Two sugar solutions were mixed: 1200 g of a solution with w = 10% and 800 g of a solution with w = 40%. What is the mass fraction of sugar in the resulting solution?
m1 solution (sugar) = 1200 g
ω1 (sugar) = 10%
m2 solution (sugar) = 800 g
ω2 (sugar) = 40%
ω3 (sugar) -?
1) m1 (sugar) = ω1 (sugar) * m1 solution (sugar) / 100% = 10% * 1200/100% = 120 g;
2) m2 (sugar) = ω2 (sugar) * m2 solution (sugar) / 100% = 40% * 800/100% = 320 g;
3) m3 (sugar) = m1 (sugar) + m2 (sugar) = 120 + 320 = 440 g;
4) m3 solution (sugar) = m1 solution (sugar) + m2 solution (sugar) = 1200 + 800 = 2000 g;
5) ω3 (sugar) = m3 (sugar) * 100% / m3 solution (sugar) = 440 * 100% / 2000 = 22%.
Answer: The mass of sugar is 22%.
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