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):

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.

Br

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).