Question

How many liters of a 3.12 M ${K_2}S{O_4}$ solution are needed to provide 80.3 g of ${K_2}S{O_4}$ (molar mass 174.01 g/mol) ? Recall that M is equivalent to mol/L.

Answer 1

Hint: In the given question we need to apply two concepts one is molarity and other is number of moles. The molarity of the solution is calculated by dividing the number of moles by volume of solution. The number of moles is calculated by dividing the mass by the molecular weight.

Complete step by step answer:
It is given that the molarity of the solution is 3.12 M. The mass of ${K_2}S{O_4}$is 80.3 g and the molar mass is 174.01 g/mol.
The molarity of the solution is defined as the number of moles of solute dissolved in one liter of solution. Molarity of the solution is in terms of mole per liter or mol/L.
The formula to calculate the molarity is shown below.
$M = \dfrac{n}{V}$
Where,
M is the molarity
n is the number of moles.
V is the volume.
In this question, we need to find the volume of the solution. For this first we need to find the number of moles.
The formula to calculate the number of moles is shown below.
$n = \dfrac{m}{M}$
Where,
n is the number of moles
m is the mass
M is the molecular weight
To calculate the moles of water, substitute the values in the above equation.
$ \Rightarrow n = \dfrac{{80.3g}}{{174.01g/mol}}$
$ \Rightarrow n = 0.461mol$
To calculate the volume, substitute the value of molarity and number of moles in the formula.
$ \Rightarrow 3.12mol/L = \dfrac{{0.461mol}}{V}$
$ \Rightarrow V = \dfrac{{0.461mol}}{{3.12mol/L}}$
$ \Rightarrow V = 0.148L$
Therefore, 0.148 liters of a 3.12 M ${K_2}S{O_4}$ solution are needed to provide 80.3 g of ${K_2}S{O_4}$

Note:
The symbol “M” is used for molarity of solution whereas the symbol “m” is used for molality of solution. Both the terms are different from each other but they used to denote the concentration of solute in the solution.