Question

The pH of blood stream is maintained by a proper balance of $H_{2}C{O}_3$ and $NaHC{O}_3$ concentration. What volume of 5 M $NaHC{O}_3$ solution should be mixed with a 10 mL sample of blood which is 2 M in $H_{2}C{O}_3$ in order to maintain its pH of 7.4?

$[p{K}_a$ for $H_{2}C{O}_3=6.1]\left[10^{1.3}=19.9\right]$

• A. 40 mL
• B. 38 mL
• C. 50 mL
• D. 79 mL

Answer 1

Answer: (D)

$pH=p{K}_a+log\frac{\left[HC{O}_3^{-}\right]}{\left[H_{2}C{O}_3\right]}$

Moles of ${\text{H}}_2{\text{CO}}_3$ presenting blood sample

$=2\times 0.01=0.02$

Let V mL of $NaHC{O}_3$ is required

$=5\times V=5V$

So $pH=p{K}_a+log\left(\frac{5V}{0.02}\right)$

$7.4=6.1+log\left(\frac{5V}{0.02}\right)$

$V=79$ mL