Multiple Choice
An aqueous solution contains 36% HCl by mass. If the density of the solution is 1.18 g/mL, what is the molality of HCl in the solution?
14. Solutions
Molality
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If 0.98 g of an unknown was dissolved in 10.30 g of solvent and the resulting solution has a molality of 0.45 m, what is the molar mass of the unknown?
A
32.5 g/mol
B
21.2 g/mol
C
18.4 g/mol
D
45.6 g/mol
Verified step by step guidance1
Understand that molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula is: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \).
Convert the mass of the solvent from grams to kilograms. Since there are 10.30 g of solvent, divide by 1000 to convert to kilograms: \( 10.30 \text{ g} = 0.01030 \text{ kg} \).
Use the given molality (0.45 m) and the mass of the solvent in kilograms to find the moles of solute. Rearrange the molality formula to solve for moles of solute: \( \text{moles of solute} = m \times \text{kilograms of solvent} \).
Substitute the known values into the equation: \( \text{moles of solute} = 0.45 \times 0.01030 \). Calculate this to find the moles of solute.
Finally, calculate the molar mass of the unknown solute using the formula: \( \text{Molar mass} = \frac{\text{mass of solute (g)}}{\text{moles of solute}} \). Use the mass of the solute (0.98 g) and the moles of solute calculated in the previous step to find the molar mass.
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