A compound is created that is known to contain only aluminum and sulfur and has a chemical formula of Al2S3. If you obtain an 8.60g sample of the compound, how many atoms of sulfur would you have?

Question

This is a high school chemistry problem, grade 10.

Answer 1

To solve this problem, let's start at the level of molecule, work our way out to the given mass, and then work our way back down to the sulfur atoms.

When we talk about the number of molecules or atoms, the way we usually do this is by relating it somehow to Avogadro's number: 6.022 * 10²³ / mol

Therefore, the number of molecules of the problem's compound found in a mole of the compound will be 6.022 * 10²³. The number of sulfur atoms per molecule of the compound is 3, given by the compound's formula. Therefore, the number of sulfur atoms in a mole of the compound will be 18.066 * 10²³ - or, more conventionally, 1.8066 * 10²⁴ sulfur atoms/ mol.

So, now we've got the number of atoms related to the number of moles, as well as a mass that has been given to us in the problem. The way the two relate are a molar mass. The molar mass of an element is found in the periodic table, but we need the molar mass of this compound. To do that, we'll calculate the molar mass of aluminum times 2 and the molar mass of sulfur times 3 and add them together. This is approximately:

2 * 26.982 + 3 * 32.065 = 53.964 + 96.195 = 150.159 g/mol

We can use unit conversions now to arrive at our final answer, starting with the given mass in the equation:

(8.60 g Al₂S₃) * (1 mol Al₂S₃ / 150.159 g Al₂S₃) * (1.8066 * 10²⁴ sulfur atoms / 1 mol Al₂S₃).

(Notice that we flipped the molar mass fraction in the middle to make sure that units cancel appropriately when we multiply, to get us to the correct units in the final answer.)

Completing this multiplication, we find that in the given mass of the compound there are 0.10347 * 10²⁴ - or, more conventionally, 1.0347 * 10²³ - sulfur atoms in the given mass of the compound. We must, finally, adjust this for the number of significant figures (or significant digits) in the mass that we were given in the problem. Because there are 3 significant figures in the number '8.60', there must be 3 significant figures in the final answer. Rounding the answer above to 3 significant figures gives us 1.03 * 10²³ sulfur atoms in the given mass of Al₂S₃.