Certainly! Let's solve the problem step-by-step to find the equilibrium constant for the given chemical reaction.
Given the reaction:
[tex]\[ \text{PCl}_5(g) \longleftrightarrow \text{PCl}_3(g) + \text{Cl}_2(g) \][/tex]
The equilibrium concentrations at 500 K are:
[tex]\[ \left[ \text{PCl}_5 \right] = 0.0095 \, M \][/tex]
[tex]\[ \left[ \text{PCl}_3 \right] = 0.020 \, M \][/tex]
[tex]\[ \left[ \text{Cl}_2 \right] = 0.020 \, M \][/tex]
The equilibrium constant [tex]\( K_{eq} \)[/tex] is given by the expression:
[tex]\[ K_{eq} = \frac{\left[ \text{PCl}_3 \right] \left[ \text{Cl}_2 \right]}{\left[ \text{PCl}_5 \right]} \][/tex]
Now we substitute the values into this expression:
[tex]\[ K_{eq} = \frac{(0.020) \times (0.020)}{0.0095} \][/tex]
Simplifying the expression:
[tex]\[ K_{eq} = \frac{0.020 \times 0.020}{0.0095} \][/tex]
[tex]\[ K_{eq} = \frac{0.0004}{0.0095} \][/tex]
[tex]\[ K_{eq} \approx 0.042 \][/tex]
Therefore, the equilibrium constant [tex]\( K_{eq} \)[/tex] for the given reaction at 500 K is approximately [tex]\( 0.042 \)[/tex].
The correct answer is:
[tex]\[ 0.042 \][/tex]
