003386 = 81570 J/mol

Therefore, the activation energy for this reaction is approximately 81.6 kJ/mol.

b) Use the Arrhenius equation again, with the given activation energy, A, and the new temperature (30°C = 303.15 K) to solve for k:

ln(k) = ln(A) - (Ea/R) × (1/T)

ln(k) = ln(2.05×10¹³) - (81570 / 8.314) × (1/303.15)

ln(k) = 31.87

k = e^(31.87) = 1.10 × 10¹³ s⁻¹

Therefore, the value of k at 30°C is approximately 1.10 × 10¹³ s⁻¹.

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