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Chapter 19: Problem 25

At \(298 \mathrm{K},\) for the reaction \(2 \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \stackrel{\text { Lest }}{\longrightarrow}\) \(2 \mathrm{POCl}_{3}(1), \Delta H^{\circ}=-620.2 \mathrm{kJ}\) and the standard molar entropies are \(\mathrm{PCl}_{3}(\mathrm{g}), 311.8 \mathrm{JK}^{-1} ; \mathrm{O}_{2}(\mathrm{g}), 205.1 \mathrm{JK}^{-1}\) and \(\mathrm{POCl}_{3}(1), 222.4 \mathrm{JK}^{-1} .\) Determine (a) \(\Delta G^{\circ}\) at \(298 \mathrm{K}\) and (b) whether the reaction proceeds spontaneously in the forward or the reverse direction when reactants and products are in their standard states.

Short Answer

Expert verified
The detailed calculation of ΔG° and the determination of the spontaneity of the reaction will be done in the steps above.

Step by step solution

01

Calculate Entropy Change

First, calculate the change in standard molar entropy (ΔS°) for the reaction by subtracting the sum of the standard molar entropies of the reactants from the sum of the standard molar entropies of the products. The standard molar entropies are given in the problem. Use the standard molar entropies and the balanced equation coefficients to calculate ΔS° using the formula ΔS° = ∑(μΔS° of products) - ∑(νΔS° of reactants). μ and ν are the stoichiometric coefficients of the products and reactants respectively.
02

Convert Entropy Change

Since ΔS°, the change in entropy, is given in J K^-1, this needs to be converted to kJ K^-1 before use in the next part. To convert from J to kJ, simply divide the result by 1000.
03

Calculate Gibbs Free Energy Change

Now we can calculate ΔG° using the formula ΔG° = ΔH° - TΔS° where T is the temperature in Kelvin. Just plug in the values of ΔH°, T, and ΔS° from Steps 1 and 2.
04

Determine if the Reaction is Spontaneous

Look at the sign of ΔG° to determine if the reaction is spontaneous in either direction. If ΔG° is negative, the reaction is spontaneous in the forward direction. If it is positive, the reaction is spontaneous in the reverse direction.

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Most popular questions from this chapter

Explain the important distinctions between each of the following pairs: (a) spontaneous and nonspontaneous processes; (b) the second and third laws of thermodynamics; (c) \(\Delta G\) and \(\Delta G^{\circ}\).

If a reaction can be carried out only by electrolysis, which of the following changes in a thermodynamic property must apply: (a) \(\Delta H>0 ;\) (b) \(\Delta S>0\) (c) \(\Delta G=\Delta H ;\) (d) \(\Delta G>0 ?\) Explain.

In your own words, define the following symbols: (a) \(\Delta S_{\text {univ }} ;\) (b) \(\Delta G_{f}^{0} ;\) (c) \(K\).

Consider the vaporization of water: \(\mathrm{H}_{2} \mathrm{O}(1) \longrightarrow\) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(100^{\circ} \mathrm{C},\) with \(\mathrm{H}_{2} \mathrm{O}(1)\) in its standard state, but with the partial pressure of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(2.0 \mathrm{atm}\) Which of the following statements about this vaporization at \(100^{\circ} \mathrm{C}\) are true? (a) \(\Delta G^{\circ}=0,\) (b) \(\Delta G=0\) (c) \(\Delta G^{\circ}>0,\) (d) \(\Delta G>0 ?\) Explain.

In biochemical reactions the phosphorylation of amino acids is an important step. Consider the following two reactions and determine whether the phosphorylation of arginine with ATP is spontaneous. $$\begin{array}{c} \mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ADP}+\mathrm{P} \quad \Delta G^{\circ \prime}=-31.5 \mathrm{kJ} \mathrm{mol}^{-1} \\ \text {arginine }+\mathrm{P} \longrightarrow \text { phosphorarginine }+\mathrm{H}_{2} \mathrm{O} \\ \Delta G^{\circ \prime}=33.2 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$
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