In what mass of H2SO4 solution (w = 32%) should 40 g of so3 be dissolved in order to obtain

In what mass of H2SO4 solution (w = 32%) should 40 g of so3 be dissolved in order to obtain an H2SO4 solution (w = 50%)?

Given:
ω1 (H2SO4) = 32%
ω2 (H2SO4) = 50%
m (SO3) = 40 g

Find:
m1 solution (H2SO4) -?

Solution:
1) find the theoretical masses of solution 1 and SO3 (we use the rule of the cross):
2) find the actual mass of solution 1 (using proportion and focusing on the solution according to the rule of the cross):
18 g m (SO3) must be added to m1 solution (H2SO4) 50 g, 40 g m (SO3) must be added to m1 solution (H2SO4) X g
18 – 50
40’s
x = 40 * 50/18 = 111.1

m1 solution (H2SO4) = x = 111.1 g

Answer: you need 111.1 g of sulfuric acid.