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Chapter 19: Problem 33

For one of the following reactions, \(K_{c} K_{p}=K .\) Identify that reaction. For the other two reactions, what is the relationship between \(K_{c}, \bar{K}_{\mathrm{p}},\) and \(K ?\) Explain. (a) \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\) (b) \(\mathrm{HI}(\mathrm{g}) \rightleftharpoons \frac{1}{2} \mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{I}_{2}(\mathrm{g})\) (c) \(\mathrm{NH}_{4} \mathrm{HCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1)\)

Short Answer

Expert verified
For reaction (b), \(K_{c}=K_{p}=K\). For reactions (a) and (c), the relation is expressed by the equation: \(K_{p} = K_{c} \times (RT)^{Δn}\).

Step by step solution

01

Identify Δn for Reactions

Determine the change in the number of moles of gas (Δn) in each reaction. For (a), Δn = (2 moles of SO3) - (2 moles of SO2 + 1 mole of O2) = -1. For (b), Δn = (0.5 mole of H2 + 0.5 mole of I2) - 1 mole of HI = 0. For (c), Δn = (1 mole of NH3 + 1 mole of CO2) - 0 moles of NH4HCO3 = 2.
02

Evaluate Relationship Between \(K_c\), \(K_p\), and \(K\) For Each Reaction

Next, the relationship between \(K_c\), \(K_p\), and \(K\) must be evaluated for each reaction. For reaction (a) with Δn = -1, the values of \(K_c\) and \(K_p\) will differ and are related by the ideal gas law, as the reaction involves a change in the number of gas molecules. For reaction (b) with Δn = 0, \(K_c = K_p = K\), as the reaction does not involve a change in the number of gas molecules. For reaction (c) with Δn = 2, the values of \(K_c\) and \(K_p\) will differ and are related by the ideal gas law.
03

Determine The Reaction For Which \(K_{c}=K_{p}=K\)

The only reaction for which \(K_{c}=K_{p}=K\) is the one with Δn=0, which is reaction (b). For reactions (a) and (c), \(K_{c}\) and \(K_{p}\) do not equate because they involve a change in the number of moles of gas. For these reactions, the relationship between \(K_{c}\), \(K_{p}\), and \(K\) is expressed by the equation: \(K_{p} = K_{c} \times (RT)^{Δn}\).

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Most popular questions from this chapter

At room temperature and normal atmospheric pressure, is the entropy of the universe positive, negative, or zero for the transition of carbon dioxide solid to liquid?

The reaction, \(2 \mathrm{Cl}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \Delta H=\) \(-161 \mathrm{kJ},\) is expected to be (a) spontaneous at all temperatures; (b) spontaneous at low temperatures, but nonspontaneous at high temperatures; (c) nonspontaneous at all temperatures; (d) spontaneous at high temperatures only.

Explain why (a) some exothermic reactions do not occur spontaneously, and (b) some reactions in which the entropy of the system increases do not occur spontaneously.

Which of the following substances would obey Trouton's rule most closely: HF, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\) (toluene), or \(\mathrm{CH}_{3} \mathrm{OH}\) (methanol)? Explain your reasoning.

Calculate the equilibrium constant and Gibbs energy for the reaction \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})\) at \(483 \mathrm{K}\) by using the data tables from Appendix D. Are the values determined here different from or the same as those in exercise \(35 ?\) Explain.
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