Chemistry · Solutions and electrolytes · Grade 11

Concentration of a solution

Saline is 0.9 % — how many mol/L is that? How is it prepared in a pharmacy?

The situation

In a pharmacy a pharmacist is preparing a solution for eye drops: the bottle is labelled “NaCl 0.9 %”. The vinegar bottle in the kitchen says “9 %”, medical alcohol “70 %”, and laboratory flasks “0.1 M” and “0.1 N”. What do these percentages and letters mean? How many mol/L is a 0.9 % solution, and how can exactly 0.1 M solution be made in a volumetric flask?

Topic

Concentration of a solution: percentage, molar and normal. Pharmacy and kitchen: 0.9% saline, 9% vinegar, 70% alcohol — preparing a 1 M solution in a volumetric flask

Key ideas

Mass fraction
Molar and normal concentration
Mixing rule

Formulas

ω = \frac{m (substance)}{m (solution)} \cdot 100 %, m (solution) = ρ V

Relation between percentage concentration (mass fraction) and the mass, volume and density of a solution.

C_{M} = \frac{n}{V} = \frac{m}{M V}

Molar concentration, mol/L: the amount of solute in 1 litre of solution.

C_{N} = z C_{M}, E = \frac{M}{z}

Normality is the number of equivalents in 1 litre; $z$ is the number of $H^{+}$ in an acid, of $OH^{-}$ in a base, and the number of electrons accepted in an oxidising agent.

C_{M} = \frac{10 ω ρ}{M}, C_{N} = \frac{10 ω ρ}{E}

Conversion formulae: $ω$ in per cent, $ρ$ in g/mL.

\frac{m_{1}}{m_{2}} = \frac{ω - ω_{2}}{ω_{1} - ω}

Mixing (the “cross” rule); and in titration $N_{1} V_{1} = N_{2} V_{2}$ .

Theory

Percentage concentration (§15–16)

Concentration of a solution is the amount of solute in a given amount of solution (or of solvent). Percentage concentration (mass fraction) $ω = m (substance) / m (solution) \cdot 100 %$ shows how many grams of substance there are in 100 g of solution. To prepare a solution, $m (substance) = ω m (solution) / 100$ is weighed on a balance, and the water $m (water) = m (solution) - m (substance)$ is measured in a cylinder (1 mL of water ≈ 1 g; more precisely 0.998 g at 20 °C). For example, 500 g of physiological saline (0.9 %) needs 4.5 g of NaCl and 495.5 g of water. In medicine 0.9 % is understood as “0.9 g in 100 mL”, that is, 9 g/L. For liquids the volume fraction is often used: “70 % alcohol” means 70 mL of ethanol in 100 mL; by mass this is roughly 62–63 %.

Mass, volume and density (§17)

We often measure a solution by volume, while the concentration is given per mass — density links them: $m = ρ V$ . Density depends on the concentration and is given in tables (20 °C): NaCl 10 % — 1.071, 20 % — 1.148 g/mL; NaOH 10 % — 1.109, 40 % — 1.430 g/mL; $H_{2} SO_{4}$ 10 % — 1.066, 96 % — 1.836 g/mL. Density is measured with a hydrometer: it floats in the solution and rises higher in a denser liquid; the reading is taken where the scale meets the surface, and $ω$ is found from the table. When solutions are mixed, the masses add but the volumes do not: the volume of the mixture is often slightly smaller (for example, sulfuric acid and water).

Molar concentration (§18)

Molar concentration $C_{M} = n / V$ is the number of moles of substance in 1 litre of solution (mol/L, “M” for short). To prepare a 0.1 M solution, $m = C_{M} V M$ is weighed out and dissolved in a volumetric flask: the substance is put into the flask through a funnel, water is poured in to half-fill it and the substance is dissolved, then water is added up to the mark — the bottom of the meniscus level with the mark, with the eye at the same height; the flask is stoppered and inverted several times. If a crystalline hydrate is weighed, its molar mass is used: for 100 mL of 0.2 M $CuSO_{4}$ , 0.02 mol · 249.7 g/mol = 4.99 g of copper sulfate pentahydrate $CuSO_{4} \cdot 5 H_{2} O$ . Other measures: the titre $T = m / V$ (g/mL) and the molality $b = n / m (solvent)$ (mol/kg), which does not depend on temperature.

