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Chapter 13: Problem 21

Calculate the molarity and the molality of \(\mathrm{NH}_{3}\) for a solution of \(30.0 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) in \(70.0 \mathrm{~g}\) of water. The density of the solution is \(0.982 \mathrm{~g} / \mathrm{mL}\).

Short Answer

Expert verified
The molarity of \(\mathrm{NH}_{3}\) solution is 17.29 M and the molality is 25.14 m.

Step by step solution

01

calculate the moles of \(\mathrm{NH}_{3}\)

This can be obtained by using the formula: n = mass/molar mass. The molar mass of \(\mathrm{NH}_{3}\) is 17.03 g/mol. Hence, \(n_{NH3} = \frac{30.0 g}{17.03 g/mol} = 1.76 mol\)
02

calculate the volume of the solution

The volume of the solution can be obtained by dividing the total mass by the density. Given the total mass is 100.0 g (30.0 g of \(\mathrm{NH}_{3}\) + 70.0 g of water) and the density is 0.982 g/mL, \(V_{sol} = \frac{100.0 g}{0.982 g/mL} = 101.83 mL = 0.10183 L\)
03

calculate molarity (M)

Molarity (M) is calculated by dividing the number of moles of solute by the volume of the solution in liters. Hence, \(M = \frac{n_{solute}}{V_{sol}} = \frac{1.76 mol}{0.10183 L} = 17.29 M\)
04

calculate molality (m)

Molality (m) is calculated by dividing the number of moles of solute by the mass of the solvent in kg. Given the mass of the solvent (water) is 70.0 g = 0.07 kg, \(m = \frac{n_{solute}}{mass_{solvent}} = \frac{1.76 mol}{0.07 kg} = 25.14 m\)

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Most popular questions from this chapter

Arrange these compounds in order of increasing solubility in water: \(\mathrm{O}_{2}, \mathrm{LiCl}, \mathrm{Br}_{2}, \mathrm{CH}_{3} \mathrm{OH}\) (methanol).

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