An impure sample containing an unknown amount of gallium bromide, GaBr3, weighs 0.379 g. It was dissolved in water and treated with silver nitrate, AgNO3, resulting in the precipitation of 0.263 g AgBr. Assuming that GaBr3 is the only source of gallium in the sample, use this data to compute the percent Ga by mass in the sample.
To compute the percent Ga by mass in the sample, we need to determine the amount of GaBr3 in the sample and then calculate its mass as a percentage of the total sample mass.
First, we need to find the mass of GaBr3 in the sample. We know that 0.263 g of AgBr was precipitated. Since the stoichiometric ratio between GaBr3 and AgBr is 1:3, we can calculate the amount of GaBr3 using the molar masses:
1 mol AgBr = 187.77 g
1 mol GaBr3 = (1 x 69.72) + (3 x 79.90) = 309.22 g
0.263 g AgBr * (1 mol AgBr / 187.77 g AgBr) * (1 mol GaBr3 / 3 mol AgBr) * (309.22 g GaBr3 / 1 mol GaBr3) = 0.0387 g GaBr3
Now we have the mass of GaBr3, which is 0.0387 g. The percent Ga by mass in the sample can be determined by dividing the mass of GaBr3 by the mass of the sample and multiplying by 100.
Percent Ga = (0.0387 g GaBr3 / 0.379 g sample) * 100 = 10.2%
Therefore, the sample contains approximately 10.2% Ga by mass.