Concentration of Solutions (Molarity) Calculations

Key Concepts

The concentration of a solution is usually given in moles per litre (mol L^{-1} OR mol/L).
This is also known as molarity^{1}.

Concentration in mol/L or mol L^{-1}, or Molarity, is given the symbol c (sometimes M).
For a 0.01 mol L^{-1} HCl solution we can write :
[HCl] = 0.01 mol L^{-1} (concentration implied by square brackets around formula)
or
c(HCl) = 0.01 mol L^{-1} (c stands for concentration, formula given in brackets)

c = n ÷ V
where
c = concentration of solution in mol L^{-1} (mol/L or M),
n = moles of substance being dissolved (moles of solute),
V = volume of solution in litres (L)

This formula can be re-arranged to find:
moles of solute given molarity and volume of solution: n = c x V
volume of solution given moles of solute and molarity: V = n ÷ c

Examples

1. Calculating Concentration (c = n ÷ V)

Calculate the concentration in mol L^{-1} (molarity) of a sodium chloride solution containing 0.125 moles sodium chloride in 0.5 litres of solution.

Extract the data from the question
n = 0.125 mol
V = 0.5 L

Write the equation:
c = n ÷ V

Substitute in the values and solve:
[NaCl_{(aq)}] = c(NaCl_{(aq)}) = 0.125 ÷ 0.5 = 0.25 mol L^{-1} (or 0.25 mol/L or 0.25 M)

2. Calculating Moles of Solute (n = c x V)

Calculate the moles of copper sulfate in 250 mL of 0.02 mol L^{-1} copper sulfate solution.

Extract the data from the question:
c = 0.02 mol L^{-1} V = 250 mL = 250 ÷ 1000 = 250 x 10^{-3} L = 0.250 L (since there are 1000 mL in 1 L)

Write the equation:
n = c x V

Substitute in the values and solve:
n = 0.02 x 250 x 10^{-3} = 0.005 mol

3. Calculating Volume of Solution (V = n ÷ M)

Calculate the volume of a 0.80 mol L^{-1} potassium bromide solution containing 1.6 moles of potassium bromide.

Extract the data from the question:
n = 1.6 mol
c = 0.80 mol L^{-1}

Write the equation:
V = n ÷ c

Substitute in the values and solve:
V = 1.6 ÷ 0.80 = 2.00 L

^{1} There are many other ways to measure concentration of solutions in chemistry. You will find tutorials dealing with these under the heading Solutions on the AUS-e-TUTE homepage.

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