Question

The $pH$ of a buffer solution prepared by dissolving $30g$ of ${Na}_2{CO}_3$ in $500mL$ of an aqueous solution containing $150mL$ of $1M$ $HCl$. $K_a$ for $H{CO}_3^{-}=5.63\times {10}^{-11}$ is $X$. Nearest integer to X is:

Answer 1

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

Number of moles of $N{a}_{2}C{O}_3=\frac{W}{M}=\frac{30}{106}=0.28moles$

Number of moles of $HCl=V\left(L\right)\times M=0.15moles$

Number of moles of $N{a}_{2}C{O}_3=0.28-0.15=0.13moles$

Concentration of $N{a}_{2}C{O}_3=\frac{0.13}{0.500+0.15}$

Concentration of salt=$\frac{0.15}{0.500+0.15}$

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

$p{k}_a=-log\left[k_a\right]=-log[5.63\times {10}^{-11}]=10.24$

$pH=10.24+log\frac{\left[0.15\right]}{\left[0.13\right]}=10.32+0.062$

$pH=10.30$