To identify the equilibrium constant expression for the given reaction:
[tex]\[ 2 N_2O_5(g) \rightleftharpoons 4 NO_2(g) + O_2(g) \][/tex]
First, we need to recall the definition of the equilibrium constant [tex]\( K_{eq} \)[/tex]. For a general chemical reaction:
[tex]\[ aA + bB \rightleftharpoons cC + dD \][/tex]
The equilibrium constant expression is given by:
[tex]\[ K_{eq} = \frac{\left[ C \right]^c \left[ D \right]^d}{\left[ A \right]^a \left[ B \right]^b} \][/tex]
For the given reaction:
[tex]\[ 2 N_2O_5(g) \rightleftharpoons 4 NO_2(g) + O_2(g) \][/tex]
- [tex]\( [N_2O_5] \)[/tex] is the concentration of [tex]\( N_2O_5 \)[/tex]
- [tex]\( [NO_2] \)[/tex] is the concentration of [tex]\( NO_2 \)[/tex]
- [tex]\( [O_2] \)[/tex] is the concentration of [tex]\( O_2 \)[/tex]
Applying the general form of the equilibrium constant expression, we have:
[tex]\[
K_{eq} = \frac{\left[ NO_2 \right]^4 \left[ O_2 \right]}{\left[ N_2O_5 \right]^2}
\][/tex]
Therefore, the correct expression for the equilibrium constant for the given reaction is:
[tex]\[ K_{\text {eq }} = \frac{\left[ NO_2 \right]^4 \left[ O_2 \right]}{\left[ N_2O_5 \right]^2} \][/tex]
