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%

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.