How many liters of 6.0 M H2SO4 are needed to make 0.50 L of 1.0 M solution?

Calculations on dilution of solution are based on the following mathematical formula:
C₁ V₁ = C₂ V₂
where C₁ and V₁ are the concentration and volume respectively before dilution, while C₂ and V₂ are the concentration and volume respectively after dilution.
It is required that both C₁ and C₂ are in the same unit. Also, V₁ and V₂ are in the same unit.

Before dilution: C₁ = 6.0 M, V₁ = ? L
After dilution: C₂ = 1.0 M, V₂ = 0.5 L

C₁ V₁ = C₂ V₂
Initial volume, V₁ = V₂ × (C₂/C₁) = (0.50 L) × (1.0/6.0) = 0.083 L (to 2 sig. fig.)

As you dilute this solution, the number of moles of sulfuric acid does not change. To determine the number of number of moles, multiply the volume in liters by the molarity.

V1 * C1 = 0.5 * 1 = 0.5
6 * C2 = 0.5
C2 = 0.5 ÷ 6

The concentration is approximately 0.083 moles per liter.

(0.50 L) x (1.0 M) / (6.0 M) = 0.083 L

The multiplication results in the number of moles required for the desired solution. The division results in the volume of 6.0 M acid that is necessary to produce that number of moles.