Calculate the mass (g) of ammonium sulfate to be added to a 500 g solution with a mass fraction of (NH4)

Calculate the mass (g) of ammonium sulfate to be added to a 500 g solution with a mass fraction of (NH4) 2SO4 10% to prepare a solution with a mass fraction of solute of 25%.

Given:
m1 solution ((NH4) 2SO4) = 500 g
ω1 ((NH4) 2SO4) = 10%
ω3 ((NH4) 2SO4) = 25%

Find:
m2 ((NH4) 2SO4) -?

Solution:
1) m1 ((NH4) 2SO4) = ω1 ((NH4) 2SO4) * m1 solution ((NH4) 2SO4) / 100% = 10% * 500/100% = 50 g;
2) Take m2 ((NH4) 2SO4) as (x) g;
3) m3 ((NH4) 2SO4) = m1 ((NH4) 2SO4) + m2 ((NH4) 2SO4) = (50 + x) g;
4) m3 solution ((NH4) 2SO4) = m1 solution ((NH4) 2SO4) + m2 ((NH4) 2SO4) = (500 + x) g;
5) Make and solve the equation:
ω3 ((NH4) 2SO4) = m3 ((NH4) 2SO4) * 100% / m3 solution ((NH4) 2SO4);
25% = (50 + x) * 100% / (500 + x);
0.25 = (50 + x) / (500 + x);
0.25 * (500 + x) = 50 + x;
125 + 0.25x = 50 + x;
75 = 0.75x;
x = 100;
m2 ((NH4) 2SO4) = x = 100 g.

Answer: The mass of (NH4) 2SO4 is 100 g.