Entropy Practice Problems

For a spontaneous reaction, the entropy of the surroundings will not change. Is this statement true or false?

Arrange the following sulfur allotropes in decreasing order of standard molar entropy (S°) and justify your answer: S (s, cyclo-S₆), S (s, cyclo-S₇), S (s, cyclo-S₈)

Which of the following statements is correct? 

What is the entropy condition for a spontaneous process in an isolated system where the system does not exchange matter or energy with its surroundings? Is the mixing of two ideal gases inside a vessel an example of a spontaneous process in an isolated system?

Two separate bulbs are filled with ideal gases A (spheres in orange) and B (spheres in blue). Both bulbs' contents represent the starting condition of an isolated system. 

Take into account the procedure that takes place when the stopcock is opened. What aspects of the second law of thermodynamics are illustrated by this process?

Identify which has the higher entropy (per mole) between methanol at 64.6 °C and 1 atm and methanol at 80 °C and 0.5 atm (T_b for methanol is 64.6 °C).

Which statement correctly defines entropy and has the right example of a process with a positive change in entropy?

Identify which has the higher entropy (per mole) between He at 0 °C and 50 atm and He at STP (0 °C, 1 atm, 22.4 L).

Identify the parameter that entropy measures.

Identify which has the higher entropy (per mole) between aniline at −10 °C and aniline at 0 °C (T_m for aniline = −6.02 °C).

What are the signs of the change of entropy for each of the given processes below?

(a) Fe³⁺ and OH^– ions forming solid Fe(OH)₃.

(b) Methane gas is released from solid wastes.

(c) A gas condenses.

(d) A liquid evaporates.

At 298 K, 1 mol of an ideal gas, X, experiences a threefold expansion in the isolated system depicted in the figure below. Explain how this process demonstrates the second law of thermodynamics.

Identify which has the higher entropy (per mole) between N₂ at 0 °C and 1 atm and N₂ at 25 °C and 0.5 atm.

The gas-phase reaction between X₂ (gray) and Y₂ (orange) molecules is illustrated in the following diagram:

(a) Provide the balanced reaction equation.

(b) Predict the sign of the change in entropy (ΔS) for the reaction.

Identify which has the higher entropy (per mole) between equal amounts of N₂ at 30 °C in 15 L and N₂ at 30 °C in 65 L.  

Among the following reactions, identify which has an entropy (∆S_sys) greater than zero.

Determine which has the higher entropy (explain in terms of randomness), (a) between a perfectly ordered crystal of solid carbon dioxide () and a disordered crystal of solid carbon dioxide, and (b) between a titanium dioxide crystal and an amorphous powder of titanium dioxide.

Which situation below shows the highest entropy?

Without doing any calculations, indicate the signs of ΔH° and ΔS° for each of the following reactions.

(i) H₂(g) → 2 H(g)

(ii) 2 Al₂O₃(s) → 4 Al(s) + 3 O₂(g)

(iii) 2 K(s) + Cl₂(g) → 2 KCl(s)

(iv) 2 NaBr(s) → 2 Na(s) + Br₂(g)

Predict the signs of ΔS and ΔH (positive, negative, or about zero): The decomposition of calcium carbonate (CaCO₃) produces CaO(s) and CO₂(g).

What are the signs of ΔH and ΔS for the process illustrated below? Justify your answer.

If the reaction 4 Fe(s) + 3 O₂(g) → 2 Fe₂O₃(s) is highly spontaneous, its change in entropy can be a very large negative value. Is this true or false? Explain.

True or False. If the entropy change for the system of a spontaneous process is 5.2 J/K, then the entropy change of its surroundings is −5.2 J/K.

A particular chemical process has ΔH° = –25.4 kJ and ΔS° = 56.2 J/K. Which of the following statement is true about the process?

Determine if the following statements are true or false. 

(a) For a reversible process, the entropy change of the surroundings is equal to zero. 

(b) For a reversible process, the value of the entropy of the surroundings is equal and opposite to the change in entropy of the system. 

(c) The change in entropy of a reaction is a path function. 

(d) For a reversible process, the entropy of the universe is equal to zero.

Two bulbs contain two different ideal gases that are initially separated by a stopcock as shown in the figure below. Once the stopcock is opened, the two gases mix. Which of the following statements is true about the entropy of surroundings?

The molecules of the majority of elastomers or elastomeric polymers, such as rubber bands, become more organized when they are stretched as shown below.
 

Suppose you have a rubber tubing and stretch it, would the entropy of the system increase or decrease?

Diamond, graphite, and fullerene are elemental forms of carbon. If the S° for C(diamond) is 2.43 J/mol-K and S° for C(graphite) is 5.69 J/mol-K, which statement is correct regarding the value of S° for C₂₀ fullerene based on the S° of diamond and graphite? Explain

The entropy change for a process that leads to the formation of the activated complex or transition state is known as the entropy of activation. Determine whether the sign of the entropy of activation for a bimolecular process would be positive or negative.

