Question

A sample of gallium bromide, GaBr₃, weighing 0.165 g was dissolved in water and treated with silver nitrate, AgNO₃, resulting in the precipitation of 0.299 g AgBr. Use these data to compute the %Ga (by mass) GaBr₃.

a) 36.0%
b) 43.8%
c) 57.3%
d) 62.1%

Answer 1

To find the %Ga by mass in GaBr₃, we determine the molar masses and use stoichiometry to convert the mass of AgBr precipitated to moles of Ga in GaBr₃. Calculating this gives a percentage of 22.4%, which is not among the provided answer choices.

Step-by-step explanation:

To determine the %Ga (by mass) in GaBr₃, we first need to find the molar mass of GaBr₃ and AgBr. Gallium (Ga) has an atomic mass of approximately 69.72 g/mol; bromine (Br) has an atomic mass of approximately 79.90 g/mol. Therefore, GaBr₃ has a molar mass of 69.72 g/mol + 3(79.90 g/mol) = 309.42 g/mol. Silver (Ag) has an atomic mass of approximately 107.87 g/mol, and the molar mass of AgBr is 107.87 g/mol + 79.90 g/mol = 187.77 g/mol.

The chemical reaction is GaBr₃ + 3AgNO₃ → 3AgBr + Ga(NO₃)₃. So, each mole of GaBr₃ produces three moles of AgBr. By using stoichiometry, we can convert the mass of AgBr precipitated to moles of GaBr₃.

0.299 g AgBr × (1 mol AgBr / 187.77 g AgBr) × (1 mol GaBr₃ / 3 mol AgBr) = 5.31 x 10⁻⁴ mol GaBr₃. Now we can find the mass of Ga in the sample: 5.31 x 10⁻⁴ mol GaBr₃ × (1 mol Ga / 1 mol GaBr₃) × 69.72 g/mol Ga = 0.0370 g Ga.

Finally, the percentage of Ga by mass in the sample is (0.0370 g Ga / 0.165 g GaBr₃) × 100 = 22.4%, which is not listed as an option, indicating there may be a mistake in the question or the solutions provided.