How many grams of phosphorus (V) oxide must be dissolved in 400 g of a phosphoric acid solution

How many grams of phosphorus (V) oxide must be dissolved in 400 g of a phosphoric acid solution with a mass fraction of H3PO4 5% to obtain a solution with a mass fraction of acid of 10%?

Given:
m solution (H3PO4) = 400 g
ω1 (H3PO4) = 5%
ω2 (H3PO4) = 10%

Find:
m (P2O5) -?

Solution:
1) Start solving the problem using the cross rule, or the mixing rule

2) Find the mass of P2O5:
Make up and solve the proportion: if 5 g of P2O5 must be added to 90 g of H3PO4 solution, then (x) g of P2O5 must be added to 400 g of H3PO4 solution:
90 – 5
400 – x
x = 400 * 5/90 = 22 g;

m (P2O5) = x = 22 g.

Answer: The mass of P2O5 is 22 g.