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Chapter 13: Problem 31

A solution is prepared by mixing \(1.28 \mathrm{mol} \mathrm{C}_{7} \mathrm{H}_{16}\) \(2.92 \mathrm{mol} \mathrm{C}_{8} \mathrm{H}_{18},\) and \(2.64 \mathrm{mol} \mathrm{C}_{9} \mathrm{H}_{20} .\) What is the (a) mole fraction and (b) mole percent of each component of the solution?

Short Answer

Expert verified
The mole fraction of the components are approximately 0.187 for \(C_{7}H_{16}\), 0.427 for \(C_{8}H_{18}\), and 0.386 for \(C_{9}H_{20}\). The mole percent of the components approximates to 18.7% for \(C_{7}H_{16}\), 42.7% for \(C_{8}H_{18}\), and 38.6% for \(C_{9}H_{20}\).

Step by step solution

01

Calculate Total Number of Moles

Firstly, calculate the total number of moles in the mixture by adding the number of moles of each component. This is done as: \(1.28 \, mol \, C_{7}H_{16} + 2.92 \, mol \, C_{8}H_{18} + 2.64 \, mol \, C_{9}H_{20} = 6.84 \, mol\) total.
02

Calculate Mole Fraction

Secondly, calculate the mole fraction of each component by dividing the number of moles of the component by the total number of moles in the mixture. For \(C_{7}H_{16}\): \(\frac{1.28 \, mol}{6.84 \, mol} = 0.187\). For \(C_{8}H_{18}\): \(\frac{2.92 \, mol}{6.84 \, mol} = 0.427\). For \(C_{9}H_{20}\): \(\frac{2.64 \, mol}{6.84 \, mol} = 0.386\)
03

Calculate Mole Percent

Thirdly, calculate the mole percent of each component by multiplying the mole fraction by 100. For \(C_{7}H_{16}\): \(0.187 * 100 = 18.7\% \). For \(C_{8}H_{18}\): \(0.427 * 100 = 42.7\% \). For \(C_{9}H_{20}\): \(0.386 * 100 = 38.6 \% \)

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