In 400 ml of water was dissolved 40 g of sulfur oxide (6) Calculate the mass fraction

In 400 ml of water was dissolved 40 g of sulfur oxide (6) Calculate the mass fraction of sulfuric acid obtained in the solution.

Given:
V (H2O) = 400 ml
m (SO3) = 40 g
ρ (H2O) = 1 g / ml

Find:
ω (Н2SO4) -?

Solution:
1) H2O + SO3 => H2SO4;
2) M (SO3) = Mr (SO3) = Ar (S) + Ar (O) * 3 = 32 + 16 * 3 = 80 g / mol;
M (H2SO4) = Mr (H2SO4) = Ar (H) * 2 + Ar (S) + Ar (O) * 4 = 1 * 2 + 32 + 16 * 4 = 98 g / mol;
3) m (H2O) = ρ (H2O) * V (H2O) = 1 * 400 = 400 g;
4) n (SO3) = m (SO3) / M (SO3) = 40/80 = 0.5 mol;
5) n (H2SO4) = n (SO3) = 0.5 mol;
6) m (H2SO4) = n (H2SO4) * M (H2SO4) = 0.5 * 98 = 49 g;
7) m solution (H2SO4) = m (SO3) + m (H2O) = 40 + 400 = 440 g;
8) ω (Н2SO4) = m (Н2SO4) * 100% / m solution (Н2SO4) = 49 * 100% / 440 = 11%.

Answer: Mass fraction of Н2SO4 in the resulting solution is 11%.