The mole fraction of potassium nitrate in an aqueous solution is 0.0194. The solution's density is 1.0627 g/mL. What is the molarity of KNO₃ in the solution? A) 0.0194 M B) 0.981 M C) 1.05 M D) 1.96 M E) 19.4 M

Question

Quizplus · Accepted Answer

Mole fraction of KNO₃ = 0.0194
This means that there are 0.0194 moles of KNO₃ for every 1 mole of solution.

Density of solution = 1.0627 g/mL
This means that there are 1.0627 grams of solution for every 1 mL of solution.

We can use these two pieces of information to find the molarity of the solution:
Molarity = (moles of solute) / (liters of solution)
moles of solute = mole fraction of KNO₃ x moles of solution
moles of solution = (1.0627 g/mL) / (mol. mass of solution)
mol. mass of solution = mol. mass of KNO₃ + mol. mass of water
mol. mass of KNO₃ = 101.1 g/mol
mol. mass of water = 18.0 g/mol
mol. mass of solution = 101.1 + 18.0 = 119.1 g/mol

moles of solution = (1.0627 g/mL) / (119.1 g/mol) = 0.00894 moles/mL

moles of solute = 0.0194 x 0.00894 = 0.000174 moles/mL

Now we need to convert moles/mL to M.
1 mL = 0.001 L
Molarity = (0.000174 moles/mL) / (0.001 L/mL) = 0.174 M

Therefore, the molarity of the KNO₃ solution is 0.174 M, which is closest to choice C (1.05 M).

The Mole Fraction of Potassium Nitrate in an Aqueous Solution