Density and Percentage

Question

Battery Acid consists of 31 % (m/m) H₂SO₄ and has a density of 1.27 g/mL. How many mL of pure H₂SO₄ must be used to create 5.0 L of battery acid? The density of pure H₂SO₄ is 1.84 g/mL.

Answer 1

This is a dilution problem hiding out as density. Remember the formula for dilution:

M₁V₁ = M₂V₂

Where M is Molarity (concentration) and V is volume. Molarity is how many moles of a substance can be found in a given volume.Density is how much mass is found in a given volume, ie concentration. So Density can be substituted for Molarity in the equation giving:

D₁V₁ = D₂V₂ I'm going to use the pure as D₁ and V₁

(1.84g/ml)V₁ = (1.27g/ml)(5.0L)

Solving for V₁ gives 3.5L in correct significant figures. The question could ask for how much water would be used for dilution and in this case would be 1.5L.