Question

The pH of blood stream is maintained by a proper balance of $H_{2}C{O}_3$ and $NaHC{O}_3$ concentrations. What volume of $5MNaHC{O}_3$ solution should be mixed with a $10mL$ sample of blood which is $2M$ in $H_{2}C{O}_3$, in order to maintain a pH of $7.4$? ( $K_a$ for $H_{2}C{O}_3$ in blood is $738\times 10^{-7})$

Answer 1

Mixing $H_{2}C{O}_3$ with $NaHC{O}_3$ results in buffer solution.
$pH=p{K}_a+log\frac{[NaHC{O}_3]}{[H_{2}C{O}_3]}=p{K}_a+log\frac{n(NaHC{O}_3)}{n(H_{2}C{O}_3)}$
$\Rightarrow 7.4=-log(7.8\times 10^{-7})+log\frac{x}{20}$
$\Rightarrow x=400mmol$
$NaHC{O}_3=5\times V\Rightarrow V=80mL$