The stepwise stability constants of a complex are given below. What is its overall reaction stability…
The stepwise stability constants of a complex are given below. What is its overall reaction stability constant \(\left(\beta_4\right)\) ?
\(\begin{aligned}
& M+L \rightleftharpoons M L ; K_1=1.0 \times 10^4 \\
& M L+L \rightleftharpoons M L_2 ; K_2=1.0 \times 10^3 \\
& M L_2+L \rightleftharpoons M L_3 ; K_3=1.0 \times 10^3 \\
& M L_3+L \rightleftharpoons M L_4 ; K_4=1.0 \times 10^2
\end{aligned}\)
(Overall reaction : \(M+4 L \rightleftharpoons M L_4\) )
\(1.0 \times 10^{12}\)
\(12.1 \times 10^3\)
\(1.0 \times 10^6\)
\(1.0 \times 10^8\)
Solution
Given,
\(\begin{gathered}
M+L \rightleftharpoons M L ; K_1=1.0 \times 10^4 \\
M L+L \rightleftharpoons M L_2 ; K_2=1.0 \times 10^3 \\
M L_2+L \rightleftharpoons M L_3 ; K_3=1.0 \times 10^3 \\
M L_3+L \rightleftharpoons M L_4 ; K_4=1.0 \times 10^2
\end{gathered}\)
Overall reaction,
\(M+4 L \rightleftharpoons M L_4\)
The overall stability constant,
\(\begin{aligned}
\beta_4 & =K_1 \times K_2 \times K_3 \times K_4 \\
\beta_4 & =1.0 \times 10^4 \times 1.0 \times 10^3 \times 1 \times 10^3 \times 1 \times 10^2 \\
& =1 \times 10^{12}
\end{aligned}\)