Problem 6 - Chemistry and Chemical Reactivity

Question

The specific heat capacity of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is \(1.74 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .\) What is its molar heat capacity (in \(\mathrm{J} / \mathrm{mol} \cdot \mathrm{K}) ?\)

Step-by-Step Solution

Answer

The molar heat capacity of benzene is \(135.93 \text{ J/mol} \cdot \text{K}\).

Step 1: Understand the Definitions

Specific heat capacity is the heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). Molar heat capacity is the heat required to raise the temperature of one mole of a substance by one degree Celsius (or one Kelvin).

Step 2: Find the Molar Mass of Benzene

Benzene (\(\mathrm{C}_6\mathrm{H}_6\)) has a molar mass calculated by adding the atomic masses of carbon and hydrogen. The atomic mass of carbon is about 12.01 g/mol, and hydrogen is about 1.01 g/mol.\[\text{Molar mass of benzene} = (6 \times 12.01) + (6 \times 1.01) = 78.12 \text{ g/mol}\]

Step 3: Convert Specific Heat to Molar Heat Capacity

To find the molar heat capacity, multiply the specific heat capacity by the molar mass of benzene.\[\text{Molar heat capacity} = 1.74 \text{ J/g} \cdot \text{K} \times 78.12 \text{ g/mol}\]\[\text{Molar heat capacity} = 135.93 \text{ J/mol} \cdot \text{K}\]

Step 4: Present the Solution

The molar heat capacity of benzene is \(135.93 \text{ J/mol} \cdot \text{K}\). This is the amount of heat required to raise the temperature of one mole of benzene by one Kelvin.

Key Concepts

Understanding Specific Heat Capacity

Specific heat capacity is a fundamental concept in thermodynamics. It describes how much heat energy is needed to change the temperature of a substance. For benzene, this specific heat capacity is given as \(1.74 \text{ J/g} \cdot \text{K}\), meaning that it takes \(1.74\) joules of energy to raise the temperature of one gram of benzene by one degree Kelvin.

Specific heat capacity is vital because it varies for different materials. Water, for example, has a very high specific heat capacity. This means it requires more energy to heat up compared to substances with lower specific heat capacities like metal.

It's a key player in controlling temperature changes, especially in chemical reactions and industrial processes where knowing the amount of heat energy involved is crucial.

• Measured in \(\text{J/g} \cdot \text{K}\)
• Essential for understanding thermal properties
• Varies per material affecting temperature control

Exploring Molar Mass

Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol). For benzene \((\text{C}_6\text{H}_6)\), finding its molar mass involves adding up the atomic masses of carbon and hydrogen.
Carbon has an atomic mass of about \(12.01 \text{ g/mol}\) and hydrogen is around \(1.01 \text{ g/mol}\). So, the calculation is as follows:

• 6 carbon atoms \((6 \times 12.01 = 72.06 \text{ g/mol})\)
• 6 hydrogen atoms \((6 \times 1.01 = 6.06 \text{ g/mol})\)

Combining these, the molar mass of benzene is \(78.12 \text{ g/mol}\).

Molar mass is crucial in chemistry for converting between moles and grams, allowing chemists to measure reactants and products accurately in chemical reactions.

• Measured in \(\text{g/mol}\)
• Links mass with the amount of substance
• Essential for stoichiometry in reactions

Properties and Significance of Benzene

Benzene \((\text{C}_6\text{H}_6)\) is a well-known organic compound in chemistry, characterized by its distinct ring structure which is aromatic, highly stable, and a fundamental structure in organic chemistry.
Benzene is a colorless and highly flammable liquid with a sweet odor. It is used in the manufacturing of numerous chemicals such as plastics, resins, and synthetic fibers.

Despite its importance in chemical synthesis, benzene is also a known carcinogen and hence must be handled with caution.
By converting the specific heat capacity to molar heat capacity, we uncover benzene's behavior regarding energy and temperature changes. This conversion is crucial for accurately calculating the thermodynamics in reactions involving benzene.

• Has a molar heat capacity of \(135.93 \text{ J/mol} \cdot \text{K}\)
• Used as a precursor in the synthesis of other compounds
• Safety considerations due to its carcinogenic nature