Problem 74 - Chemistry: An Atoms-Focused Approach

Question

What is the volume of 1.00 mol of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) at \(20^{\circ} \mathrm{C} ?\) The density of benzene at \(20^{\circ} \mathrm{C}\) is \(0.879 \mathrm{g} / \mathrm{mL}\)

Step-by-Step Solution

Answer

Answer: The volume of 1.00 mol of benzene at 20°C is 88.86 mL.

Step 1: Calculate the molecular weight of benzene

To find the molecular weight of benzene (C6H6), we will add the atomic weights of all the carbon and hydrogen atoms in the molecule. The atomic weight of carbon is 12.01 g/mol, and hydrogen is 1.008 g/mol. Therefore, the molecular weight of benzene is: Molecular weight = (6 * 12.01) + (6 * 1.008) = 72.06 + 6.048 = 78.108 g/mol

Step 2: Calculate the mass of 1.00 mol of benzene

Using the molecular weight of benzene, we can now find the mass of 1.00 mol of benzene: Mass = (Moles of benzene) * (Molecular weight of benzene) Mass = (1.00 mol) * (78.108 g/mol) = 78.108 g

Step 3: Calculate the volume of 1.00 mol of benzene at 20°C

Using the given density of benzene at 20°C, we can now convert the mass to volume: Volume = (Mass of benzene) / (Density of benzene at 20°C) Volume = (78.108 g) / (0.879 g/mL) = 88.86 mL Hence, the volume of 1.00 mol of benzene at 20°C is 88.86 mL.

Key Concepts

Molecular Weight

Molecular weight, also known as molecular mass, is the sum of the atomic masses of all atoms in a molecule. It is an important concept in chemistry. This allows us to convert between grams and moles, a unit crucial for chemical reactions.

For benzene (\( C_6H_6 \), the molecular weight is found by adding the atomic weights of its constituent atoms. Carbon (\( C \)) has an atomic weight of 12.01 g/mol and hydrogen (\( H \)) has an atomic weight of 1.008 g/mol. Consequently, the molecular weight of benzene is calculated as:

• 6 carbons: \( 6 \times 12.01 = 72.06 \, \text{g/mol} \)
• 6 hydrogens: \( 6 \times 1.008 = 6.048 \, \text{g/mol} \)

Adding these values gives us the total molecular weight: \( 78.108 \, \text{g/mol} \).

This knowledge helps in understanding how much one mole of benzene, or any substance, weighs. It is a basic yet fundamental step in finding further properties like volume when density is known.

Molar Volume

The concept of molar volume refers to the volume that one mole of a substance occupies. Knowing the molar volume is particularly useful for gases, but it is equally applicable to liquids and solids.

In this exercise, to find the molar volume of benzene, we determined the mass of one mole of benzene, which is 78.108 grams. We then used the density of benzene, 0.879 g/mL, to find its volume:

• Density equation: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \)
• Rearranged to find Volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \)
• Plugging in our values: \( \text{Volume} = \frac{78.108 \, \text{g}}{0.879 \, \text{g/mL}} = 88.86 \, \text{mL} \)

This result means that at 20°C, one mole of benzene takes up 88.86 milliliters. Understanding molar volume helps us compare different substances. It also aids in chemical equation scaling and industrial applications where quantities are large.

Benzene

Benzene is a fundamental organic chemical compound with the formula \( C_6H_6 \). It consists of a ring structure of six carbon atoms, each bonded to one hydrogen atom. This cyclic arrangement is known as an aromatic ring, and benzene is the simplest aromatic hydrocarbon.

Benzene is known for its stability and unique properties due to its resonance structures. In chemistry, it serves as a building block for more complex molecules. It's utilized in industries for the production of various materials, including plastics and synthetic fibers.

At room temperature, benzene is a liquid, and understanding its physical properties like density and molar volume, as outlined in the exercise, is crucial when handling and using it. It's also a key study molecule for understanding organic chemistry principles such as electrophilic aromatic substitution reactions. However, benzene is hazardous. It is important to handle benzene with care, as it is carcinogenic and must be used under strict safety guidelines.