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Chapter 9: Problem 101

The compound \(\mathrm{P}_{4} \mathrm{O}_{10}\) has an empirical formula of \(\mathrm{P}_{2} \mathrm{O}_{5} .\) By what factor will the percent by mass composition differ for each element between these two formulas? Explain your answer.

Short Answer

Expert verified
The percent by mass composition for each element in both the molecular formula (P4O10) and its empirical formula (P2O5) is the same (P - 43.64%, O - 56.36%). Therefore, the factor by which the percent by mass composition differs for each element between these two formulas is 1, meaning there is no difference.

Step by step solution

01

Determine the molar mass of each formula

First, we need to determine the molar mass of each formula: For P2O5: Molar mass of P: \(2\times30.97\text{ g/mol} = 61.94\text{ g/mol}\) Molar mass of O: \(5\times16.00\text{ g/mol} = 80.00\text{ g/mol}\) Total molar mass for P2O5: \(61.94\text{ g/mol} + 80.00\text{ g/mol} = 141.94\text{ g/mol}\) For P4O10: Molar mass of P: \(4\times30.97\text{ g/mol} = 123.88\text{ g/mol}\) Molar mass of O: \(10\times16.00\text{ g/mol} = 160.00\text{ g/mol}\) Total molar mass for P4O10: \(123.88\text{ g/mol} + 160.00\text{ g/mol} = 283.88\text{ g/mol}\)
02

Calculate the percent by mass composition for each formula

Next, we need to calculate the percent by mass composition for both formulas: For P2O5: Percent by mass of P: \(\frac{61.94\text{ g/mol}}{141.94\text{ g/mol}} \times 100 = 43.64\%\) Percent by mass of O: \(\frac{80.00\text{ g/mol}}{141.94\text{ g/mol}} \times 100 = 56.36\%\) For P4O10: Percent by mass of P: \(\frac{123.88\text{ g/mol}}{283.88\text{ g/mol}} \times 100 = 43.64\%\) Percent by mass of O: \(\frac{160.00\text{ g/mol}}{283.88\text{ g/mol}} \times 100 = 56.36\%\)
03

Determine the difference between the percent by mass composition

As we can see from the above calculations, the percent by mass composition for each element in both formulas is: P2O5: P - 43.64%, O - 56.36% P4O10: P - 43.64%, O - 56.36% Both the molecular formula (P4O10) and its empirical formula (P2O5) have the same percent by mass composition for each element (P and O). Therefore, the factor by which the percent by mass composition differs for each element between these two formulas is 1, meaning there is no difference.

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Most popular questions from this chapter

Ethylene glycol, used for antifreeze, has the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\). Calculate the mass percent of each element in ethylene glycol.

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