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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