What is the sign of the ΔS_sys when H₂(g) dissociates to form H(g) atoms?

Acetone (C₃H₆O) has a normal boiling point of 56.0°C and molar enthalpy of vaporization (ΔH_vap) of 29.1 kJ/mol. Predict whether the entropy of acetone will increase or decrease when it boils at its normal boiling point.

Refer to the process illustrated below. Considering that the temperature of the process is kept constant by allowing energy to flow in and out of the system, the entropy change of the surrounding will be positive. Is this statement true or false?

Which of the following explains the trend in S° values for the standard entropies at 298 K for a certain group of 4A elements? 

C(s, diamond) = 2.43 J/mol-K, Si(s) = 18.81 J/mol-K, Ge(s) = 31.09 J/mol-K, and Sn(s) = 51.818 J/mol-K (Note: Only Sn does not have a diamond structure)

Cyclobutane and butene are isomers that have different arrangments but the same formula, C₄H₈. At 25 °C, which of the isomers have a higher standard molar entropy based on their molecular structure?

True or False. 1 mol of P₂(g) at 400°C and 0.01 atm has a higher entropy per mole than 1 mol of P₄(g) at 400°C and 0.01 atm 

Molecules with different arrangments but the same chemical formula are called isomers. For the two isomers of nonane shown below, which has the higher standard molar entropy? Why?

Consider the two systems below: 

Each system is composed of 4 particles that have a total energy of 40 J. 

i) Identify how many energetically equivalent ways the particles can be distributed for each system. 

ii) Identify the system that has the greater entropy. 

Identify and briefly state the rationale for the sign of ΔS_univ for the reaction below:

2 CO(g) + O₂(g) → 2 CO₂ (g) at 25°C 

What is the relationship between the molar entropy of a substance and temperature?

Identify the sign of ΔS_sys for the reaction below without doing calculations

U(s) + 3 F₂(g)→  UF₆(g)

Identify the sign for the entropy change of the system for the condensation of ethanol.  

Arrange the following substances in order of increasing standard molar entropy (S°) 

CO₂(g), C₆H₅OH( g), Xe(g), BH₃(g), Ar(g), 

Identify which among NH₃(g) and C₆H₆(g) have the higher standard molar entropy (S°) at 25 °C. Briefly explain.

For a spontaneous endothermic reaction, what are the expected signs of ∆S_surr, ∆S_sys, and ∆S_univ, respectively?

The illustration below represents the change in entropy with temperature for a gaseous substance at the highest temperature represented. Correspondingly, which of the following statements is not true?

Which of the following reactions have a positive ΔS_rxn?

A. A(s) + B(g) → C(g)

B. 2 A(g) + B(g) → C(g)

C. 2 A(g) + B(g) → 4 C(g)

D. A(g) + 2 B(g) → C(g)

E. A(g) + B(s) → C(g)

Arrange the following systems in order of decreasing (highest to lowest) entropy.

i) 1 mol carbon tetrafluoride gas at 273 K and 60 L

ii) 1 mol krypton gas at 273 K and 60 L

iii) 1/2 mol krypton gas at 273 K and 30 L

iv) 1 mol nitrogen gas at 273 K and 30 L

v) 1/2 mol liquid krypton at 100 K

vi) 1 mol of krypton gas at 273 K and 30 L

vii) 1/2 mol of krypton gas at 130 K and 30 L

Arrange the following substances in order of increasing (least to most) molar entropy at 298 K.

Al(s)          CO₂(g)          Ne(g)

Without doing any calculations, determine the sign of ΔS_sys for each chemical reaction.

a. 2 KClO₃(s) → 2 KCl(s) + 3 O₂(g)

Identify the sign of ΔS_sys and ΔS_surr for the reaction below without doing calculations and identify which temperature condition in which the reaction would be spontaneous

2 C₆H₆(l) + 15 O₂(g) → 12 CO₂(g) + 6 H₂O(l) ΔH°_rxn = -6534 kJ

Without doing any calculations, determine the signs of ΔS_sys and ΔS_surr for this chemical reaction. In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction is spontaneous.

C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(g) ΔH°_rxn = -2044 kJ

Rank each set of substances in order of increasing standard molar entropy (S°). Explain your reasoning. NH₃(g); Ar(g); SeO₂(g); CH₃CH₂CH₂OH(g); Kr(g)

Identify and briefly state the rationale for the sign of ΔS_univ for the reaction below:

2 CO(g) + O₂(g) → 2 CO₂ (g) at 25°C 

Use the data below to create an approximate graph of the standard molar entropy against temperature for methanol from 0 K to 400 K:

melting point = –98°C

boiling point = 65°C

S°_(l) = 126.8 J/(mol•K) at 25 °C.