Dilution of Solutions

When a solution is diluted, more solvent is added to it. 
    Since M = mole／V, and mole is the same for the original solution and the new diluted solution, it follows that M₁V₁ = M₂V₂ 
    where M₁=original concentration of solution 
              V₁=original volume of solution 
              M₂=new concentration of solution after dilution 
              V₂=new volume of solution after dilution


Examples

1.Calculate the new concentration (molarity) if enough water is added to 100mL of 0.25M sodium chloride to make up 1.5L.

M₂=(M₁V₁) ÷ V₂
M₁ = 0.25M
V₁ = 100mL = 100 ÷ 1000 = 0.100L (volume must be in litres)
V₂ = 1.5L
[NaCl(aq)]_new = M₂ = (0.25 x 0.100) ÷ 1.5 = 0.017M 
    (or 0.017 mol/L or 0.017 mol L^-1)

2.Calculate the volume to which 500mL of 0.02M coppper sulfate solution must be diluted to make a new concentration of 0.001M.

V₂=(M₁V₁) ÷ M₂
M₁ = 0.02M
V₁ = 500mL = 500 ÷ 1000 = 500 x 10^-3L = 0.500L (since there are 1000mL in 1L)
M₂ = 0.001M
V(CuSO₄)_new = V₂ = (0.02 x 0.500) ÷ 0.001 = 10.00L