A solution of the same acid weighing 800 g with a mass fraction of H3PO4 of 5% was added to a solution of phosphoric

A solution of the same acid weighing 800 g with a mass fraction of H3PO4 of 5% was added to a solution of phosphoric acid weighing 200 g with a mass fraction of H3PO4 10%. Determine the mass fraction in% of phosphoric acid in the resulting solution

Given:
m1 = 200 g;
m2 = 800 g;
w1% = 10%;
w2% = 5%.
To find:
w3% =?
Decision:
1. The problem can be solved by the method of proportions:
First we find the total mass of the solution:
m3 = 3 m1 + m2 = 200 + 800 = 1000 g.
The mass of the substance in the first solution is found by the method of proportions, based on the definition: the percentage concentration of the solution shows how many grams of dissolved substance are in 100 g of solution:
100 g of a 10% solution – 10 g of H3PO4;
200 g of a 10% solution – x g of H3PO4;
x = 200 * 10/100 = 20 g of H3PO4.
For the second solution we make a similar proportion:
100 g of a 5% solution – 5 g of H3PO4;
800 g of a 5% solution – y g of H3PO4;
y = 800 * 5/100 = 25 g of H3PO4.
Therefore, 100 g of a new solution contains 20 + 40 = 60 g of a dissolved substance.
Now you can determine the concentration of the new solution:
1000 g of solution – 60 g of H3PO4,
100 g of solution – z g of H3PO4,
z = 100 * 60/1000 = 6 g, or 6%
Answer: w3% = 6%.
2. This problem can be solved by the algebraic method:
w3% = m3 (H3PO4) * 100% / m3 (solution) =
= {[m1 (H3PO4) * w1%] + [m2 (H3PO4) * w2%]} / (m1 + m2) =
(200g * 0.1 + 800g * 0.05) * 100% / (200gn + 800g) = 6%
Answer: w3% = 6%