The pH of blood stream is maintained by a proper balance of and concentrations. What volume of 5 M – — Ionic Equilibrium Chemistry Question
Question
The pH of blood stream is maintained by a proper balance of $\text{H}_2\text{CO}_3$ and $\text{NaHCO}_3$ concentrations. What volume of 5 M – $\text{NaHCO}_3$ solution should be mixed with a 10 ml sample of blood which is 2 M in $\text{H}_2\text{CO}_3$ in order to maintain a pH of 7.4? $K_a$ for $\text{H}_2\text{CO}_3$ in blood is $8.0 \times 10^{-7}$. ($\log 2 = 0.3$)
💡 Solution & Explanation
$\text{pH} = pK_a + \log\frac{[\text{Salt}]}{[\text{Acid}]}$. $pK_a = -\log(8.0 \times 10^{-7}) = 7 - 3\log 2 = 7 - 0.9 = 6.1$. Thus, $7.4 = 6.1 + \log\frac{[\text{Salt}]}{[\text{Acid}]} \implies \log\frac{[\text{Salt}]}{[\text{Acid}]} = 1.3$. Since $1.3 = \log 10 + \log 2 = \log 20$, the ratio is 20. The moles of acid initially = $10\text{ ml} \times 2\text{ M} = 20\text{ mmol}$. The required moles of salt = $20 \times 20 = 400\text{ mmol}$. The volume of 5 M salt solution needed is $400\text{ mmol} / 5\text{ M} = 80\text{ ml}$. Formatted to four digits, this is 0080.