What volume of hydrogen chloride needs to be dissolved in 1 liter of water to obtain a 36% (by weight) solution?

Given:
V (H2O) = 1 L = 1000 ml
ω (HCl) = 36%
ρ (H2O) = 1 g / ml

To find:
V (HCl) -?

Decision:
1) M (HCl) = Mr (HCl) = Ar (H) + Ar (Cl) = 1 + 35.5 = 36.5 g / mol;
2) Let the amount of substance HCl – (x) mol;
3) m (HCl) = n (HCl) * M (HCl) = x * 36.5 = (36.5x) g;
4) m (H2O) = ρ (H2O) * V (H2O) = 1 * 1000 = 1000 g;
5) m solution (HCl) = m (HCl) + m (H2O) = (36.5x + 1000) g;
6) m (HCl) = ω (HCl) * m solution (HCl) / 100% = 36% * (36.5x + 1000) / 100% = (13.14x + 360) g;
7) 36.5x = 13.14x + 360;
23.36x = 360;
x = 15.41;
n (HCl) = x = 15.41 mol;
8) V (HCl) = n (HCl) * Vm = 15.41 * 22.4 = 345.2 liters.

Answer: The volume of HCl is 345.2 liters.