Question

The pH of blood stream is maintained by a proper balance of $H_2{CO}_3$ and $NaH{CO}_3$ concentrations. What volume of $5M$ $NaH{CO}_3$ solution should be mixed with a $10mL$ sample of blood which is $2M$ in $H_2{CO}_3$ in blood is $7.8\times {10}^{-7}$?

Answer 1

Let $V$ mL of $5M$ $NaH{CO}_3$ solution be mixed
Total volume $=(V+10)mL$
Conc. of $H_2{CO}_3$ and $NaH{CO}_3$ in the solution becomes
$\left[NaH{CO}_3\right]=\frac{5\times V}{(V+10)}M$
and $\left[H_2{CO}_3\right]=\frac{2\times 10}{V+10}M$
Now applying Henderson's equation
$pH=-\log K_a+\log \frac{\left[NaH{CO}_3\right]}{\left[H_2{CO}_3\right]}$
$7.4=-\log 7.8\times {10}^{-7}+\log \frac{5\times V}{(V+10)}\times \frac{(V+10)}{2\times 10}$
or $\log \frac{V}{4}=7.4+\log 7.8\times {10}^{-7}$
$V=78.32mL$