Concentration and Solubility: Quick Revision

A brief note on Concentration and Solubility. Read it before a test. Try each question at the end before you open its answer.

The measures of concentration

• Mass percent: $\dfrac{\text{mass of solute}}{\text{mass of solution}} \times 100$.
• Mole fraction: $x_A = \dfrac{n_A}{n_A + n_B}$. The mole fractions add up to $1$.
• Molarity: moles of solute per litre of solution, in $\text{mol/L}$.
• Molality: moles of solute per kilogram of solvent, in $\text{mol/kg}$.
• Volume percent: millilitres of solute in $100\ \text{mL}$ of solution.
• Mass by volume percent: grams of solute in $100\ \text{mL}$ of solution.
• ppm: $1\ \text{ppm} = 1\ \text{mg}$ of solute in $1\ \text{kg}$ of solution. In water, about $1\ \text{mg/L}$.
• Only the measures that use a volume change with temperature. Molarity falls when a solution is heated. Molality, mole fraction, mass percent and ppm do not.

Changing from one measure to another

• Pick $1\ \text{L}$ of solution, $100\ \text{g}$ of solution or $1\ \text{kg}$ of solvent.
• Fill in the moles and masses of solute and solvent, and the volume of solution.
• The density joins mass and volume: mass of solution $=$ volume $\times$ density.
• Dilution: $M_1V_1 = M_2V_2$. Mixing: $M = \dfrac{M_1V_1 + M_2V_2}{V_1 + V_2}$.
• An ion has the concentration of the salt times its number in the formula.

Solubility of solids

• Solubility is usually grams of solute per $100\ \text{g}$ of solvent, at a stated temperature.
• Saturated: dissolving and crystallising go on at the same rate. Supersaturated: more than the solubility allows. It crystallises when a seed crystal is added.
• Like dissolves like. Pressure hardly matters for a solid.
• Dissolving takes in heat: the solubility rises with temperature. Dissolving gives out heat: it falls.
• Crystals from cooling $= (s_{hot} - s_{cold}) \times \dfrac{\text{mass of water}}{100}$.
• A saturated solution of a weakly soluble salt is dilute.

Gases in liquids

• Henry's law: $p = K_H\, x$. The amount dissolved is proportional to the partial pressure.
• $K_H$ has the unit of pressure. A larger $K_H$ means a smaller solubility.
• The solubility of a gas falls when the temperature rises.
• Uses: fizzy drinks, the bends in divers, anoxia at high altitude.

A worked example

A glucose solution ($180\ \text{g/mol}$) is $0.70\ \text{mol/kg}$, with a density of $1.05\ \text{g/mL}$. Find its molarity.

1. Take 1 kg of water. The glucose is $0.70 \times 180 = 126\ \text{g}$.
2. The solution. Its mass is $1000 + 126 = 1126\ \text{g}$. Its volume is $\dfrac{1126}{1.05} = 1072\ \text{mL} = 1.072\ \text{L}$.
3. Molarity. $\dfrac{0.70\ \text{mol}}{1.072\ \text{L}} = 0.653\ \text{mol/L}$.

Practice with new numbers

A program to try

The program follows the steps of the worked example.

Mistakes to avoid

• Dividing by the volume of the solvent in a molarity. Use the whole solution.
• Averaging two molarities to find a mixture. Add the moles, then divide by the total volume.
• Reading g per 100 g of water as a mass percent.
• Saying saturated means strong. A weakly soluble salt gives a dilute saturated solution.
• Using the total pressure in Henry's law. Use the partial pressure of the gas.
• Leaving $K_H$ in kilobar. Change it to bar first.

Check yourself

1. Which measures of concentration change when a solution is heated?

2. A saturated solution is cooled and crystals form. Why?

3. Gas A has a larger $K_H$ than gas B at the same temperature. Which dissolves more at the same pressure?

4. A water sample has $7\ \text{ppm}$ of a pollutant. How many milligrams are in $2\ \text{kg}$ of it?