On combustion of 15.4 g of a mixture of magnesium and zinc, 20.2 g of a mixture of reaction products

On combustion of 15.4 g of a mixture of magnesium and zinc, 20.2 g of a mixture of reaction products were formed. Determine the mass fractions of magnesium and zinc in the initial mixture.

Given:
m mixture (Mg, Zn) = 15.4 g
m mixture (MgO, ZnO) = 20.2 g

To find:
ω (Mg) -?
ω (Zn) -?

Decision:
1) 2Mg + O2 => 2MgO;
2Zn + O2 => 2ZnO;
2) Let m (Mg) = (x) r, then m (Zn) = (15.4 – x) r;
3) n (Mg) = m (Mg) / M (Mg) = (x / 24) mol;
4) n (MgO) = n (Mg) = (x / 24) mol;
5) m (MgO) = n (MgO) * M (MgO) = (x / 24) * 40 = (5x / 3) g;
6) n (Zn) = m (Zn) / M (Zn) = ((15.4 – x) / 65) mol;
7) n (ZnO) = n (Zn) = ((15.4 – x) / 65) mol;
8) m (ZnO) = n (ZnO) * M (ZnO) = (((15.4 – x) / 65) * 81) g;
9) m mixture (MgO, ZnO) = m (MgO) + m (ZnO);
20.2 = (5x / 3) + (((15.4 – x) / 65) * 81);
x = 2.4;
m (Mg) = x = 2.4 g;
10) ω (Mg) = m (Mg) * 100% / m mixture (Mg, Zn) = 2.4 * 100% / 15.4 = 15.6%;
11) ω (Zn) = 100% – ω (Mg) = 100% – 15.6% = 84.4%.

Answer: The mass fraction of Mg is 15.6%; Zn – 84.4%.