What volume of a solution with a mass fraction of sulfuric acid 60% density 1.5 g / ml and a solution

What volume of a solution with a mass fraction of sulfuric acid 60% density 1.5 g / ml and a solution with a mass fraction of sulfuric acid 30% density 1.2 g / ml should be taken to prepare a solution of H2So4 with a mass of 240 g with a mass fraction of acid 50%.

Let’s calculate the masses of the components of the solution.

This requires multiplying their mass fraction by the weight of the solution.

Determine the weight of sulfuric acid.

M acid = 240 x 0.5 = 120 grams;

Let’s find the weight of the water.

M water = 240 x 0.5 = 120 grams;

It is necessary to solve the system of equations.

0.6 X + 0.3 Y = 120

X + Y = 240

Where X is the weight of a 60% solution, and Y is the weight of a 30% solution.

Y = 240 – X;

0.6 X + 0.3 (240 – X) = 120;

0.3 X = 48;

X = 160 grams;

Y = 80 grams;

The volume of a 60% solution will be 160 / 1.5 = 106.7 ml;

The volume of a 30% solution will be 80 / 1.2 = 66.7 ml;

Let’s check:

160 x 0.6 + 80 x 0.3 = 96 + 24 = 120;