Question 3.FP.1: When heated in air some element, X, reacts with the oxygen p...
When heated in air some element, X, reacts with the oxygen present to form an oxide with the chemical formula, X_{2}O_{3}. If a 0.5386-g sample of this unknown element yields an oxide with a mass of 0.7111 g, describe how you would determine the atomic mass of the element.
Strategy
Chemical formulas are expressed in terms of numbers of particles. In this problem, we have to start with masses and somehow infer information about the numbers of particles. We did a similar problem in this chapter: the determination of an empirical formula from percentage by mass data. In this case, with the experiment described, we can determine the mass information for each element in the unknown compound—providing the same type of data we had from percentage mass calculations. Then, because we know the empirical formula and we know the molar mass of the oxygen, we can determine the molar mass of the unknown metal.
First we would determine the mass composition. The amount of the metal in the oxide sample must be assumed to be the 0.5386 g that was used to generate the oxide. Subtracting this value from the 0.7111 g of the oxide sample then provides the mass of the oxygen. The mass of oxygen can be converted to moles of oxygen using the molar mass (which could be looked up if we don’t know it). Then, we could use the mole ratio from the empirical formula given in the problem to assert that whatever value we obtain, the number of moles of metal would be two-thirds of this result. (This follows from the fact that there are two metal atoms for every three oxygen atoms.) Then, we would have a value for the number of moles of the metal and the mass of the metal in the sample—taking the ratio provides the molar mass, from which we could use a periodic table to look up the identity of the metal.