Answer:
Tin: 54.3%
Zinc: 45.7%
Step-by-step explanation:
The molar masses of the elements are:
Tin: Sn = 117.710 g/mol
Zinc: Zn = 65.409 g/mol
Fluorine: F = 18.998 g/mol
The fluorine gas in excess, so the reaction consumes all the alloy, and all the tin is converted to SnF₄ and all the zinc is converted to ZnF₂. The molar masses of the fluorides are:
SnF₄ = 117.710 + 4*18.998 = 193.702 g/mol
ZnF₂ = 65.409 + 2*18.998 = 103.405 g/mol
If we call x the number of moles of SnF₄, and y the number of moles of ZnF₂, the total mass can be calculated knowing that the mass is the number of moles multiplied by the molar mass:
193.702x + 103.405y = 2.489
The number of moles of Sn is the same as SnF₄ (1:1), and also the number of moles of Zn is the same as ZnF₂ (1:1), so the mass of the alloy:
117.710x + 65.409y = 1.540
if we multiply it by -1.581 and sum with the other equation:
117.710x*(-1.581) + 65.409y*(-1.581) + 193.702x + 103.405y = 1.540*(-1.581) + 2.489
7.60249x = 0.05426
x = 0.0071 mol of Sn
117.710*0.0071 + 65.409y = 1.540
65.409y = 0.704259
y = 0.0108 mol of Zn
The masses are the molar mass multiplied by the number of moles:
Sn: 117.710*0.0071 = 0.836 g
Zn: 65.409*0.0108 = 0.704 g
The percent composition is the mass of the substance divided by the total mass multiplied by 100%:
Sn: (0.836/1.540)*100% = 54.3%
Zn: (0.704/1.540)*100% = 45.7%