Zinc and magnesium metal each reacts with hydrochloric acid to make chloride salts of the respective metals, and hydrogen gas. a 11.20-g mixture of zinc and magnesium produces 0.6854 g of hydrogen gas upon being mixed with an excess of hydrochloric acid. determine the percent magnesium by mass in the original mixture.

M=11.20 g

m (H₂) = 0.6854 g

M (H₂) = 2.016 g/mol

M (Mg) = 24.305 g/mol

M (Zn) = 65.39 g/mol

w-?

m (Mg) = wm

m (Zn) = (1-w) m

Zn + 2HCl = ZnCl₂ + H₂

m₁ (H₂) = M (H₂) m (Zn) / M (Zn) = M (H₂) (1-w) m/M (Zn)

Mg + 2HCl = MgCl₂ + H₂

m₂ (H₂) = M (H₂) m (Mg) / M (Mg) = M (H₂) wm/M (Mg)

m (H₂) = m₁ (H₂) + m₂ (H₂)

m (H₂) = M (H₂) (1-w) m/M (Zn) + M (H₂) wm/M (Mg) = M (H₂) m{ (1-w) / M (Zn) + w/M (Mg) }

m (H₂) = M (H₂) m{ (1-w) / M (Zn) + w/M (Mg) }

(1-w) / M (Zn) + w/M (Mg) = m (H₂) / {M (H₂) m}

1/M (Zn) - w/M (Zn) + w/M (Mg) = m (H₂) / {M (H₂) m}

w (1/M (Mg) - 1/M (Zn)) = m (H₂) / {M (H₂) m}-1/M (Zn)

w=[m (H₂) / {M (H₂) m}-1/M (Zn) ] / (1/M (Mg) - 1/M (Zn))

w=0.583 (58.3%)