Problem 27 - Chemistry The Molecular Science

Question

The specific heat capacity of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) is 1.74 J \(\mathrm{g}^{-1} \mathrm{~K}^{-1}\). Calculate its molar heat capacity.

Step-by-Step Solution

Answer

The molar heat capacity of benzene is 136.93 J/mol K.

Step 1: Find the Molar Mass of Benzene

To find the molar heat capacity, we first need to determine the molar mass of benzene. Benzene's chemical formula is \( \text{C}_6\text{H}_6 \). The molar mass can be calculated by adding the atomic masses of carbon (C) and hydrogen (H). \[ \text{Molar mass of benzene} = 6 \times 12.01 \text{ g/mol} + 6 \times 1.01 \text{ g/mol} \]

Step 2: Calculate the Molar Mass of Benzene

Using the atomic masses, calculate the molar mass of benzene: \[ \text{Molar mass of benzene} = 72.06 \text{ g/mol} + 6.06 \text{ g/mol} = 78.12 \text{ g/mol} \]

Step 3: Convert Specific Heat Capacity to Molar Heat Capacity

The molar heat capacity is found by multiplying the specific heat capacity by the molar mass of benzene: \[ \text{Molar heat capacity} = 1.74 \text{ J g}^{-1} \text{ K}^{-1} \times 78.12 \text{ g/mol} \]

Step 4: Perform the Multiplication

Now perform the multiplication to find the molar heat capacity: \[ \text{Molar heat capacity} = 1.74 \times 78.12 = 136.93 \text{ J/mol} \text{ K} \]

Step 5: Conclusion

The molar heat capacity of benzene can be expressed as: \( 136.93 \text{ J/mol} \cdot \text{K} \).

Key Concepts

Specific Heat Capacity

Specific heat capacity is a property that describes the heat required to raise the temperature of 1 gram of a substance by 1 Kelvin. It is very useful for understanding how substances absorb and retain heat. Benzene, a common organic compound used as a starting material in chemical synthesis, has a specific heat capacity of 1.74 J/g·K.
This value means for every gram of benzene, 1.74 Joules of energy are needed to increase its temperature by 1 degree Kelvin (or Celsius, since the increment is the same).

• Consider this as a measure of how resistant a substance is to changing temperature.
• A higher specific heat capacity indicates a substance can absorb more heat before its temperature changes significantly.

This is important in many chemical processes where maintaining stable temperatures is critical, such as in reactions or storage conditions.

Molar Mass Calculation

To calculate properties like molar heat capacity, determining the molar mass of a compound is essential. Molar mass is the mass of one mole of a substance, calculated by summing atomic masses of the constituent atoms in a molecule.
For benzene, \( ext{C}_6 ext{H}_6\), the calculation involves:

• Carbon (C) has an atomic mass of approximately 12.01 g/mol.
• Hydrogen (H) has an atomic mass of approximately 1.01 g/mol.

You multiply these by the number of each type of atom in a benzene molecule:

• Six carbons: \((6 \times 12.01) \, \text{g/mol} = 72.06 \, \text{g/mol}\).
• Six hydrogens: \((6 \times 1.01) \, \text{g/mol} = 6.06 \, \text{g/mol}\).
• Adding these together gives benzene's molar mass as \(78.12 \, \text{g/mol}\).

This molar mass is a crucial factor when converting between specific and molar properties.

Chemical Formula of Benzene

The chemical formula of benzene is \( ext{C}_6 ext{H}_6\). This simple aromatic compound consists of a ring of six carbon atoms, each bonded to one hydrogen atom, forming a planar hexagonal structure.

To understand benzene's properties, it is helpful to note:

• The formula indicates equal parts carbon and hydrogen.
• The configuration imparts unique chemical properties due to its stable ring structure, allowing for resonance.
• Benzene's stability and ability to undergo substitution rather than addition reactions make it a key building block in many organic compounds.

The molecular structure derived from the formula explains why benzene has particular heat capacity values and reactivity profiles, both crucial in practical chemical applications.