Complete Question:
You have a 275 mg sample of a compound that contains aluminum and a group 7A element (F, Cl, Br, I or At). This compound reacts with excess silver nitrate as follows (“X” represents the unknown element): AlX3 + 3 AgNO3 → 3 AgX + Al(NO3)3. This reaction forms 581 mg of AgX. Identify element X.
Answer:
Br
Step-by-step explanation:
By the stoichiometry of the reaction, 1 mol of AlX3 will form 3 moles of AgX. If we call the molar mass of X as m, and by the periodic table the molar masses of Al is 26.982 g/mol, and of Ag is 107.87, thus the molar masses of the compounds will be:
AlX3 = 26.982 + 3m
AgX = 107.87 + m
And the mass relationship will be the number of moles multiplied by the molar mass. So, by a simple direct rule of three:
26.982 + 3m g of AlX3 ------------- 3*(107.87 + m) g of AgX
275 mg of AlX3 ----------- 581 mg
825*(107.87 + m) = 15676.542 + 1743m
88992.75 + 825m = 15676.542 + 1743m
-918m = -73316.208
m = 79.86 g/mol
So, comparing with the values of the masses of the group 7 elements, X must be Br (79.904 g/mol).