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.