Given the reaction:
[tex]\[ \text{H}_{2}(g) + \text{I}_{2}(g) \leftrightarrow 2 \text{HI}(g) \][/tex]
The equilibrium constant expression [tex]\( K_p \)[/tex] is related to the partial pressures of the gases involved. For the general reaction:
[tex]\[ aA + bB \leftrightarrow cC + dD \][/tex]
The equilibrium constant [tex]\( K_p \)[/tex] is expressed as:
[tex]\[ K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b} \][/tex]
For the given reaction, the equilibrium constant expression [tex]\( K_p \)[/tex] will be:
[tex]\[ K_p = \frac{(P_{\text{HI}})^2}{(P_{\text{H}_2})(P_{\text{I}_2})} \][/tex]
Interpreting the given options:
- Option A: [tex]\( K_p = \frac{1}{P_{\text{H}_2} P_{\text{I}_2}} \)[/tex] (Incorrect)
- Option B: [tex]\( K_p = \frac{(P_{\text{HI}})^2}{(P_{\text{H}_2})(P_{\text{I}_2})} \)[/tex] (Correct)
- Option C: [tex]\( K_p = \frac{P_{\text{H}_2} P_{\text{I}_2}}{(P_{\text{HI}})^2} \)[/tex] (Incorrect)
- Option D: [tex]\( K_p = P_{\text{H}_2} P_{\text{I}_2} \)[/tex] (Incorrect)
Thus, the correct expression for [tex]\( K_p \)[/tex] is:
[tex]\[ \boxed{B. \; K_p = \frac{(P_{\text{HI}})^2}{(P_{\text{H}_2})(P_{\text{I}_2})}} \][/tex]
For a reaction to shift towards the product direction, the reaction quotient [tex]\( Q \)[/tex] needs to be compared to the equilibrium constant [tex]\( K \)[/tex]. The reaction quotient [tex]\( Q \)[/tex] is given by:
[tex]\[ Q_c = \frac{[\text{products}]}{[\text{reactants}]} \][/tex]
For the reaction to proceed towards the products' direction:
[tex]\[ Q_c < K_c \][/tex]
Interpreting the given options:
- Option a: [tex]\( Q_c = K_c = 0 \)[/tex] (Not logical, both cannot be zero)
- Option B: [tex]\( Q_c < K_c \)[/tex] (Correct)
- Option C: [tex]\( Q_c > K_c \)[/tex] (Incorrect, would shift towards reactants)
- Option D: [tex]\( Q_c = K_c \)[/tex] (Indicates equilibrium, no shift)
Therefore, for a reaction to shift towards the product direction, the correct condition is:
[tex]\[ \boxed{B. \; Q_c < K_c} \][/tex]
