Question

The number of ${{H}^{+}}$ ions in 1cc of a solution of $pH=13$ is:
a.) $6.023\times {{10}^{7}}$
b.) $1\times {{10}^{-13}}$
c.) $6.023\times {{10}^{13}}$
d.) $1\times {{10}^{16}}$

Answer 1

Hint: 1 mole of an element contains Avogadro number of atoms or ions. From the given $pH$ try to find out the number of moles of the ${{H}^{+}}$ present in the solution and multiply it with the Avogadro number to obtain the number of moles of the hydrogen ions present in the solution.

Complete Solution :
Given the value of $pH$ is equal to 13
It means that the number of moles of ${{H}^{+}}$ present in the solution is equal to Antilog(-$pH$) that is equal to ${{10}^{-13}}$
- This is present in one liter of the solution. We know that one liter is equal to 1000 ml or cc
Therefore one milliliter or cc is equal to 0.001 liters.
So the number of moles present in 1 milliliter of cc is = ${{10}^{-3}}\times {{10}^{-3}}={{10}^{-16}}$
 - We know that 1 mole of anything contains Avogadro number of ions.
Therefore the number of ions present in ${{10}^{-16}}$moles of ${{H}^{+}}$ is = $6.023\times {{10}^{23}}\times {{10}^{-16}} = 6.023\times {{10}^{7}}$
So, the correct answer is “Option A”.

Note: The relation between hydrogen ion concentration and $pH$ is $pH=-\log \left( \left[ {{\text{H}}^{+}} \right] \right)$ . Using this relation we can find either hydrogen ion concentration present in the solution or $pH$ of the solution if we have $pH$ of the solution or hydrogen ion concentration present in the solution respectively.