Answer: The equilibrium constant for the overall reaction is [tex]K_1\times K_2[/tex]
Explanation:
Equilibrium constant is defined as the ratio of concentration of products to the concentration of reactants each raised to the power their stoichiometric ratios.
a) [tex]A\rightarrow B+C[/tex]
[tex]K_1=\frac{[B]\times [C]}{[A]}[/tex]
b) [tex]B+C\rightarrow D[/tex]
[tex]K_2=\frac{[D]}{[B]\times [C]}[/tex]
For overall reaction on adding a and b we get c
c) [tex]A\rightarrow D[/tex]
[tex]K_3=\frac{[D]}{[A]}[/tex]
[tex]K_3=K_1\times K_2=\frac{[B]\times [C]}{[A]}\times \frac{[D]}{[B]\times [C]}[/tex]
[tex]K_3=K_1\times K_2=\frac{[D]}{[A]}[/tex]
The equilibrium constant for the overall reaction is [tex]K_1\times K_2[/tex]