Question

The ratio of pH of $\text{0}\text{.05 M}$ and $\text{0}\text{.005 M}$ ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$ solution will be –
A.2:1
B.1:2
C.1:$1.5$
D.$1.5$:1

Answer 1

The pH of a solution is a measure of the hydrogen ion concentration of a solution and is defined as the negative logarithm to the base 10 of the hydrogen ion concentration of a solution.

Formula Used:
$\text{pH = - log}{{\text{ }}_{\text{10}}}\left[ {{\text{H}}^{\text{+}}} \right]$

Complete step by step answer:
Sulphuric acid is a strong diprotic acid and the equation for ionization is –
${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\rightleftharpoons \text{2}{{\text{H}}^{\text{+}}}\text{+ S}{{\text{O}}_{\text{4}}}^{\text{2-}}$,
Each molecule of sulphuric acid, releases two protons and one sulphate anion. The concentration of hydrogen ions in the solution is, $\text{0}\text{.05}\times \text{2 = 0}\text{.1 moles/litre}$
Therefore for $\text{0}\text{.005 M}$ ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$ solution, the hydrogen ion concentration is equal to $\text{0}\text{.01 moles/litre}$. As per the above formula, the pH of $\text{0}\text{.05 M}$ ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$ solution will be:
$\text{pH = - log}{{\text{ }}_{\text{10}}}\left[ {{10}^{-1}} \right]=1$, and that for the $\text{0}\text{.005 M}$ sulphuric acid solution, it is equal to,
$\text{pH = - log}{{\text{ }}_{\text{10}}}\left[ {{10}^{-2}} \right]=2$.
Therefore the ratio of the pH of $\text{0}\text{.05 M}$ and $\text{0}\text{.005 M}$ ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$ solution will be 1:2.
Hence, option B is correct.

Note:
The pH of the solution is a measure of the hydrogen ion concentration of the solution and so its value is used to determine whether the acidity or the basicity of the solution. If the pH of the solution ranges from $0-6.9$, then it is said to be acidic, with the most acidic substance having pH value) while the least acidic substance having pH$6.9$. pH 7 is considered to be neutral while pH $7.1$ to pH 14 is considered to be the basic range, with pH 14 being the most basic and pH $7.1$ having least basicity.