Methane can be synthesized from graphite and hydrogen through a series of coupled…

CHEMISTRY · Multi-part · A Level · Chemistry · Chemical equilibria (Le Chatelier’s principle and Kc) · Chemical equilibria (Le Chatelier’s principle and Kc)

Problem

Methane can be synthesized from graphite and hydrogen through a series of coupled equilibria. At a certain high temperature the following elementary reactions have been studied (all species gaseous except solid graphite): Step 1: C(s, graphite)+O2(g)⇌CO2(g)K1=8.3×1080C(\text{s, graphite}) + O_2(\text{g}) \rightleftharpoons CO_2(\text{g}) \quad K_1 = 8.3 \times 10^{80} Step 2: CO2(g)+H2(g)⇌CO(g)+H2O(g)K2=2.1×10−1CO_2(\text{g}) + H_2(\text{g}) \rightleftharpoons CO(\text{g}) + H_2O(\text{g}) \quad K_2 = 2.1 \times 10^{-1} Step 3: CO(g)+3 H2(g)⇌CH4(g)+H2O(g)K3=1.4×102CO(\text{g}) + 3\,H_2(\text{g}) \rightleftharpoons CH_4(\text{g}) + H_2O(\text{g}) \quad K_3 = 1.4 \times 10^{2} Step 4: H2O(g)⇌H2(g)+12 O2(g)K4=1.3×10−5H_2O(\text{g}) \rightleftharpoons H_2(\text{g}) + \frac{1}{2}\,O_2(\text{g}) \quad K_4 = 1.3 \times 10^{-5} The overall reaction of technological interest is C(s, graphite)+2 H2(g)⇌CH4(g)C(\text{s, graphite}) + 2\,H_2(\text{g}) \rightleftharpoons CH_4(\text{g}) Complete the tasks below. (a) Construct a sequence of manipulations (reversals, coefficient changes, additions) of Steps 1–4 that yields the overall reaction. Present the adjusted form of each step prior to adding them. (b) Using the sequence in part (a), calculate the equilibrium constant, KoverallK_{\text{overall}}, for the formation of methane. Express the final answer in scientific notation. (c) Discuss whether the value of KoverallK_{\text{overall}} you obtained would favor methane production at this temperature, and briefly relate your conclusion to the relative stabilities of the species involved.

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