Question

5g of an unknown solute is dissolved in 295 g solvent. If molarity and density of solution are 0.05M and 1.5 g/cc respectively. The molecular weight of unknown solute is:
A. 375
B. 425
C. 400
D. 500

Answer 1

Calculate the volume of the solution using the density and mass of solution. Calculate the moles of solute using molar concentration and volume of solution. Finally, calculate the molecular weight of unknown solute from moles and mass of the solute.

Step by step answer: We have given mass of solute and mass of solvent. So, calculate the mass of the solution as follows:

Mass of solution = mass of solute + mass of solvent

Substitute 5 g for a mass of solute and 295 g for the mass of solvent and calculate the mass of solution.

Mass of solution = 5 g +295 g = 300 g

Now, we have a mass solution and also we have given the density of the solution so, calculate the volume of the solution as follows:

${\text{Density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$
${\text{volume = }}\dfrac{{{\text{mass}}}}{{{\text{Density }}}}$

Substitute 300 g for a mass of solution and 1.5g/cc for the density of the solution and calculate the volume of the solution.

${\text{volume of solution = }}\dfrac{{300{\text{ g}}}}{{{\text{1}}{\text{.5 g/cc }}}}$

${\text{volume of solution = 200 cc}}$

Now, to calculate the moles of solute using the volume of solution and molarity of solution convert the volume of solution in L.

1 L = 1000 cc

${\text{200 cc }} \times \dfrac{{1{\text{ L}}}}{{1000{\text{ cc }}}} = 0.2{\text{ L}}$

Substitute 0.05 M for molarity and 0.2 L for the volume of solution and calculate the moles of solute as follows:

${\text{Molarity = }}\dfrac{{{\text{moles of solute}}}}{{{\text{L of solution }}}}$

${\text{moles of solute = Molarity }} \times {\text{L of solution }}$

${\text{moles of solute = 0}}{\text{.05 M}} \times 0.2L{\text{ = 0}}{\text{.01 mol}}$

Now, we have moles of solute and mass of solute so calculate the molecular weight of solute as follows:

${\text{molecular weight = }}\dfrac{{{\text{mass}}}}{{{\text{mole}}}}$

Substitute 0.01 mol for moles of solute and 5 g for a mass of solution and calculate the molecular weight of the unknown solute.
${\text{molecular weight = }}\dfrac{{{\text{5 g}}}}{{0.01{\text{ mol}}}}$

${\text{molecular weight = }}\dfrac{{{\text{5 g}}}}{{0.01{\text{ mol}}}}$

${\text{molecular weight = 500 g/mol}}$

Thus, the molecular weight of the unknown solute is ${\text{500 g/mol}}$.

Hence, the correct option is (D) 500

Note: Molar concentration of the solution is moles of solute per liter of solution. So, use the volume of solution in L. Molecular weight is the mass of 1 mol of substance so the unit of molecular weight is g/mol.