Merged 2 solutions of hydrochloric acid: 200 g 15% and 50 g 5%. Calculate the mass fraction

Merged 2 solutions of hydrochloric acid: 200 g 15% and 50 g 5%. Calculate the mass fraction of acid in the resulting solution.

Given:
m1 solution (HCl) = 200 g
ω1 (HCl) = 15%
m2 solution (HCl) = 50 g
ω2 (HCl) = 5%

To find:
ω3 (HCl) -?

Decision:
1) m1 (HCl) = ω1 (HCl) * m1 solution (HCl) / 100% = 15% * 200/100% = 30 g;
2) m2 (HCl) = ω2 (HCl) * m2 solution (HCl) / 100% = 5% * 50/100% = 2.5 g;
3) m3 (HCl) = m1 (HCl) + m2 (HCl) = 30 + 2.5 = 32.5 g;
4) m3 solution (HCl) = m1 solution (HCl) + m2 solution (HCl) = 200 + 50 = 250 g;
5) ω3 (HCl) = m3 (HCl) * 100% / m3 solution (HCl) = 32.5 * 100% / 250 = 13%.

Answer: Mass fraction of HCl is 13%.