Question

What is the $pH$ of the resulting solution when equal volumes of $0.1M$ $NaOH$ and $0.01M$ $HCl$ are mixed?
$\left( 1 \right)7.0$
$\left( 2 \right)1.04$
$\left( 3 \right)12.65$
$\left( 4 \right)2.0$

Answer 1

If the acids and bases are mixed in equal volumes, look for the one with higher concentration. Here the concentration of the base is higher which proves that the resultant solution due to mixture will be alkaline. Therefore the $pOH$ can be determined in the solution from which the $pH$ can be calculated for that specific mixture.

Complete step by step answer:
Equal volumes of $HCl$ and $NaOH$ are used for the mixture of acid and base. Let the volume of $HCl$ be $1$ volume and the same volume of $NaOH$ is added with the acid which can be considered as $1$ volume. The resultant mixture of the two has $2$ volumes of the mixture of acid and base.
But the concentration differs because of changes in molarity. The $NaOH$ solution taken is $0.1M$ and the $HCl$ is $0.01M$. If the two solutions are added into a mixture, the equation used for the process will be: ${N_1}{V_1} - {N_2}{V_2} = NV$
The molarity and volume of $NaOH$ is defined by ${N_1}$ and ${V_1}$ respectively. This is because the concentration of $NaOH$ is higher. The molarity and volume of $HCl$ is defined by the and ${V_2}$ respectively. The $N$ and $V$ are final normality and volumes of the mixture. Putting all the given values in the equation we get,
$\Rightarrow 2N = 0.1 - 0.01$ $0.1 \times 1 - 0.01 \times 1 = N \times 2$
From here we get,
$\Rightarrow N = \dfrac{{0.09}}{2}$
$\Rightarrow N = 0.045$
Therefore, the normality of the mixture of the acid and base is $0.045N$. Since the base is of a higher concentration here, the given normality is for the $\left[ {O{H^ - }} \right]$ level in the mixture.
$\left[ {O{H^ - }} \right] = 0.045N$
Therefore, for finding the $pOH$ in the solution, the negative logarithm of the $\left[ {O{H^ - }} \right]$ ion level in the mixture. Hence in the given mixture:
$pOH = - \log (0.045)$
$\Rightarrow pOH = 1.35$
It is known that the total level of $pH$ and $pOH$ together sums up to 14, which is the highest level of the $pH$ scale. According to the given condition:
$pH + pOH = 14$
Here $pOH = 1.35$, hence the value of $pH = 14 - 1.35 = 12.65$
The value of $pH$ for the given mixture is $12.65$ when the acid and base is mixed. Therefore, the answer for the given condition with the given mixture is $\left( 3 \right)12.65$.

Note: The $pH$ of a solution is defined as the negative logarithm of the concentration of ${H^ + }$ ions in the solution. The same is applicable for $pOH$ with respect to the concentration of $O{H^ - }$. This is why while determining the nature of the solution any of the values can be determined.