Chapter 6, Problem 27RE

MATHEMATICAL The kinetic data in the following table were obtained for the reaction of carbon dioxide and water to produce bicarbonate and hydrogen ion catalyzed by carbonic anhydrase:

${\text{CO}}_2+{\text{H}}_{\text{2}}\text{O}\to {\text{HCO}}_3^{-}+{\text{H}}^{+}$

[H. De Voe and G. B. Kistiakowsky, J. Am. Chem. Soc. 83, 274 (1961)]. From these data, determine $K_{\text{M}}$ and $V_{\text{max}}$ for the reaction.

$\begin{array}{cc}\text{Carbon Dioxide concentration }\left({\text{mmolL}}^{-1}\right)& \text{1/Velocity }\left(M^{-1}\sec \right)\\ \begin{array}{l}1.25\\ 2.5\\ 5.0\\ 20.0\\ 0.250\end{array}& \begin{array}{l}36\times {10}^3\\ 20\times {10}^3\\ 12\times {10}^3\\ 6\times {10}^3\\ 0.256\end{array}\end{array}$