The pH of the solution containing 50mL each of 0 . 10M sodium...

The given solution is an acidic buffer solution.

According to the Henderson equation for acidic buffer,

$pH = {pK}_{a} + \log_{10}\dfrac{\left[salt\right]}{\left[acid\right]}$

Given that,

${pK}_{a} = 4 . 57\left[salt\right] = \left[sodiumacetate\right] = 0 . 1M\left[Acid\right] = \left[Aceticacid\right] = 0 . 01M$

Hence, the

$pH = 4 . 57 + log\dfrac{0 . 1}{0 . 01} = 4 . 57 + 1 = 5 . 57$