Question

Given,100ml of 1M HCl, 200ml of 2M HCl and 300ml of 3M HCl are mixed with enough water to get 1M solution. The volume of water to be added is:

Answer 1

Hint: The volume of water used to dilute a solution is found from the total volume and the volume of solute of the solution. In the above question concentration of the solute is given and the total volume can be calculated from the total number of moles of solute.

Complete answer:
Molarity (M) is defined as the amount of a substance in unit volume of the solution. The formula for molarity is,
 ${\text{M = }}\dfrac{{\text{n}}}{{\text{V}}}$
Where, n is the number of moles of the solute and V is the volume in litres.
Given data is the mixture of 100ml of HCl, 200ml of 2M HCl, 300ml of 3M HCl.
The total volume is to make it one molar solution can be known by the above formula of molarity. We need to calculate the total number of moles of HCl from the given data. Number of moles is given by the formula,
\[{\text{n = }}\dfrac{{\text{w}}}{{{\text{GMW}}}}\]
Where, w is the weight of the solute and GMW is the gram molar mass of the solute, here for HCl the molar mass is 36.5g.
Therefore, the no. of moles of 100ml HCl$=\dfrac{100}{36.5}\simeq 2.74\,moles$
No. of moles of 200ml HCl $=\dfrac{200}{36.5}\simeq 5.48\,moles$ and
The no. of moles of 300ml HCl$=\dfrac{300}{36.5}\simeq 8.22\,moles$
The total number of moles of HCl in the solution is 16.44moles.
Now the total volume of the solution would be,
${\text{M = }}\dfrac{{\text{n}}}{{\text{V}}}$
$1=\dfrac{16.44\times 1000}{V\left( ml \right)}$
V = 1640ml or 1.64L. Now the total volume of HCl has to be removed from the total volume of the solution in order to get volume of water, so, 1640-600=1040ml or 1.04 L.
Therefore the volume of water to be added is 1.04L.

Note:
A solution is made by adding a substance to proper solvent by dissolving in it. In the given question, 600ml of HCl of different molarities is mixed with water to make it 1M solution because the best solvent for hydrochloric acid is water.