Calculate the volume of sulfuric acid (mass fraction 85%, density 1.05 g / ml), which will be required to prepare a solution

Calculate the volume of sulfuric acid (mass fraction 85%, density 1.05 g / ml), which will be required to prepare a solution with a mass fraction of sulfuric acid 2% in a volume of 450 ml (density 1.01 g / ml).

Given:
ω1 (H2SO4) = 85%
ρ1 solution (H2SO4) = 1.05 g / ml
ω2 (H2SO4) = 2%
ρ2 solution (H2SO4) = 1.01 g / ml
V2 solution (H2SO4) = 450 ml

To find:
V1 solution (H2SO4) -?

Decision:
1) to prepare this solution, you must use H2O
2) find the theoretical masses of solution 1, water and solution 2 (we use the rule of the cross):
m2 solution (H2SO4) = m1 solution (H2SO4) + m (Н2О) = 2 + 83 = 85 g
3) find the actual mass of solution 2 (given by the condition of the problem):
m2 solution (H2SO4) = V2 solution (H2SO4) * ρ2 solution (H2SO4) = 450 * 1.01 = 454.5 g
4) find the actual mass of solution 1 (using proportion and focusing on the solution according to the rule of the cross):
to obtain m2 solution (H2SO4) 85 g it is necessary to use 2 g m1 solution (H2SO4), then to obtain m2 solution (H2SO4) 454.5 g it is necessary to use X g m1 solution (H2SO4)
85 – 2
454.5 – x
x = 454.5 * 2/85 = 10.7
m1 solution (H2SO4) = x = 10.7 g
5) find the volume of solution 1:
V1 solution (H2SO4) = m1 solution (H2SO4) / ρ1 solution (H2SO4) = 10.7 / 1.05 = 10.2 ml
Answer: The required volume of sulfuric acid is 10.2 ml.