The $pH$ of the solution containing $50\text{mL}$ each of $0.10\text{M}$ sodium acetate and $0.01\text{M}$ acetic acid is [Given $p{K}_a$ of ${\text{CH}}_3\text{COOH}=4.57$ ]:

This is an acidic buffer solution. Using the Henderson-Hasselbalch equation:
$$pH=p{K}_a+\log \left(\frac{[\text{Salt}]}{[\text{Acid}]}\right)$$
Since volumes are equal, the ratio of molarities is equal to the ratio of concentrations:
$$pH=4.57+\log \left(\frac{0.10}{0.01}\right)$$
$$pH=4.57+\log (10)$$
$$pH=4.57+1=5.57$$