Determine the mass fractions of metals in a mixture of iron and magnesium if it is known that when processing

Determine the mass fractions of metals in a mixture of iron and magnesium if it is known that when processing 0.4 g of this mixture with an excess of a mixture of hydrochloric acid 0.224 L of hydrogen

Let’s find the amount of the substance hydrogen.

n = V: Vn.

n = 0.224 L: 22.4 L / mol = 0.01 mol.

Mg + 2HCl = MgCl2 + H2.

Fe + 2HCl = FeCl2 + H2.

Let the amount of substance Mg – x mol, and Fe – y mol.

Then the mass of Mg will be 24x, and Fe – 56y. The mass of the mixture is 0.4 g. We obtain the equation

24 x + 56y = 0.4 g.

x + y = 0.01.

Let’s solve the system of equations.

{x + y = 0.01.

{24 x + 56y = 0.4.

x = 0.01 – y.

24 (0.01 – y) + 56y = 0.4.

0.24 – 24y + 56 y = 0.4.

0.24 – 0.4 = 24 y – 56 y.

– 0.16 = – 32 y.

y = -0.16: (- 32),

y = 0.005.

x = 0.01 – 0.005 = 0.005.

n (Mg) = 0.005 mol.

n (Fe) = 0.005 mol.

Let’s find the mass of Mg and Fe.

m = nM.

M (Mg) = 24 g / mol.

M (Fe) = 56 g / mol.

m (Mg) = 24 g / mol × 0.005 g / mol = 0.12 g.

m (Fe) = 56 g / mol × 0.005 g / mol = 0.28 g.

w (Mg) = (0.12: 0.4) × 100% = 30%

w (Fe) = (0.28: 0.4) × 100% = 70%.

Answer: 30%; 70%.