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Chapter 17: Problem 111

Consider the reaction: $$\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)$$ At \(25^{\circ} \mathrm{C}, \Delta G^{\circ}=-92.50 \mathrm{kJ}\) Which of the following statements is (are) true? a. This is an endothermic reaction. b. \(\Delta S^{\circ}\) for this reaction is negative. c. If the temperature is increased, the ratio \(\frac{\mathrm{PCl}_{5}}{\mathrm{PCl}_{3}}\) will increase. d. \(\Delta G^{\circ}\) for this reaction has to be negative at all temperatures. e. When \(\Delta G^{\circ}\) for this reaction is negative, then \(K\) is greater than 1.00 .

Short Answer

Expert verified
The short answer based on the step-by-step solution is: a. False b. False (Cannot be determined) c. False (Cannot be determined) d. False e. True

Step by step solution

01

(Determine if the reaction is endothermic or exothermic)

The given reaction has a ΔG° = -92.50 kJ at 25°C. An endothermic reaction is one in which the standard enthalpy change (ΔH°) is positive, and an exothermic reaction is one in which ΔH° is negative. Keep in mind that there isn't enough information to directly evaluate ΔH°. However, since the question refers to ΔG, and we know that ΔG = ΔH - TΔS (ΔS being the entropy), we can infer that a negative ΔG value indicates a spontaneous reaction. Answer: a. False #Step 2: Determine the sign of ΔS° (entropy change)#
02

(Determine the sign of ΔS°)

Given that ΔG = ΔH - TΔS, with T > 0, a negative ΔG° suggests that the term (ΔH - TΔS) is negative. We can't uniquely determine the signs of ΔH or ΔS from this reaction, but the following statement is not necessarily true. Answer: b. False (Cannot be determined) #Step 3: Effect of temperature on the reaction equilibrium#
03

(Effect of temperature on the reaction equilibrium)

Le Chatelier's principle states that if an external stress (e.g., temperature, pressure, or concentration) is applied to a system in equilibrium, the system will adjust to counteract the stress and restore equilibrium. In this case, we consider the effect of increasing temperature. However, we do not have enough information available currently to determine how the temperature will impact the equilibrium concentration ratio. Answer: c. False (Cannot be determined) #Step 4: ΔG° at different temperatures#
04

(ΔG° at different temperatures)

ΔG° is not constant at all temperatures - its value depends on the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) according to the equation ΔG = ΔH - TΔS. We don't have enough information about these variables to determine if ΔG° has to be negative at all temperatures. Answer: d. False #Step 5: Relate ΔG° to K (equilibrium constant)#
05

(Relate ΔG° to K)

There is a relationship between ΔG° and the equilibrium constant K, according to the equation \(ΔG° = -RT \ln{K}\) (where R is the gas constant and T is the temperature). When ΔG° is negative, it implies that the Natural logarithm (ln) of K is positive (because -RT is negative), meaning K > 1.00. Answer: e. True

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Most popular questions from this chapter

Consider two perfectly insulated vessels. Vessel 1 initially contains an ice cube at \(0^{\circ} \mathrm{C}\) and water at \(0^{\circ} \mathrm{C}\) . Vessel 2 initially contains an ice cube at \(0^{\circ} \mathrm{C}\) and a saltwater solution at \(0^{\circ} \mathrm{C}\) . Consider the process $\mathrm{H}_{2} \mathrm{O}(s) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)$ a. Determine the sign of \(\Delta S, \Delta S_{\text { sum }}\) and $\Delta S_{\text { univ }}$ for the process in vessel 1 . b. Determine the sign of \(\Delta S, \Delta S_{\text { sum }},\) and $\Delta S_{\text { univ }}\( for the process in vessel \)2 .$ (Hint: Think about the effect that a salt has on the freezing point of a solvent.)

The following reaction occurs in pure water: $$\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q)$$ which is often abbreviated as $$\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q)$$ For this reaction, \(\Delta G^{\circ}=79.9 \mathrm{kJ} / \mathrm{mol}\) at \(25^{\circ} \mathrm{C}\) . Calculate the value of \(\Delta G\) for this reaction at \(25^{\circ} \mathrm{C}\) when \(\left[\mathrm{OH}^{-}\right]=0.15 M\) and \(\left[\mathrm{H}^{+}\right]=0.71 M .\)

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. \(\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\)

Which of the following involve an increase in the entropy of the system? a. melting of a solid b. sublimation c. freezing d. mixing e. separation f. boiling

At 1 atm, liquid water is heated above \(100^{\circ} \mathrm{C}\) . For this process, which of the following choices (i-iv) is correct for $\Delta S_{\text { surr }} ? \Delta S ?\( \)\Delta S_{\text { univ }} ?$ Explain each answer. i. greater than zero ii. less than zero iii. equal to zero iv. cannot be determined
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