Question

The pH of a buffer solution prepared by dissolving 80g of ${Na}_2{CO}_3$ in 1000mL of an aqueous solution containing 100mL of 1M $HCl$. $K_a$ for $H{CO}_3^{-}=5.63\times {10}^{-11}$ is

• A. 10.5
• B. 10.3
• C. 9.43
• D. 11.5

Answer 1

The correct option is C 9.43

$N{a}_{2}C{O}_3+2HCl\to 2NaCl+H_{2}C{O}_3$

Number of moles of $N{a}_{2}C{O}_3=\frac{W}{M}=\frac{80}{106}=0.75moles$

Number of moles of $HCl=V\left(L\right)\times M=0.1moles$

Number of moles of $N{a}_{2}C{O}_3=0.75-0.1=0.65moles$

Concentration of $N{a}_{2}C{O}_3=\frac{0.65}{1.0+0.1}$

Concentration of salt=$\frac{0.1}{1.0+0.1}$

$pH$ of buffer=$p{k}_a+log\frac{\left[salt\right]}{\left[base\right]}$

$p{k}_a=-log\left[k_a\right]=-log[5.63\times {10}^{-11}]=10.25$

$pH=10.25+log\frac{\left[0.10\right]}{\left[0.65\right]}=10.25-0.815$

$pH=9.43$