Multiple Choice
Commercial grade hydrochloric acid is typically sold as an aqueous solution that is 39.0% HCl by mass and has a density at 20 °C of 1.20 g/mL. Determine the molality of the HCl solution.
14. Solutions
Molality
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The molarity of an aqueous solution is 1.58 M with a density of 0.976 g/mL. The molar mass of the solute is 195 g/mol. What is the molality (m) of the solution?
A
1.50 m
B
1.70 m
C
1.45 m
D
1.62 m
Verified step by step guidance1
Calculate the mass of the solution using its density. Assume you have 1 liter (1000 mL) of solution. Multiply the volume by the density: \( \text{mass of solution} = 1000 \text{ mL} \times 0.976 \text{ g/mL} \).
Determine the mass of the solute in the solution. Use the molarity to find the moles of solute in 1 liter of solution: \( \text{moles of solute} = 1.58 \text{ mol/L} \times 1 \text{ L} \). Then, convert moles to grams using the molar mass: \( \text{mass of solute} = \text{moles of solute} \times 195 \text{ g/mol} \).
Calculate the mass of the solvent (water) by subtracting the mass of the solute from the total mass of the solution: \( \text{mass of solvent} = \text{mass of solution} - \text{mass of solute} \).
Convert the mass of the solvent from grams to kilograms, as molality is expressed in moles of solute per kilogram of solvent.
Calculate the molality of the solution using the formula: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \).
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