# 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%