Chemistry

Problem

At 298 K the synthesis of ammonia proceeds according to the following three balanced equations, each written with its own label. A.

\dfrac12\,\mathrm{N_2(g)}+\dfrac32\,\mathrm{H_2(g)}\;\rightleftharpoons\;\mathrm{NH_3(g)}

2\,\mathrm{NH_3(g)}\;\rightleftharpoons\;\mathrm{N_2(g)}+3\,\mathrm{H_2(g)}

\mathrm{N_2(g)}+3\,\mathrm{H_2(g)}\;\rightleftharpoons\;2\,\mathrm{NH_3(g)}

(the industrial Haber process,

K_P=6.0\times10^{5}

) Without performing any arithmetic on the value

6.0\times10^{5}

, answer the questions below. (a) Rank the equilibrium constants

K_{\text{A}}

K_{\text{B}}

, and

K_{\text{C}}

from largest to smallest. Clearly indicate any that are equal. (b) For reaction A, predict the sign of

\Delta G^{\circ}

at 298 K and explain your reasoning in terms of the magnitude of

K_{\text{A}}

relative to 1. (c) If reaction B were carried out in a rigid, closed container starting with pure ammonia at 298 K, would the partial pressure of hydrogen increase, decrease, or remain unchanged as equilibrium is approached? Justify your answer using your ranking from part (a).

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