The problem has an insufficient data. For the purpose of answering the problem, I've searched for the missing data. "Measurements also show that a certain sample of the unknown compound contains 2.8mol of phosphorus and 8.08mol of chlorine. Write the complete chemical formula for the unknown compound."
To determine the complete chemical formula for the unknown compound, we need to divide each given moles with the least number of moles in the compound (i.e. 2.8 moles of P). Dividing the 8.08 moles of Cl with 2.8 moles of P would give us 2.9. Rounding this value would give us 3. This means 3 moles of Chlorine comprises the unknown compound. That's why Cl3. Same thing is done to get the number of Phosphorous in the compound (i.e. 2.8 moles P/2.8 moles). This would give us the value of 1. Therefore, x = 1. The unknown compound is PCl3 (Phosphorous Trichloride).
If the missing data is correct, then our answer is deemed correct as well.
