The chemist has two vessels with sodium chloride solutions. In the first vessel, 300 g with a mass fraction

The chemist has two vessels with sodium chloride solutions. In the first vessel, 300 g with a mass fraction of salt of 20%, in the second – 500 g with a mass fraction of salt of 40%. Both solutions were mixed. Find the mass fraction (in%) of the resulting sodium chloride solution.

Given:
m1 solution (NaCl) = 300 g
ω1 (NaCl) = 20%
m2 solution (NaCl) = 500 g
ω2 (NaCl) = 40%

To find:
ω3 (NaCl) -?

Solution:
1) m1 (NaCl) = ω1 (NaCl) * m1 solution (NaCl) = 20% * 300/100% = 60 g;
2) m2 (NaCl) = ω2 (NaCl) * m2 solution (NaCl) = 40% * 500/100% = 200 g;
3) m3 (NaCl) = m1 (NaCl) + m2 (NaCl) = 60 + 200 = 260 g;
4) m3 solution (NaCl) = m1 solution (NaCl) + m2 solution (NaCl) = 300 + 500 = 800 g;
5) ω3 (NaCl) = m3 (NaCl) / m3 solution (NaCl) = 260 * 100% / 800 = 32.5%.

Answer: The mass fraction of NaCl is 32.5%.