Question

A sulphuric acid solution has pH = 3. Its normality is

Answer 1

Hint: Normality (N) is equal to molarity (M) multiplied by the n factor. So first we have to find the molarity with the help of pH and we should also know the n factor for sulphuric acid.
Formula used:
\[N = M \times n - factor\]
Here, \[N\] = Normality
\[M\] = Molarity
\[n - factor\] = number of replaceable hydrogen ion

Complete step by step answer:
The pH of a reaction is given as the negative logarithm (base 10) of its hydrogen ion concentration.
We can represent mathematically as:
\[pH = - {\log _{10}}\left[ {{H^ + }} \right]\]
We have given pH=3 in the question:
\[3 = - {\log _{10}}\left[ {{H^ + }} \right]\]
Now by taking the negative sign on the left side of the equation we get:
\[ - 3 = {\log _{10}}\left[ {{H^ + }} \right]\]
Now by taking the log on the left side we get antilog:
\[AL\left( { - 3} \right) = \left[ {{H^ + }} \right]\]
So we get the concentration of hydrogen ion as:
\[\left[ {{H^ + }} \right] = {10^{ - 3}}\] (equation 1)
Now let us see the dissociation of sulphuric acid:
\[{H_2}S{O_4} \to 2{H^ + } + S{O_4}^{ - 2}\]
Now let the initial concentration of sulphuric acid be C i.e. \[\left[ {{H_2}S{O_4}} \right] = C\]
So at equilibrium, the concentration of hydrogen ion becomes 2C i.e. \[\left[ {{H^ + }} \right] = 2C\]
Now comparing the concentration of hydrogen ion with equation 1:
\[2C = {10^{ - 3}}\]
So the value of C will come:
\[C = \dfrac{{{{10}^{ - 3}}}}{2}\]
But we know that the initial concentration of sulphuric acid is denoted by C. So we can write:
\[\left[ {{H_2}S{O_4}} \right] = C = \dfrac{{{{10}^{ - 3}}}}{2}\]
Now, we know that in sulphuric acid we have two replaceable hydrogen atoms. So, we can write:
\[n - factor = 2\]
So normality can be given as:
\[N = M \times n - factor\]
By substituting the value we get:
\[N = \dfrac{{{{10}^{ - 3}}}}{2} \times 2\]
By canceling the 2 we get:
\[N = {10^{ - 3}}Normal\]

Therefore we can conclude that the answer to this question is \[{10^{ - 3}}N\].

Note:
To find the n-factor for sulphuric acid, focus on finding the concentration from the given pH as normality depends on both concentration and n-factor of the substance.