What mass of potassium hydroxide is contained in 120 g of a 15% solution of this substance? What mass of alkali must be added

What mass of potassium hydroxide is contained in 120 g of a 15% solution of this substance? What mass of alkali must be added to this solution so that the mass fraction of potassium hydroxide becomes 25%?

Given: m (solution) = 120 g, ω (KOH) = 15%, or 0.15, ω2 (KOH) = 25%, or 0.25.
Find: m (KOH) – ?, m3 (KOH) -?
Decision.
1. Calculate the mass of the solute (KOH) in the initial solution:
m (KOH) = m (solution) • ω (KOH) = 120 g • 0.15 = 18 g.
2. Calculate the mass of water in the initial solution:
m (water) = m (solution) – m (KOH) = 120 g – 18 g = 102 g.
3. Let the mass of the solute be x g, then substituting the values ​​into the formula for calculating the mass fraction ω (r.v.) = m (r.v.) / (M (r.v.) + M (water)), we obtain the algebraic equation for calculating the mass of a solute in a 25% solution:
0.25 = x / (x + 102)
0.25 • (x + 102) = x
0.25x + 25.5 = x
x – 0.25 x = 25.5
0.75 x = 25.5
x = 25.5: 0.75
x = m2 (KOH) = 34
4. Calculate the mass of the solute (KOH), which must be added to the solution:
m3 (KOH) = m2 (KOH) – m (KOH) = 34 g – 18 g = 16 g.
Answer: the mass of potassium hydroxide in a 15% solution is 18 g; it is necessary to add 16 g of potassium hydroxide to obtain a 25% solution.