Question

In a mixture of ${K_2}S{O_4}$ and $MgS{O_4}$, the mass percentage of ${K_2}S{O_4}$is 80%. Its mol-fraction in the mixture is:
1. 0.66
2. 0.75
3. 0.80
4. 0.87

Answer 1

Hint:The mole fraction is calculated by the moles of solute divided by the total number of moles of solute and solvent or total moles of the mixture. The number of solutes is calculated by dividing the mass with the molecular mass.

Complete answer:Given,
Mass percentage of ${K_2}S{O_4}$ is 80%.
In a 100 % mixture, of ${K_2}S{O_4}$ and $MgS{O_4}$, 80% of ${K_2}S{O_4}$ is present and the remaining 20% of $MgS{O_4}$ is present.
Mass percent means in 100 g of mixture 80 g of ${K_2}S{O_4}$ is present and 20 g of $MgS{O_4}$ is present.
To find out the mole fraction of the compounds present in the mixture, first the moles of the respective compound is calculated.
The formula for calculating the moles of the compound is shown below.
$n = \dfrac{m}{M}$
Where,
n is the number of moles of the compound
m is the mass of compound
M is the molecular mass of the compound.
The molar mass of ${K_2}S{O_4}$ is 174.25g/mol.
To calculate the moles of ${K_2}S{O_4}$, substitute the values of mass and molecular mass in the equation.
$\Rightarrow n = \dfrac{{80g}}{{174.25g/mol}}$
$\Rightarrow n = 0.459mol$
The molecular mass of $MgS{O_4}$ is 120.36 g/mol.
To calculate the moles of $MgS{O_4}$, substitute the values of mass and molecular mass in the equation.
$\Rightarrow n = \dfrac{{20g}}{{120.36g/mol}}$
$\Rightarrow n = 0.166mol$
The formula for calculating the mole fraction is shown below.
${X_A} = \dfrac{{{n_A}}}{{{n_A} + {n_B}}}$
Where,
${X_A}$ is the mole fraction of compound A.
${n_A}$ is the number of moles of compound A.
${n_B}$is the number of moles of compound B.
To calculate the mole fraction of ${K_2}S{O_4}$, substitute the values in the above equation.
$\Rightarrow X = \dfrac{{0.459}}{{0.459 + 0.166}}$
$\Rightarrow X = \dfrac{{0.459}}{{0.625}}$
$\Rightarrow X = 0.75$
Thus, the mole fraction of ${K_2}S{O_4}$ is 0.75.
Therefore, the correct option is 2.

Note:The mass percentage is the mass of compound divided by the total mass multiplied by 100. The mole fraction of both the compounds in the mixture can be calculated by the same formula but differently.