To determine the equilibrium constant ([tex]\( K_{\text{eq}} \)[/tex]) for the given reaction, we need to use the standard formula for the equilibrium constant of a chemical reaction. The reaction provided is:
[tex]\[ H_2(g) + CO_2(g) \rightleftharpoons H_2O(g) + CO(g) \][/tex]
The general form for the equilibrium constant expression [tex]\( K_{\text{eq}} \)[/tex] of a reaction:
[tex]\[ aA + bB \rightleftharpoons cC + dD \][/tex]
is given by:
[tex]\[ K_{\text{eq}} = \frac{[C]^c[D]^d}{[A]^a[B]^b} \][/tex]
where [tex]\([A]\)[/tex], [tex]\([B]\)[/tex], [tex]\([C]\)[/tex], and [tex]\([D]\)[/tex] are the equilibrium concentrations of the reactants and products, and [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] are their respective coefficients in the balanced chemical equation.
For the reaction:
[tex]\[ H_2(g) + CO_2(g) \rightleftharpoons H_2O(g) + CO(g) \][/tex]
the equilibrium constant expression will be:
[tex]\[ K_{\text{eq}} = \frac{[H_2O] \cdot [CO]}{[H_2] \cdot [CO_2]} \][/tex]
Out of the given options, we need to select the one that matches this expression.
The options are:
A. [tex]\( K_{\text{eq}} = [H_2O][CO] \)[/tex]
B. [tex]\( K_{\text{eq}} = \frac{[H_2O][CO]}{[H_2][CO_2]} \)[/tex]
C. [tex]\( K_{\text{eq}} = \frac{[H_2O][CO]}{[H_2]^2[CO_2]^2} \)[/tex]
D. [tex]\( K_{\text{eq}} = \frac{[H_2][CO_2]}{[H_2O][CO]} \)[/tex]
Matching the correct form:
The correct expression for [tex]\(K_{\text{eq}}\)[/tex] based on the given reaction is:
B. [tex]\( K_{\text{eq}} = \frac{[H_2O][CO]}{[H_2][CO_2]} \)[/tex]
Thus, the equilibrium constant for the reaction [tex]\( H_2(g) + CO_2(g) \rightleftharpoons H_2O(g) + CO(g) \)[/tex] is best described by option B.
