Question

If \(45.0 \mathrm{~g}\) of \(\mathrm{C}_{6} \mathrm{H}_{6}\) and \(60.0 \mathrm{~g}\) of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\) are mixed together, what is the mole fraction of each component?

Short answer

Mole fraction of \(C_6H_6\) is 0.469 and \(C_6H_5CH_3\) is 0.531.

Step-by-step solution

Calculate moles of C6H6

First, determine the number of moles of benzene (C_{6}H_{6}) using its molar mass, which is approximately 78.11 g/mol. Use the formula: \( ext{moles} = \frac{\text{mass}}{\text{molar mass}} \). Thus, \( ext{moles of } C_{6}H_{6} = \frac{45.0\, \text{g}}{78.11\, \text{g/mol}} \approx 0.576\, \text{mol} \).

Calculate moles of C6H5CH3

Next, calculate the moles of toluene (C_{6}H_{5}CH_{3}). Its molar mass is approximately 92.14 g/mol. Use the same formula: \( ext{moles} = \frac{\text{mass}}{\text{molar mass}} \). Hence, \( ext{moles of } C_{6}H_{5}CH_{3} = \frac{60.0\, \text{g}}{92.14\, \text{g/mol}} \approx 0.651\, \text{mol} \).

Calculate total moles

Add the moles of both components together to find the total number of moles in the mixture. So, \( ext{total moles} = 0.576\, \text{mol} + 0.651\, \text{mol} = 1.227\, \text{mol} \).

Calculate mole fraction of C6H6

To find the mole fraction of benzene, divide the moles of benzene by the total moles in the mixture. Therefore, \( X_{C_{6}H_{6}} = \frac{0.576\, \text{mol}}{1.227\, \text{mol}} \approx 0.469 \).

Calculate mole fraction of C6H5CH3

For the mole fraction of toluene, divide its moles by the total moles. Thus, \( X_{C_{6}H_{5}CH_{3}} = \frac{0.651\, \text{mol}}{1.227\, \text{mol}} \approx 0.531 \).

Key concepts

Moles Calculation

Calculating moles is a fundamental concept in chemistry that aids in quantifying the amount of a substance. The number of moles of a particular substance can be determined using the formula:

• \(\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\)

This formula requires knowing the mass of the substance and its molar mass, which is the weight of one mole of a compound calculated in grams per mole.

For instance, to determine the moles of benzene in a mixture, identify its mass and molar mass. If benzene has a mass of 45.0 g and its molar mass is 78.11 g/mol, the number of moles would be \(\frac{45.0}{78.11} \approx 0.576\) moles.

Similarly, for toluene with a mass of 60.0 g and a molar mass of 92.14 g/mol, the moles would be \(\frac{60.0}{92.14} \approx 0.651\) moles. Such calculations help you understand the quantity of each component in a molecular mix.

Benzene

Benzene, represented by the chemical formula \(\text{C}_{6}\text{H}_{6}\), is one of the simplest aromatic hydrocarbons and a crucial building block in organic chemistry. Recognized for its stable ring structure, benzene consists of six carbon atoms bonded in a ring, with alternating double bonds, and each carbon is bonded to a single hydrogen atom.

Benzene's molar mass is approximately 78.11 g/mol, which is essential in calculating its mole fraction when combined with other substances like toluene. Despite its simple structure, benzene is quite significant due to its properties and uses. It serves as a precursor in the manufacture of plastics, resins, synthetic fibers, rubber lubricants, dyes, detergents, and drugs.

• Highly flammable with a sweet odor
• Commonly used as a solvent in labs
• Has implications in health and safety due to its carcinogenic nature

Toluene

Toluene, known in scientific terms as \(\text{C}_{6}\text{H}_{5}\text{CH}_3\), is a clear, volatile liquid carrying a distinct sweet smell. A derivative of benzene, it carries a methyl group replacing one hydrogen atom in the benzene ring. This structure enhances its chemical stability and increases the molecular weight, giving it a molar mass of around 92.14 g/mol.

Toluene is used extensively in the industrial sector due to its versatile solvent properties. It's often found in paint thinners, nail polish removers, and is also involved in the production of chemical products like polyurethane and TNT (trinitrotoluene). This compound participates in complex reaction mechanisms which renders it a vital substance in labs and manufacturing.

• Important solvent used across different sectors
• Less toxic compared to benzene but requires careful handling
• Involved in making various chemicals and materials

Its calculated mole fraction, when mixed with benzene, is crucial to understand the solution's overall composition by dividing the calculated moles by the total number of moles in the mixture.