Question

200 ml of 1 M ${{H}_{2}}S{{O}_{4}}$, 300 ml of 3 M HCl and 100 ml of 2 M HCl are mixed and made up to 1 litre. The proton concentration in the resulting solution is:
A) 1.25 M
B) 1.5 M
C) 2.5 M
D) 0.75 M

Answer 1

Hint: The molarity of a mixed solution can be given by
${{M}_{mixture}}=\dfrac{{{M}_{1}}{{V}_{1}}+{{M}_{2}}{{V}_{2}}+{{M}_{3}}{{V}_{3}}}{{{V}_{1}}+{{V}_{2}}+{{V}_{3}}}$
The numerator here is just a total (sum) of all the moles of solute and the denominator is a total (sum) of all the volumes.

Complete step by step solution:

- Molarity is the number of moles of a solute per litre of a solution. Molarity is also known as the molar concentration of a solution.
- Concentration in molarity (mol/L or M) is often depicted with square brackets around the solute of interest. For example, the concentration of hydrogen ion can be written as [${{H}^{+}}$]
By applying the molarity mixture formula
We can see that the 1M ${{H}_{2}}S{{O}_{4}}$, number of ${{H}^{+}}$ions are two in number and the volume is 0.2L.
Therefore, the number moles of ${{H}^{+}}$in 1M of ${{H}_{2}}S{{O}_{4}}$ is, ${{M}_{1}}{{V}_{1}}$ = 2 × 0.2L × 1mol/L = 0.4

Similarly, in 3M of HCl, the number of ${{H}^{+}}$ is one and the volume is 0.3L.
Thus, the number of moles of ${{H}^{+}}$in 3M of HCl is, ${{M}_{2}}{{V}_{2}}$ = 0.3L × 3mol/L = 0.9
In 2M of HCl, the number of ${{H}^{+}}$ions is one and the volume is 0.2L.
The total number of moles of ${{H}^{+}}$ions in 2M of HCl is, ${{M}_{3}}{{V}_{3}}$ = 0.1L × 2mol/L = 0.2

So, total moles of ${{H}^{+}}$ions, ${{M}_{1}}{{V}_{1}}+{{M}_{2}}{{V}_{2}}+{{M}_{3}}V$ = 0.4 + 0.9 + 0.2
= 1.5

We have been given here that the total volume is, ${{V}_{1}}+{{V}_{2}}+{{V}_{3}}$= 1 L.
From using the above formula in hint,
${{M}_{mixture}}=\dfrac{{{M}_{1}}{{V}_{1}}+{{M}_{2}}{{V}_{2}}+{{M}_{3}}{{V}_{3}}}{{{V}_{1}}+{{V}_{2}}+{{V}_{3}}}$
${{M}_{mixture}}=\dfrac{1.5\,mole}{1\,L}$

So, [${{H}^{+}}$]= 1.5mol/L

Therefore, we can say that the correct answer is (b).

Note: Don't get confused between molarity and molality, molality is the number of moles of solute present in per kilogram of solvent. Its SI unit is mol/kg and a solution with molality 2mol/kg is said to be 2 m.