Question

The $pH$ of $0.005M$ ${H_2}S{O_4}$ solution is:
A. 3.3
B. 5.0
C. 2.0
D. 4.0

Answer 1

Hint- In order to solve such types of problems, first we have to write its reaction in terms of $H + $ ions and find the total $H + $ ions further then we have to use the formula of $pH$ to get the required answer.

Complete step-by-step answer:
Let us first understand the term $pH$
$pH$ ( denoting 'potential of hydrogen' or 'power of hydrogen') is a scale used to specify the acidity or basicity of an aqueous solution. Lower $pH$ values refer to solutions that are more acidic in nature, while higher values refer to more stable or alkaline solutions. At room temperature $\left( {{{25}^0}C{\text{ or }}{{77}^0}F} \right)$ , pure water is neutral (neither acidic nor basic) and therefore has a $pH$ of 7.
The $pH$ scale is logarithmic and inversely indicates the concentration of hydrogen ions in the solution (a lower $pH$ indicates a higher concentration of hydrogen ions). This is because the formula used to calculate $pH$ approximates the negative of the base 10 logarithm of the molar concentration[a] of hydrogen ions in the solution. More precisely, $pH$ is the negative of the base 10 logarithm of the activity of the hydrogen ion.
As we know that ${H_2}S{O_4}$ is a strong, diprotic acid. The equation for its ionization is
\[{H_2}S{O_4}\left( {aq} \right) \to 2{H^ + } + SO_4^{2 - }\]
Since the equation tells us that each molecule of acid will produce 2 hydrogen ions, the concentration of the \[{H^ + }\] ion must be
\[
  2 \times 0.005M = 0.01M \\
   \Rightarrow \left[ {{H^ + }} \right] = 0.01M \\
 \]
 Using the definition of pH
$
  pH = - \log \left[ {{H^ + }} \right] \\
   \Rightarrow pH = - \log \left( {0.01} \right) \\
   \Rightarrow pH = - \log \left( {{{10}^{ - 2}}} \right) \\
   \Rightarrow pH = - 1 \times \left( { - 2} \right)\log \left( {10} \right){\text{ }}\left[ {\because \log \left( {{m^n}} \right) = n\log \left( m \right)} \right] \\
   \Rightarrow pH = 2{\text{ }}\left[ {\because \log \left( {10} \right) = 1} \right] \\
 $
Hence, the $pH$ of $0.005M$ ${H_2}S{O_4}$ solution is 2.0
So, the correct answer is option C.

Note- Sulfuric acid is mainly used in fertilizer production, e.g., lime superphosphate, and ammonium sulfate. It is widely used in chemical manufacturing, for example in the production of hydrochloric acid, nitric acid, sulfate salts, synthetic detergents, colorants and pigments, explosives and medicines.