Problem 30 - Chemistry in 30 days

Question

In a solution of \(7.8 \mathrm{~g}\) of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and \(46 \mathrm{~g}\) of toluene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\right)\), the mole frac of benzene is (a) \(1 / 6\) (b) \(1 / 5\) (c) \(1 / 2\) (d) \(1 / 3\)

Step-by-Step Solution

Answer

(a) \(1/6\)

Step 1: Finding Moles of Benzene

First, we need to calculate the moles of benzene, which has a molecular formula of \(\mathrm{C}_6\mathrm{H}_6\). Its molar mass is calculated as: \(6 \times 12.01 + 6 \times 1.01 = 78.12\,\mathrm{g/mol}\). So, the moles of benzene are \(\frac{7.8}{78.12} = 0.1\) moles.

Step 2: Finding Moles of Toluene

Next, calculate the moles of toluene, with a molecular formula of \(\mathrm{C}_6\mathrm{H}_5\mathrm{CH}_3\). Its molar mass is \(7 \times 12.01 + 8 \times 1.01 = 92.14\,\mathrm{g/mol}\). Therefore, the moles of toluene are \(\frac{46}{92.14} = 0.5\) moles.

Step 3: Calculating Total Moles

Add the moles of benzene and toluene to find the total moles: \(0.1 + 0.5 = 0.6\) moles.

Step 4: Finding Mole Fraction of Benzene

The mole fraction of benzene is the ratio of the moles of benzene to the total moles of the mixture: \(\frac{0.1}{0.6} = \frac{1}{6}\).

Step 5: Select the Correct Answer

Based on our calculations, the mole fraction of benzene is \(\frac{1}{6}\). Therefore, the correct answer is (a) \(1/6\).

Key Concepts

Moles Calculation

Calculating moles is an essential part of chemistry that allows us to understand how different substances interact at the molecular level. The mole is a basic unit in chemistry that represents a specific number of molecules or atoms, typically Avogadro's number, which is approximately \(6.022 imes 10^{23}\).
The formula for calculating the number of moles \(n\) of a substance given its mass \(m\) and molar mass \(M\) is:

• \[ n = \frac{m}{M} \]

The process involves dividing the mass of the substance by its molar mass. This calculation helps chemists convert a mass measurement into a count of actual molecules or atoms, facilitating stoichiometric calculations in chemical reactions.

Molecular Mass

Molecular mass is a critical concept when dealing with chemical substances. It is the sum of the atomic masses of all the atoms in a molecule. For diatomic molecules such as benzene (\(\mathrm{C}_6\mathrm{H}_6\)), this requires summing the atomic masses of carbon and hydrogen atoms:

• Carbon (C) has an atomic mass of approximately \(12.01 \, \mathrm{u}\).
• Hydrogen (H) has an atomic mass of approximately \(1.01 \, \mathrm{u}\).

For benzene, the calculation is:

• \[ \text{Molecular mass of benzene} = 6 \times 12.01 + 6 \times 1.01 = 78.12 \, \mathrm{g/mol} \]

Similarly, the molecular mass for toluene (\(\mathrm{C}_6\mathrm{H}_5\mathrm{CH}_3\)) can be calculated by considering both carbon and hydrogen atoms:

• \[ \text{Molecular mass of toluene} = 7 \times 12.01 + 8 \times 1.01 = 92.14 \, \mathrm{g/mol} \]

Understanding molecular mass allows chemists to perform precise conversions between mass and moles.

Benzene

Benzene is a well-known aromatic hydrocarbon with the formula \(\mathrm{C}_6\mathrm{H}_6\). It forms the basis for various organic compounds due to its stable ring structure bonded by alternating double and single bonds, known as an aromatic ring. This gives benzene unique chemical properties, such as resonance stability.

• Benzene is a colorless liquid with a sweet odor and is highly flammable.
• It is used as a precursor in the synthesis of various chemicals and materials, like plastics and resins.
• Benzene is crucial for producing substances that form the backbone of modern industry, although it is toxic if not handled properly.

Its role in organic chemistry is vast, making understanding benzene essential for students learning about molecular interactions.

Toluene

Toluene, also an aromatic hydrocarbon, is similar to benzene but with a methyl group (\(\mathrm{CH}_3\)) attached, giving it the formula \(\mathrm{C}_6\mathrm{H}_5\mathrm{CH}_3\). Toluene is a clear, water-insoluble liquid with a distinctive smell. It is widely used in industry and chemistry:

• Toluene serves as an excellent solvent for paints, coatings, rubbers, and resins due to its ability to dissolve substances that water cannot.
• In addition to being a solvent, toluene is crucial in the production of benzene and isocyanates, which are used to make polyurethane.
• It also exhibits good blending power, enhancing gasoline characteristics and performance.

Toluene's application in industry underscores its importance, but like benzene, handling toluene requires caution due to its toxic effects.