Problem 8 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

The molar heat capacity of benzene is 135.922 J/mol·K.

Step 1: Determine the Molar Mass of Benzene

First, calculate the molar mass of benzene (C₆H₆). The atomic mass of carbon (C) is 12.01 g/mol, and the atomic mass of hydrogen (H) is 1.008 g/mol. Hence, the molar mass of benzene is \((6 \times 12.01) + (6 \times 1.008) = 72.06 + 6.048 = 78.108\;\text{g/mol}\).

Step 2: Use the Formula for Molar Heat Capacity

To find the molar heat capacity, multiply the specific heat capacity by the molar mass. The formula is \(\text{Molar Heat Capacity} = \text{Specific Heat Capacity} \times \text{Molar Mass}\).

Step 3: Perform the Calculation

Insert the values into the formula: \(\text{Molar Heat Capacity} = 1.74\;\text{J/g} \cdot \text{K} \times 78.108\;\text{g/mol} = 135.922\;\text{J/mol} \cdot \text{K}\).

Key Concepts

Specific Heat Capacity

Specific heat capacity is a property of a substance that describes how much heat is required to change the temperature of one gram of the substance by one degree Celsius (or Kelvin). This is an intrinsic property that varies from one material to another. For benzene, the specific heat capacity is given as 1.74 J/g·K.

To understand this concept deeply:

• Specific heat capacity is often measured in joules per gram per Kelvin (J/g·K).
• It allows us to predict how a certain amount of energy will change the temperature of a given mass of the substance.
• This value helps in calculating energy changes in processes involving temperature changes.

Specific heat capacity is crucial in applications such as designing thermal systems, where managing heat efficiently is essential.

Molar Mass Calculation

Calculating molar mass involves summing the atomic masses of all atoms in a molecule, as provided by the periodic table. For benzene (\(\text{C}_6\text{H}_6\)), follow these steps:

• Find the atomic mass of carbon (C), which is 12.01 g/mol.
• Hydrogen (H) has an atomic mass of 1.008 g/mol.
• Benzene has six carbon atoms and six hydrogen atoms.
• Therefore, multiply the atomic mass of carbon by six and hydrogen by six.

By calculating:
\((6 \times 12.01) + (6 \times 1.008) = 72.06 + 6.048 = 78.108\; \text{g/mol}\).

This tells us that one mole of benzene weighs 78.108 grams. Molar mass is a crucial concept as it helps convert between the mass of a substance and the amount of substance in moles, a standard unit in chemistry.

Benzene (C₆H₆)

Benzene is a simple aromatic hydrocarbon consisting of six carbon atoms bonded in a hexagonal ring with alternating double bonds, and each carbon is bonded to one hydrogen atom. This stable structure is often depicted as a circle inside a hexagon in chemistry.

Benzene is found naturally in crude oil and has many industrial uses, primarily as a precursor to various chemicals and plastics. Here are key features:

• Its formula is C₆H₆, indicating each molecule has six carbon and six hydrogen atoms.
• It is a clear, colorless liquid with a characteristic sweet smell.
• Benzene's unique bonding makes it a subject of interest in studying resonance and aromaticity in organic chemistry.

In experiments involving heat and temperature, knowing benzene's physical and chemical properties, such as specific and molar heat capacity, is vital. This knowledge helps predict reactions and manage energy use efficiently in chemical processes.