Question

A solution is made by adding 5.6 grams of (molar mass 56 grams) to enough water to make 1.0 litre of solution. What is the approximate pH of the resulting solution?
A.1
B.3
C.7
D.9
E.13

Answer 1

We need to know the steps to calculate $pH$ and some properties of the given compound $KOH$ . $pH$ is the negative logarithm of concentration of hydrogen ions. Greater the concentration of hydrogen ion in a solution, the lower will be the $pH$ and hence the solution can be considered as acidic. If more $O{H^ - }$ are present in a solution, it is considered to be basic and the term $pH$ is replaced by $pOH$ which is the negative logarithm of hydroxyl ions. One such example is the strong base $KOH$ which completely dissociates when dissolved in water to produce a bulk amount of $O{H^ - }$ .

Complete step by step answer:
As given in the question, 5.6 grams of $KOH$ is added to water. In order to calculate $pH$ of the resulting solution, we first need to calculate the concentration of $KOH$ with the given data.
5.6 grams of KOH having molar mass of $56$grams when dissolved in water to make a solution of $1.0$ litre will have a concentration of $\dfrac{{5.6}}{{56 \times 1.0}} = 0.1M$
Since, $KOH$ is a strong base which will completely dissociate into its ions, the concentration of $KOH$can be considered as concentration of $O{H^ - }$ i.e. $\left[ {O{H^ - }} \right] = 0.1M$
Therefore, from the definition of $pOH$ , =$- log\left[ {{{10}^{ - 1}}} \right]$
$= 1$
Since $KOH$ having $pOH = 1$ is dissolved in water, the $pH$ of the solution must be equal to $14$ since $pH + pOH = 14$ (since for water, $pH = 7$ and $pOH$ is $7$ ,the total of which comes to $14$ making water neutral in the $pH$ scale).
Therefore $pH = 14 - pOH$
$= 13$
Hence, the correct option is option (E).

Note:
We have to note that the concentration of a given compound can be considered to be the concentration of their dissociated ions in case of strong acids and bases only. In case of weak acids or weak bases where they do not dissociate completely, the concentration of the acid or the base will be more than its dissociated ions. Also, A basic solution has a $pOH$ less than $7$ , while an acidic solution has a $pOH$ of greater than $7$ .