# Expressing Concentration of Solutions

**Expressing Concentration of Solutions**

**Mass percentage**

The mass percentage of a component in a given solution is the mass of the component per 100 g of the solution.

**For example:** If W_{A} is the mass of component A and W_{B} is the mass of component B in a solution, then

**Mass percentage of A = **W_{A }/ (W_{A} + W_{B}) × 100

A 10% (w/w) solution of sodium chloride means that 10 g of sodium chloride is present in 90 g of water so that the total mass of the solution is 100 g or simply 10 g of sodium chloride is present in 100 g of solution.

**Volume percentage**

The volume percentage is defined as the volume of the component per 100 parts by volume of the solution.

If V_{A} and V_{B} are the volume of two components A and B respectively in a solution, then

Volume percentage of A = V_{A }/ (V_{A} + V_{B}) x 100

**For example:** 10% by volume of ethanol solution means that 10 mL of ethanol is dissolved in enough water so that the the solution is 100 mL. Solutions containing liquids are commonly expressed as volume percentage.

**Mass by volume percentage**

We express the concentrations as weight/volume. It is the mass of solute dissolved in 100 mL of the solution.

**For example:** A 10% solution of sodium chloride (w/v) means that 10 g of sodium chloride are dissolved in 100 mL of solution.

**Parts per million**

When a solute is present in very minute amounts (trace quantities), the concentration is expressed in parts per million abbreviated as ppm.

It is the parts of a component per million parts of the solution. It is expressed as

**Mole fraction**

It is the ratio of number of moles of one component to the total number of moles (solute and solvent) present in the solution.

A solution contains n_{A} moles of solute and n_{B} moles of the solvent.Then

The sum of mole fractions of all the components in solution is always equal to one.

If the mole fraction of one component of a binary solution is known, that of the other can be calculated.

X_{A} =1-X_{B }

X_{B} =1- X_{A}

**Molarity**

It is the number of moles of the solute dissolved per litre of the solution. It is represented as M. Thus, a solution which contains one gram mole of the solution dissolved per litre of the solution is regarded as one molar solution.

**For example:** 1M Na_{2}CO_{3} (molar mass = 106) solution has 106 g of the solute present per litre of the solution.

**Molarity = **(Moles of solute / Volume of solution in litres) × 1000

The **units of molarity** are moles per litre (mol L^{-1})

or moles per cubic decimetre (mol dm^{-3}).

The symbol M is used for mol L^{-1} or mol dm^{-3}

If n_{B} moles of solute are present in V mL of solution, then

**Molarity = **n_{B / V x 1000}

**Moles of solute = **Moles of solute / Molar mass of solute

Molarity has one disadvantage. It changes with temperature because of expansion or contraction of the liquid with temperature.

**Molality**

Molality is considered better for expressing the concentration as compared to molarity because the molarity changes with temperature because of expansion on contraction of the liquid with temperature. However, molality does not change with temperature because mass of the solvent does not change with change in temperature.

It is the number of moles of the solute dissolved per 1000 g (or 1 kg) of the solvent. It is denoted by m.

Thus, a solution which contains one gram mole of a solute dissolved in 1 kg of water is regarded as 1 molal solution.

For example: 1.0 m solution of KCl means that 1 mol (74.5 g) of KCl is dissolved in 1 kg or

1000 g of water.

The units of molality are moles per kilogram i.e., mol kg^{-1}. It is represented by the symbol m.

If n_{B} moles of solute are dissolved in W grams of solvent, then

**Molality = **n_{B / V x 100}