In order to solve this problem, you will also need to know the percent by mass of the other element in the compound. The percent by mass of the other element should be given in your question.
Example: Given the compound, `~XS_2` , determine the mass of element X. The compound is 40.064% S by mass. "X" is the unknown element in the compound.
Step 1: Determine the grams of elements X and S.
Grams of S: Assume that you have a 100 g sample of compound `~XS_2` . Since `~XS_2` is 40.064% S, there would be 40.064 g of S in a 100 g sample.
Grams of X: Grams of X can be calculated by subtracting grams of S from 100 g.
(100 g `~XS_2` ) - (40.064 g S) = 59.936 g X
Step 2: Determine the moles of the known element S.
In order to convert grams of S to moles, multiply grams of S by the conversion factor, 1 mole S = 32.065 g S. 32.065 g is the atomic mass of S as shown in the periodic table.
(40.064 g S)(1 mol S/32.065 g S) = 1.2495 mol S
*Notice that the conversion factor is oriented such that the unit "grams" is on the bottom - this enables you to cancel out gram units and be left in units of moles.
Step 3: Set up a mole ratio to determine the moles of unknown element X.
Notice that the ratio of subscripts in the compound `~XS_2` is 1 M:2 S. This means that the ratio of moles of element M to moles of element S in the compound is 1:2. Set up equivalent mole ratios as shown below.
(? mol X/1) = (1.2495 mol S/2)
Rearrange the equation or "cross-multiply" to solve for unknown moles of X.
? mol X = [(1.2495 mol S)(1)]/2
? mol X = 0.62475 mol X
Step 4: Determine the atomic mass of unknown element X by dividing grams of element X (from Step 1) by moles of element X (from Step 3).
(59.936 g X)/(0.62475 mol X) = 95.936 g/mol
The element in the periodic table with this mass is molybdenum (Mo). Therefore, the formula of the compound is `~MoS_2`
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