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Chapter 12: Problem 23

Calculate the molarity and the molality of an \(\mathrm{NH}_{3}\) solution made up 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 the \(NH_{3}\) solution is \(17.28 \, M\) and the molality is \(25.14 \, m\).

Step by step solution

01

Calculate the moles of \(NH_{3}\)

The first step is to calculate the number of moles of \(NH_{3}\). To do this, use the molar mass of \(NH_{3}\), which is about \(17.03 \, g/mol\). Apply the formula \(n = \frac{m}{M}\), where \(n\) is the number of moles, \(m\) is the mass and \(M\) is the molar mass. Thus, the number of moles of \(NH_{3}\) is \(\frac{30.0 \, g}{17.03 \, g/mol} = 1.76 \, mol\).
02

Calculate Molarity

Molarity is the number of moles of solute divided by the volume of the solution in liters. Firstly, the volume of the solution needs to be calculated. From the question, we know that the total mass of the solution is \(30.0 \, g + 70.0 \, g = 100.0 \, g\) and the density is \(0.982 \, g/ml\). So, the volume is \(\frac{100.0 \, g}{0.982 \, g/ml} = 101.84 \, ml\), which is \(0.10184 \, L\). Now, the molarity (\(M\)) is calculated as \(M = \frac{n}{V} = \frac{1.76 \, mol}{0.10184 \, L} = 17.28 \, M\).
03

Calculate Molality

Molality, unlike molarity, uses the mass of the solvent (water in this case) instead of the volume of the solution. Given that the mass of water is \(70.0 \, g = 0.070 \, kg\), molality (\(m\)) is calculated as follows: \(m = \frac{n}{W} = \frac{1.76 \, mol}{0.070 \, kg} = 25.14 \, m\).

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