The equilibrium constants for three reactions | vedclass

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(B) The given reactions are:$(I) \, CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2_{(g)}} + H_{2_{(g)}} ; \, k_1$$(II) \, CH_{4_{(g)}} + H_2O_{(g)} \r

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$k_3 = k_1 k_2$

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(B) The given reactions are:$(I) \, CO_{(g)} + H_2O_{(g)} ightleftharpoons CO_{2_{(g)}} + H_{2_{(g)}} ; \, k_1$$(II) \, CH_{4_{(g)}} + H_2O_{(g)} ightleftharpoons CO_{(g)} + 3H_{2_{(g)}} ; \, k_2$$(III) \, CH_{4_{(g)}} + 2H_2O_{(g)} ightleftharpoons CO_{2_{(g)}} + 4H_{2_{(g)}} ; \, k_3$Observe that adding reaction $(I)$ and reaction $(II)$ gives reaction $(III)$:$(CO_{(g)} + H_2O_{(g)}) + (CH_{4_{(g)}} + H_2O_{(g)}) ightleftharpoons (CO_{2_{(g)}} + H_{2_{(g)}}) + (CO_{(g)} + 3H_{2_{(g)}})$Canceling common terms $(CO_{(g)})$ on both sides:$CH_{4_{(g)}} + 2H_2O_{(g)} ightleftharpoons CO_{2_{(g)}} + 4H_{2_{(g)}}$Since reaction $(III) = (I) + (II)$,the equilibrium constant $k_3$ is the product of $k_1$ and $k_2$:$k_3 = k_1 	imes k_2$

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