Answer:
The answer is
The percentage by mass of Aluminium is 62.479% Al
The percentage by mass of Magnesium is 37.52% Mg
Explanation:
The solution to this can be found by listing out the known variables
mass of alloy = 9.87 grams
Mass of hydrogen gas produced = 0.998 grams
Molar mass of Al = 26.98 g/mol
Molar mass of Mg = 24.3 g/mol
Molar mass of H₂(g) = 2.016 g/mol
The reaction between aluminium, magnesium and HCl aare as follows
2Al(s) + 6HCl(aq) → 2AlCl₃(aq) + 3H₂(g)
Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)
From the quation for the reactions, it is seen that 2 moles of Al produces 3 moles of H₂(g) thus if the mass of aluminium in the alloy is say x we have
2×x/26.98 moles of Aluminium produces 3×x/26.98 moles of H₂
or one mole produces 0.0555967x moles H₂ (g)
Also 1 mole of magnesium produces 1 mole of H₂(g)
hence since the mass of magnesium in the sample is (9.87 - x) grams, we have
(9.87-x)/24.3 moles of Mg produces (9.87 - x)/24.3 moles of H₂(g)
However the number of moles of H₂ actually produced = 0.998/2.016 = 0.495 moles H₂
Therefore 0.0555967x moles + (9.87 - x)/24.3 moles = 0.495 moles
or 0.0555967x + 0.4062 - 0.04115x = 0.495
0.0144x = 0.0888 , Terefore x = 6.16 grams
and the percentage by mass of Al in the alloy is
6.16/9.87 × 100 = 62.479% Al and
(100 - 62.47) or 37.52% Mg
The percentage by mass of Aluminium is 62.479% Al
The percentage by mass of Magnesium is 37.52% Mg
