Question

Calculate the pH value in ${10}^{-8}M$ $NaOH$
(A) 7.4
(B) 8
(C) 6
(D) 6.96

Answer 1

Hint: $NaOH$ is a basic solution which consists of ${Na}^{+}$ and ${OH}^{-}$ ions and dissociate in water to give out ${OH}^{-}$ ions, which shows the basic nature of the solution. So, don’t go directly for the pH of solution.

Complete step by step solution:
Sodium hydroxide or $NaOH$ is commonly known as caustic soda, lye or sodium hydrate. It is commonly used in laboratories for cleaning equipment, as buffer solutions, some titrations and many more. In households, it is used as cleaning agents, is found in soaps and can even be found in food.
It is a white in colour and consists of ${Na}^{+}$ and ${OH}^{-}$ ions, which means 1 mole of $NaOH$ produces 1 mole of sodium ions and 1 mole of hydroxide ions.
pH is a measure of acidity or basicity of an aqueous solution. It is basically a measure of the amount of free hydrogen or hydroxyl ions when a solution is dissolved in water.
We know that both, the hydrogen concentration and the hydroxide ion concentration in neutral water is ${10}^{-7}$.
Now, the hydroxide ion concentration in ${10}^{-8}$ M NaOH solution will be the sum of the concentration of hydroxide ion in both NaOH and water, i.e., ${10}^{-8}$ + ${10}^{-7}$
Therefore, the concentration of hydroxide ion in NaOH = ${10}^{-7} \times 1.1$
To calculate the pH of NaOH, we need to first calculate the pOH of NaOH since it is a basic solution.
The pOH of a solution can be calculated as follows:
$pOH = -log[{OH}^{-}]$ --(1)
We are given with:
$[{OH}^{-}] = {10}^{-7} \times 1.1$
Putting these values in equation (1) we get,
$pOH = -log({10}^{-7} \times 1.1) $
$\implies pOH = 7log10 \quad - \quad log(1.1)$
$\implies pOH = 7 \quad - \quad 0.04=6.96$
To calculate the pH of the solution, we use the pH equation:
pH + pOH = 14
$\implies pH = 14 - pOH$
$\implies pH = 14 - 6.96$ (Substituting the value of pOH)
$\implies pH = 7.04$

Hence, the pH of the solution is 7.04. Hence, the correct option is option (A).

Note: Calculation of the pH value depends on the nature of the solution. That is, if the solution is acidic in nature, we directly calculate the pH value but if the solution is basic in nature we first calculate the pOH value of the solution and then calculate the pH in reference to the calculated value of pOH.