How do I compute percent compound in a mixture, given mixture mass and element percents?

If I have 10 g of a solution made up of PCl₃ and PCl₅ and 81.04% of the mixture by mass is due to Cl, how many grams of PCl₃ and PCl₅ is there? I don't think there is enough information here!
Ed Tremblay 11/22/99

There are two unknowns (grams of PCl₃ and grams of PCl₅) so you'll have to write two independent equations to solve the problem. If there's nothing in the mixture but PCl₃ and PCl₅,

10 g = grams of PCl₃ + grams of PCl₅

You know that 81.04% of the mass of the mixture is Cl, so there are a total of 8.104 g of Cl in the sample. The total mass of chlorine has to be equal to the mass of Cl in the PCl₃ plus the mass of Cl in the PCl₅. 77.45% of PCl₃ and 85.13% of PCl₅ is chlorine, so:

8.104 g Cl = 0.7745 × g of PCl₃ + 0.8513 × g of PCl₅

Now all you have to do is solve the two equations simultaneously (e. g. solve the first equation for PCl₃ and substitute the result into the second equation). Can you take it from here?

Author: Fred Senese senese@antoine.frostburg.edu

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