What volume of a 35% solution of phosphoric acid (density 1.216 g / cm ^ 3) is

What volume of a 35% solution of phosphoric acid (density 1.216 g / cm ^ 3) is required to prepare 13 liters of a solution of this acid with an equivalent molar concentration of 0.15 mol / l?

Given:
ω1 (H3РO4) = 35%
ρ1 solution (H3PO4) = 1.216 g / cm ^ 3
V2 solution (H3PO4) = 13 l
C2 solution (H3PO4) = 0.15 mol / l

Find:
V1 solution (H3PO4) -?

Solution:
1) Find the amount of substance H3PO4:
n (H3PO4) = C2 solution (H3PO4) * V2 solution (H3PO4) = 0.15 * 13 = 0.195 mol;

2) Find the mass of dry matter H3PO4:
m (H3PO4) = n (H3PO4) * Mr (H3PO4) = 0.195 * 98 = 19.11 g;

3) Find the mass of the initial H3PO4 solution:
m1 solution (H3PO4) = m (H3PO4) * 100% / ω1 (H3PO4) = 19.11 * 100% / 35% = 54.6 g;

4) Find the volume of the initial H3PO4 solution:
V1 solution (H3PO4) = m1 solution (H3PO4) / ρ1 solution (H3PO4) = 44.9 cm ^ 3.

Answer: The required volume of the H3PO4 solution is 44.9 cm ^ 3.