Chemical and Ionic Equilibrium 2 Question 65
65. The $\mathrm{pH}$ of blood stream is maintained by a proper balance of $\mathrm{H}{2} \mathrm{CO}{3}$ and $\mathrm{NaHCO}{3}$ concentrations. What volume of $5 \mathrm{M}$ $\mathrm{NaHCO}{3}$ solution should be mixed with a $10 \mathrm{~mL}$ sample of blood which is $2 \mathrm{M}$ in $\mathrm{H}{2} \mathrm{CO}{3}$, in order to maintain a $\mathrm{pH}$ of 7.4? $\left(K_{a}\right.$ for $\mathrm{H}{2} \mathrm{CO}{3}$ in blood is $7.8 \times 10^{-7}$ )
(1993, 2M)
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Solution:
- Mixing $\mathrm{H}{2} \mathrm{CO}{3}$ with $\mathrm{NaHCO}_{3}$ results in buffer solution.
$\mathrm{pH}=\mathrm{p} K_{a}+\log \frac{\left[\mathrm{NaHCO}{3}\right]}{\left[\mathrm{H}{2} \mathrm{CO}{3}\right]}=\mathrm{p} K{a}+\log \frac{n\left(\mathrm{NaHCO}{3}\right)}{n\left(\mathrm{H}{2} \mathrm{CO}_{3}\right)}$
$$ \Rightarrow \quad 7.4=-\log \left(7.8 \times 10^{-7}\right)+\log \frac{x}{20} $$
$\Rightarrow \quad x=400 \mathrm{mmol}$
$$ \mathrm{NaHCO}_{3}=5 \times V \Rightarrow V=80 \mathrm{~mL} $$
