# How many grams of a 25% by mass solution of KOH should be added to 400 ml of water to obtain a 15% by mass solution?

July 24, 2021 | education

| Given:

ω1 (KOH) = 25%

V (H2O) = 400 ml

ω2 (KOH) = 15%

To find:

m1 solution (KOH) -?

Solution:

1) Let m1 solution (KOH) = (x) z;

2) m1 (KOH) = ω1 (KOH) * m1 solution (KOH) / 100% = 25% * x / 100% = (0.25x) g;

3) m2 (KOH) = m1 (KOH) = (0.25x) g;

4) m (H2O) = ρ (H2O) * V (H2O) = 1 * 400 = 400 g;

5) m2 solution (KOH) = m1 solution (KOH) + m (H2O) = (x + 400) g;

6) ω2 (KOH) = m2 (KOH) * 100% / m2 solution (KOH);

15% = 0.25x * 100% / (x + 400);

x = 600;

7) m1 solution (KOH) = x = 600 g.

Answer: The mass of the KOH solution is 600 g.

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