Question

Number of ${{H}^{+}}$ ions present in 250ml lemon juice of pH=3 is:
(A) $1.506\times {{10}^{22}}$
(B) $1.506\times {{10}^{23}}$
(C) $1.506\times {{10}^{20}}$
(D) $3.012\times {{10}^{21}}$
(E) $2.008\times {{10}^{23}}$

Answer 1

Hint: Use the formula, $pH=-{{\log }_{10}}\left[ {{H}^{+}} \right]$ and find out the concentration of protons present in acidic solution. Then the obtained value will be equal to one litre, so cross-multiply and calculate the number of protons present in 250ml.

Complete answer:
- We have been given pH of the lemon juice solution is 3.
- We know that, $pH=-{{\log }_{10}}\left[ {{H}^{+}} \right]$
- So, to calculate the concentration of ${{H}^{+}}$ ions we will have to take antilog of the inverse of pH. Then we obtain, $\left[ {{H}^{+}} \right]={{10}^{-3}}$
- So, 1000ml of solution contains 0.001M ${{H}^{+}}$ ion concentration.
- Now, we need to calculate the concentration of ${{H}^{+}}$ ions in a 250ml solution.
\[\begin{align}
  & \left[ {{H}^{+}} \right]=1000ml={{10}^{-3}} \\
 & =250ml=x
\end{align}\]
- Therefore, $x=\dfrac{250}{1000}\times {{10}^{-3}}=2.5\times {{10}^{-4}}M$
- Therefore, the concentration of ${{H}^{+}}$ ions in a 250ml solution is $2.5\times {{10}^{-4}}M$.
- Now, we have got the concentration. We need to find the number of molecules present in $2.5\times {{10}^{-4}}M$ solution of 250ml.
- To calculate, number of molecules we just need to multiply the concentration term with Avogadro’s number.
- Therefore, number of molecules is $2.5\times {{10}^{-4}}\times 6.023\times {{10}^{23}}=1.506\times {{10}^{20}}$
- Therefore, number of ${{H}^{+}}$ ions present in 250ml lemon juice of pH=3 is $1.506\times {{10}^{20}}$

Hence, the correct option is option (A).

Note:
Systematically follow the steps in this type of problem. Remember to calculate the number of molecules of any solution we need to multiply the number of moles by Avogadro’s number.