High School

A solution is prepared by dissolving 2.736 g of MgCl\(_2\) in 50.0 g of water. The volume of the solution is found to be 51.7 mL.

a. What is the molarity of the solution?

b. Calculate the mole fraction of magnesium chloride in the solution.

c. Calculate the mass percentage of magnesium chloride in this solution.

Answer :

a. To determine the molarity of the solution, we need to calculate the number of moles of magnesium chloride (MgCl2) dissolved in the solution.

First, we convert the mass of MgCl2 to moles using its molar mass. The molar mass of MgCl2 is calculated by adding the atomic masses of magnesium (Mg) and two chlorine (Cl) atoms:

Molar mass of MgCl2 = (1 × atomic mass of Mg) + (2 × atomic mass of Cl)

Once we have the molar mass, we can calculate the number of moles of MgCl2 by dividing the given mass of MgCl2 by its molar mass.

b. To calculate the mole fraction of magnesium chloride in the solution, we need to determine the moles of MgCl2 and moles of water present.

The mole fraction is calculated by dividing the moles of the component of interest (in this case, MgCl2) by the total moles of all components in the solution.

c. To calculate the mass percentage of magnesium chloride in the solution, we need to determine the mass of MgCl2 and the total mass of the solution.

The mass percentage is calculated by dividing the mass of the component of interest (MgCl2) by the total mass of the solution and multiplying by 100.

Now, let's calculate the molarity, mole fraction, and mass percentage using the given values:

a. Molarity (M) = moles of solute / volume of solution (in liters)
First, convert the volume of the solution from milliliters (mL) to liters (L).
Molarity = moles of MgCl2 / volume of solution (in L)

b. Mole fraction (X) = moles of MgCl2 / (moles of MgCl2 + moles of water)

c. Mass percentage = (mass of MgCl2 / total mass of solution) × 100

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