Question

How do I find the mass of potassium in a 50.0⋅g mass of potassium sulphate?

Answer 1

Hint: The mass of a given atom in a compound can be found by the number of atoms of each element in the compound and by finding the no. of moles of the compound given. In here we’ll first find the molar mass of potassium sulphate and then the no. of moles of potassium sulphate given to us.

Complete answer:
The chemical formula for potassium sulphate is ${K_2}S{O_4}$. It contains two atoms of potassium and 1 molecule of sulphate. When disintegrated the compound gives:
${K_2}S{O_4} \to 2K + 1S{O_4}$
The molar mass of the compound = molar mass of potassium $ \times 2$ + molar mass of sulphate
The molar mass of Potassium $ = 39.0983g/mol$
Molar mass of Sulphate = Molar mass of sulphur + molar mass of Oxygen $ \times 4$
Molar mass of sulphate = $32.065 + 4 \times 15.999$
Molar mass of Potassium Sulphate = $39.093 \times 2 + 32.065 + 15.999 \times 4 = 174.26g/mol$
The mass of Potassium Sulphate given to us = 50.0g
The no. of moles of Potassium sulphate $ = \dfrac{{mass(g)}}{{Molar{\text{ }}Mass(g/mol)}}$
The no. of moles of potassium sulphate in 59.0g $ = \dfrac{{50}}{{134.26}} = 0.287mol$ of ${K_2}S{O_4}$
One molecule of Potassium Sulphate contains two atoms of potassium. Therefore, the number of moles of Potassium in 50.g of ${K_2}S{O_4}$ = $2 \times 0.287mol = 0.574mol$ of Potassium.
Now the amount of potassium in grams can be given as $ = mass \times molar{\text{ }}mass$
Mass of potassium in 50.0 g ${K_2}S{O_4}$ $ = 0.574 \times 39.098 = 22.4422g$ of potassium. This is the required answer.

Note:
In a compound if the mass or no. of moles of a specific atom is being asked, first we’ll have to disintegrate the compound into its constituent atoms. The no. of moles of each atom will be equal to the integral multiple of the no. of atoms of that element present in the compound.