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Chapter 19: Problem 76

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: $$ \begin{array}{l}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (b) } 2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)} \\ {\text { (c) } 2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)}\end{array} $$

Short Answer

Expert verified
In summary, increasing the partial pressure of \(\mathrm{H}_{2}\) in the given reactions leads to the following changes in \(\Delta G\): (a) \(\Delta G\) decreases (b) \(\Delta G\) increases (c) \(\Delta G\) decreases

Step by step solution

01

Reaction (a)

Reaction (a) is given by: \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) As per Le Chatelier's principle, if we increase the partial pressure of \(\mathrm{H}_{2}\), the system will respond by shifting the equilibrium to counteract this change. In this case, the equilibrium will shift to the right, favoring the formation of \(\mathrm{NH}_{3}\). This indicates a decrease in \(\Delta G\) because the reaction is becoming more spontaneous in the forward direction.
02

Reaction (b)

Reaction (b) is given by: \(2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)\) Here, if we increase the partial pressure of \(\mathrm{H}_{2}\), the equilibrium will shift to the left according to Le Chatelier's principle, which will favor the formation of \(\mathrm{HBr}\). This shift leads to an increase in \(\Delta G\), as the reaction is becoming less spontaneous in the forward direction.
03

Reaction (c)

Reaction (c) is given by: \(2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\) When we increase the partial pressure of \(\mathrm{H}_{2}\) in reaction (c), the equilibrium will shift to the right to counteract the change, as per Le Chatelier's principle. This will favor the formation of \(\mathrm{C}_{2} \mathrm{H}_{6}(g)\). This shift corresponds to a decrease in \(\Delta G\) because the reaction is becoming more spontaneous in the forward direction. In conclusion: For reaction (a), the \(\Delta G\) decreases. For reaction (b), the \(\Delta G\) increases. For reaction (c), the \(\Delta G\) decreases.

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Most popular questions from this chapter

(a) Does the entropy of the surroundings increase for spontaneous processes? (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of \(\Delta S_{\text { surr. }} ?(\mathbf{c})\) During a certain reversible process, the surroundings undergo an entropy change, \(\Delta S_{\text { surr }}=-78 \mathrm{J} / \mathrm{K}\) . What is the entropy change of the system for this process?

The normal boiling point of \(\mathrm{Br}_{2}(l)\) is \(58.8^{\circ} \mathrm{C},\) and its molar enthalpy of vaporization is \(\Delta H_{\mathrm{vap}}=29.6 \mathrm{kJ} / \mathrm{mol}\) (a) When \(\mathrm{Br}_{2}(l)\) boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when 1.00 mol of \(\mathrm{Br}_{2}(l)\) is vaporized at \(58.8^{\circ} \mathrm{C}\) .

Free Energy and Equilibrium (Section) Consider the reaction 2 \(\mathrm{NO} 2(g) \rightarrow \mathrm{N} 2 \mathrm{O} 4(g) .\) (a) Using data from Appendix C, calculate \(\Delta G^{\circ}\) at 298 \(\mathrm{K}\) (b) Calculate \(\Delta G\) at 298 \(\mathrm{K}\) if the partial pressures of \(\mathrm{NO} 2\) and \(\mathrm{N} 2 \mathrm{O} 4\) are 0.40 atm and 1.60 atm, respectively.

In chemical kinetics, the entropy of activation is the entropy change for the process in which the reactants reach the activated complex. Predict whether the entropy of activation for a bimolecular process is usually positive or negative.

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix C to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G\) at \(800 \mathrm{K},\) assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at 800 \(\mathrm{K} ?\) (c) Calculate \(\Delta G\) at 1000 \(\mathrm{K} .\) Is the reaction spontaneous under standard conditions at this temperature?
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