Question

The density of a 10.0 % by mass of KCl solution in water is 1.06 g/ml. calculate the (mass/volume) percentage of solution?

Answer 1

Hint: There is a formula to calculate the molarity of the by using density and it is as follows.
\[Density=\dfrac{mass}{volume}\]
Number of moles $=\dfrac{weight}{molecular\text{ }weight}$
Molarity = $\dfrac{\text{number of moles}}{\text{volume in litre}}$
By using the above formulas we can calculate the molarity of the solution.

Complete step by step answer:
- In the question it is given to calculate the molarity (mass/volume) of the solution.
- The density of the water is 1.06 g/ml for 100 gm of solution.
- The mass of the solution is 10.0 % which means 100 gm of solution.
- From the above data we can calculate the volume of the solution and it is as follows.
\[Volume=\dfrac{mass}{density} = \dfrac{100}{1.06}=94.33ml\]
- Number of moles of KCl = $\dfrac{\text{Weight of KCl}}{\text{Molecular weight of the KCl}} = \dfrac{10}{74.5} = 0.13422mol$
- Now we have a number of moles of KCl and volume of the solution in litre.
- Substitute the both known values in the below formula to get the molarity of the solution and it is as follows.
Molarity = $\dfrac{\text{number of moles KCl}}{\text{volume in litre}} = \dfrac{0.13422}{94.33}\times 1000 = 1.42M$
- The molarity of the solution containing 10.0 % of KCl in water is 1.42 M.

Note: We should know the number of moles of the solute and volume of the solution in litre to calculate the molarity of the solution. By using the density of the solution we can calculate the volume of the solution in litre. If we are going to calculate the volume in Kg then we will get the molality of the solution. The Molality of the solution is different from the molarity of the solution.