Normality (§19)

An equivalent is the part of a substance that corresponds to one $H^{+}$ or one $OH^{-}$ (or one electron); the equivalent mass is $E = M / z$ . For an acid, $z$ is the number of exchangeable hydrogen ions ( $HCl$ — 1, $H_{2} SO_{4}$ — 2); for a base, the number of hydroxide groups; for a salt, the product of the cation's charge and number ( $Na_{2} CO_{3}$ — 2, $CuSO_{4}$ — 2); for an oxidising or reducing agent, the number of electrons one particle accepts or gives: in acidic medium $MnO_{4}^{-} + 8 H^{+} + 5 e^{-} \overset{}{\to} Mn^{2 +} + 4 H_{2} O$ , so for $KMnO_{4}$ $z$ = 5 and a 0.02 M solution is 0.1 N. Normality $C_{N} = n (equiv) / V = z C_{M}$ (equiv/L, “N”): 1 M $H_{2} SO_{4}$ = 2 N. The advantage is that substances always react in equal equivalents, so in titration $N_{1} V_{1} = N_{2} V_{2}$ — you can calculate without writing out the coefficients.

Conversion formulae and mixing (§20–21)

1 L of solution has a mass of $1000 ρ$ g and contains $10 ω ρ$ g of substance, so $C_{M} = 10 ω ρ / M$ and $C_{N} = 10 ω ρ / E$ . For example, 96 % $H_{2} SO_{4}$ ( $ρ$ = 1.8355 g/mL): $C_{M}$ = 10 · 96 · 1.8355 / 98.08 ≈ 18 M, that is ≈ 36 N. On dilution the mass of substance is conserved: $m_{1} ω_{1} = m_{2} ω_{2}$ (in volumes, $C_{1} V_{1} = C_{2} V_{2}$ ). When two solutions are mixed, $ω = (m_{1} ω_{1} + m_{2} ω_{2}) / (m_{1} + m_{2})$ ; from this comes the cross (diagonal) rule: write $ω_{1}$ and $ω_{2}$ on the left, the required $ω$ in the middle, and on the right the differences $ω - ω_{2}$ and $ω_{1} - ω$ — these give the ratio of the masses to take. For water $ω_{2} = 0$ .

Safety and the model

Safety: add acid to water, never the reverse — if water falls on concentrated $H_{2} SO_{4}$ it boils and the acid spatters. Work with NaOH and acids wearing safety goggles and gloves; the solution heats up when NaOH dissolves. If alkali gets on the skin or in the eyes, rinse immediately with plenty of water. Never draw a pipette by mouth. Model: 20 °C; densities are linearly interpolated from CRC tables; the balance precision is 0.01 g, and the volumetric flask is filled exactly to the mark; in titration the pH is calculated from the charge balance (ideal solution), with $H_{2} SO_{4}$ taken as a strong acid in both steps; heat and evaporation on mixing are not taken into account.

Did you know?

Physiological saline contains 9 g of NaCl in 1 litre, that is 154 mmol/L $Na^{+}$ and the same amount of $Cl^{-}$ . Its osmotic concentration is ≈ 286 mOsm/L — very close to that of blood plasma (≈ 285), so it neither swells nor shrinks blood cells.
Industrial “concentrated” sulfuric acid is 98.3 %: its density is ≈ 1.84 g/mL and its molar concentration ≈ 18.4 mol/L. When it is diluted, the acid is poured into the water little by little, with stirring — a lot of heat is released.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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Electrolytic dissociation — Grade 9
Hydrolysis of salts and the medium — Grade 9
Solutions and solubility — Grade 11
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