Expression of Concentration of Solutions — Revision Notes

⚡ 30-Second Revision

Mass % (w/w%) — $\frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100$
Volume % (v/v%) — $\frac{\text{Volume of solute}}{\text{Volume of solution}} \times 100$
Mass/Volume % (w/v%) — $\frac{\text{Mass of solute (g)}}{\text{Volume of solution (mL)}} \times 100$
ppm — $\frac{\text{Mass of solute}}{\text{Mass of solution}} \times 10^6$ (or mg/L for aqueous solutions)
Mole Fraction (x) — $x_A = \frac{n_A}{n_A + n_B}$ (dimensionless, temperature-independent)
Molarity (M) — $\frac{\text{Moles of solute}}{\text{Volume of solution (L)}}$ (mol/L, temperature-dependent)
Molality (m) — $\frac{\text{Moles of solute}}{\text{Mass of solvent (kg)}}$ (mol/kg, temperature-independent)
Density ($\\rho$) — $\frac{\text{Mass}}{\text{Volume}}$ (g/mL or kg/L, crucial for interconversions)

2-Minute Revision

Concentration expressions quantify the amount of solute in a solution. Mass Percentage (w/w%) is mass of solute per 100 mass units of solution, useful for solids. Volume Percentage (v/v%) is volume of solute per 100 volume units of solution, for liquids.

Mass by Volume Percentage (w/v%) is grams of solute per 100 mL of solution, common in pharmacy. For very dilute solutions, Parts Per Million (ppm) and Parts Per Billion (ppb) are used, representing parts of solute per $10^6$ or $10^9$ parts of solution, respectively.

Mole Fraction (x) is the ratio of moles of a component to total moles, dimensionless and temperature-independent, vital for colligative properties. Molarity (M) is moles of solute per liter of solution, temperature-dependent due to volume changes.

Molality (m) is moles of solute per kilogram of solvent, temperature-independent and preferred for colligative property calculations. Remember to use solution density for interconversions between mass-based and volume-based units, and always pay attention to units (g, kg, mL, L) and molar masses.

5-Minute Revision

A solution's concentration defines the relative amounts of solute and solvent. We have several ways to express this quantitatively. Mass Percentage (w/w%) is simply $(\text{mass of solute} / \text{mass of solution}) \times 100$.

For example, a 10% w/w NaCl solution means 10g NaCl in 100g of solution. Similarly, Volume Percentage (v/v%) is $(\text{volume of solute} / \text{volume of solution}) \times 100$, used for liquid-liquid solutions like alcohol in water.

Mass by Volume Percentage (w/v%) is $(\text{mass of solute (g)} / \text{volume of solution (mL)}) \times 100$, often seen in medical contexts.

For extremely dilute solutions, Parts Per Million (ppm) and Parts Per Billion (ppb) are used. $1\,\text{ppm} = (\text{mass of solute} / \text{mass of solution}) \times 10^6$. For aqueous solutions, $1\,\text{ppm} \approx 1\,\text{mg/L}$.

Mole Fraction (x) is a fundamental unit: $x_{\text{solute}} = n_{\text{solute}} / (n_{\text{solute}} + n_{\text{solvent}})$. It's dimensionless and temperature-independent, crucial for colligative properties. For example, if 1 mol urea is in 9 mol water, $x_{\text{urea}} = 1/(1+9) = 0.1$.

Molarity (M) is moles of solute per liter of solution ($M = n_{\text{solute}} / V_{\text{solution (L)}}$). It's temperature-dependent because volume changes with temperature. A 2M solution has 2 moles of solute per liter of solution.

Molality (m) is moles of solute per kilogram of solvent ($m = n_{\text{solute}} / m_{\text{solvent (kg)}}$). It's temperature-independent, making it ideal for colligative property calculations. A 0.5m solution has 0.5 moles of solute per kilogram of solvent.

Interconversions are key. To convert between mass-based and volume-based units (e.g., molality to molarity), you *must* use the density of the *solution*. Remember to convert units carefully: grams to kilograms, milliliters to liters, and vice versa. Always use molar masses to convert between mass and moles.

Prelims Revision Notes

1
Mass Percentage (w/w%) — Mass of solute in 100 g of solution. Formula: $(\text{mass of solute} / \text{mass of solution}) \times 100$. Temperature-independent.
2
Volume Percentage (v/v%) — Volume of solute in 100 mL of solution. Formula: $(\text{volume of solute} / \text{volume of solution}) \times 100$. Temperature-dependent.
3
Mass by Volume Percentage (w/v%) — Mass of solute (g) in 100 mL of solution. Formula: $(\text{mass of solute (g)} / \text{volume of solution (mL)}) \times 100$. Temperature-dependent.
4
Parts Per Million (ppm) — Used for very dilute solutions. $\text{ppm} = (\text{mass of solute} / \text{mass of solution}) \times 10^6$. For aqueous solutions, $1\,\text{ppm} \approx 1\,\text{mg/L}$.
5
Mole Fraction (x) — Ratio of moles of a component to total moles. $x_A = n_A / (n_A + n_B)$. Sum of mole fractions is 1. Dimensionless and temperature-independent.
6
Molarity (M) — Moles of solute per liter of solution. $M = n_{\text{solute}} / V_{\text{solution (L)}}$. Units: mol/L or M. Temperature-dependent (volume changes with T).
7
Molality (m) — Moles of solute per kilogram of solvent. $m = n_{\text{solute}} / m_{\text{solvent (kg)}}$. Units: mol/kg or m. Temperature-independent (mass and moles are constant with T). Preferred for colligative properties.
8
Density ($\\rho$) — $\rho = \text{mass} / \text{volume}$. Essential for interconverting mass-based and volume-based concentration units. Always use density of the *solution*.
9
Interconversions — To convert between Molarity and Molality, or between percentage concentrations and Molarity/Molality, you will typically need the solution's density and molar masses of components. Assume 100g or 100mL of solution/solvent as a basis for calculations involving percentages.
10
Key Distinction — Molarity is volume-dependent (temperature-dependent); Molality is mass-dependent (temperature-independent). This is a frequent conceptual question.

Vyyuha Quick Recall

To remember temperature dependence: 'My Volume Thrives on Temperature, but My Mass Is Temperature-Independent.'

Molarity (Volume) is Temperature-Dependent.
Molality (Mass) is Temperature-Independent.