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Chapter 17: Problem 52

For the reaction $$\mathrm{CS}_{2}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{SO}_{2}(g)$$ \(\Delta S^{\circ}\) is equal to \(-143 \mathrm{JK}\) . Use this value and data from Appendix 4 to calculate the value of \(S^{\circ}\) for $\mathrm{CS}_{2}(g) .$

Short Answer

Expert verified
The standard entropy of carbon disulfide (CS₂) gas is approximately 89.0 J/(K·mol).

Step by step solution

01

Write the Formula for Entropy Change in a Reaction

We will use the following equation to find the standard entropy of CS₂: ΔS° = ΣS°(products) - ΣS°(reactants) Where ΔS° is the standard entropy change of the reaction, ΣS°(products) is the sum of the standard entropies of the products, and ΣS°(reactants) is the sum of the standard entropies of the reactants. We are given: - ΔS° = -143 J/K - Standard entropies of O₂, CO₂, and SO₂ from Appendix 4 #Step 2: Write the Standard Entropy Change Equation#
02

Write the Standard Entropy Change Equation for the Given Reaction

With the known reaction and given values, the equation becomes: -143 J/K = [(S°(CO₂) + 2S°(SO₂)) - (S°(CS₂) + 3S°(O₂))] #Step 3: Find Standard Entropy Values from Appendix 4#
03

Find Standard Entropy Values of O₂, CO₂, and SO₂ from Appendix 4

Using Appendix 4, we can find the standard entropy values of O₂, CO₂, and SO₂. They are: S°(O₂) = 205.2 J/(K·mol) S°(CO₂) = 213.8 J/(K·mol) S°(SO₂) = 248.2 J/(K·mol) #Step 4: Substitute Known Values into the Equation#
04

Substitute the Known Standard Entropy Values into the Equation

Now substitute the standard entropy values of O₂, CO₂, and SO₂ into the equation: -143 J/K = [(213.8 J/(K·mol) + 2 × 248.2 J/(K·mol)) - (S°(CS₂) + 3 × 205.2 J/(K·mol))] #Step 5: Solve for S°(CS₂)#
05

Solve the Equation for the Standard Entropy of CS₂

Simplify and solve the equation for S°(CS₂): -143 J/K = (213.8 + 496.4 - 3 × 205.2 - S°(CS₂)) J/(K·mol) S°(CS₂) = [(213.8 + 496.4) - 143 - 3 × 205.2] J/(K·mol) S°(CS₂) ≈ 89.0 J/(K·mol) Thus, the standard entropy of carbon disulfide (CS₂) gas is approximately 89.0 J/(K·mol).

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Most popular questions from this chapter

Predict the sign of \(\Delta S^{\circ}\) and then calculate \(\Delta S^{\circ}\) for each of the following reactions. a. $\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)$ b. $2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$ c. \(\mathrm{HCl}(g) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Cl}^{-}(a q)\)

For the process \(\mathrm{A}(l) \longrightarrow \mathrm{A}(g),\) which direction is favored by changes in energy probability? Positional probability? Explain your answers. If you wanted to favor the process as written, would you raise or lower the temperature of the system? Explain.

Consider the reaction $$\mathrm{H}_{2}(g)+\mathrm{B} \mathrm{r}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)$$ where \(\Delta H^{\circ}=-103.8 \mathrm{kJ} / \mathrm{mol}\) . In a particular experiment, equal moles of \(\mathrm{H}_{2}(g)\) at 1.00 \(\mathrm{atm}\) and \(\mathrm{Br}_{2}(g)\) at 1.00 atm were mixed in a \(1.00-\mathrm{L}\) flask at \(25^{\circ} \mathrm{C}\) and allowed to reach equilibrium. Then the molecules of \(\mathrm{H}_{2}\) at equilibrium were counted using a very sensitive technique, and \(1.10 \times 10^{13}\) molecules were found. For this reaction, calculate the values of \(K, \Delta G^{\circ},\) and \(\Delta S^{\circ} .\)

Given the following data: $$2 \mathrm{C}_{6} \mathrm{H}_{6}(l)+15 \mathrm{O}_{2}(g) \longrightarrow 12 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\Delta G^{\circ}=-6399 \mathrm{kJ}$$ $$\mathrm{C}(s)+\mathrm{o}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \quad \Delta G^{\circ}=-394 \mathrm{kJ}$$ $$\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta G^{\circ}=-237 \mathrm{kJ}$$ calculate \(\Delta G^{\circ}\) for the reaction $$6 \mathrm{C}(s)+3 \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(l)$$

Which of the following reactions (or processes) are expected to have a negative value for \(\Delta S^{\circ} ?\) a. $\mathrm{SiF}_{6}(a q)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)+\mathrm{SiF}_{4}(g)$ b. $4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)$ c. \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{COCl}_{2}(g)\) d. $\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)$ e. \(\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\)
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