Expressing Concentration of Solutions
Quick Notes
- Concentration: The amount of solute present in a given quantity of solution or solvent.
- Mass % (w/w) = (mass of solute / mass of solution) × 100
- Volume % (v/v) = (volume of solute / volume of solution) × 100
- Mass by volume % = (mass of solute / volume of solution in mL) × 100
- Parts per million (ppm) = (mass of component / total mass of solution) × 106
- Mole fraction (χ) = moles of component / total moles of all components
- Molarity (M) = moles of solute / volume of solution in litres
- Molality (m) = moles of solute / mass of solvent in kg
Full Notes
The concentration of a solution refers to the quantity of solute present in a given amount of solvent or solution.
There are several standard ways of expressing the concentration of a solution. These are chosen based on the nature of the experiment, accuracy required, and the physical state of the solute and solvent.
Mass Percentage (w/w)
Used when both solute and solvent are solids or when mass measurement is convenient.
Formula:
Volume Percentage (v/v)
Used when both solute and solvent are liquids.
Formula:
Mass by Volume Percentage (w/v)
Frequently used in medical or laboratory settings.
Mass of solute dissolved in 100 mL of solution
Example: A 5% w/v NaCl solution contains 5 g NaCl in 100 mL solution.
Parts per Million (ppm)
Used for expressing very low concentrations, especially in environmental chemistry.
Formula:
Example: 1 ppm = 1 mg solute per kg solution = 1 mg/L for water.
Mole Fraction (χ)
A ratio of moles, useful in thermodynamics and phase equilibrium.
Formula:
Mole fraction of component A:
Where nA and nB are moles of A and B respectively. The sum of all mole fractions in a solution is always 1.
Molarity (M)
Defined as the number of moles of solute per litre of solution.
Formula:
Note: Molarity is temperature dependent because volume changes with temperature.
Molality (m)
Number of moles of solute per kg of solvent.
Formula:
m = n / mass of solvent (kg) (1.9)
Advantage: Molality is temperature independent as it is based on mass, not volume.
Comparison of Molarity and Molality
Make sure you know the difference between molarity and molality — both are used in chemistry and it is easy to get the two confused.
| Aspect | Molarity (M) | Molality (m) |
|---|---|---|
| Definition | moles per litre | moles per kg of solvent |
| Temperature | Dependent | Independent |
| Use case | Solutions with fixed volume | Thermodynamic calculations |
Q: A solution contains 20 g of NaOH in 500 g of water. What is its molality?
- Molar mass of NaOH = 40 g/mol
- Moles of NaOH = 20 / 40 = 0.5 mol
- Mass of solvent (water) = 500 g = 0.5 kg
- Molality = 0.5 mol / 0.5 kg = 1 m
Summary
- Concentration measures how much solute is present in a given amount of solvent or solution.
- Common expressions include mass %, volume %, ppm, mole fraction, molarity and molality.
- Molarity depends on temperature while molality does not.
- Select the unit that best suits the experiment and required accuracy.