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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 \(\mathrm{J} / \mathrm{mol} \cdot \mathrm{K}) ?\)

Short Answer

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

Step by step solution

01

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).
02

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.\[\text{Molar mass of benzene} = (6 \times 12.01) + (6 \times 1.01) = 78.12 \text{ g/mol}\]
03

Convert Specific Heat to Molar Heat Capacity

To find the molar heat capacity, multiply the specific heat capacity by the molar mass of benzene.\[\text{Molar heat capacity} = 1.74 \text{ J/g} \cdot \text{K} \times 78.12 \text{ g/mol}\]\[\text{Molar heat capacity} = 135.93 \text{ J/mol} \cdot \text{K}\]
04

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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

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Most popular questions from this chapter

The freezing point of mercury is \(-38.8^{\circ} \mathrm{C} .\) What quantity of energy, in joules, is released to the surroundings if \(1.00 \mathrm{mL}\) of mercury is cooled from \(23.0^{\circ} \mathrm{C}\) to -38.8 \(^{\circ} \mathrm{C}\) and then frozen to a solid? (The density of liquid mercury is \(13.6 \mathrm{g} / \mathrm{cm}^{3} .\) Its specific heat capacity is 0.140 J/g \(\cdot\) K and its heat of fusion is \(11.4 \mathrm{J} / \mathrm{g} .\) )

A piece of chromium metal with a mass of \(24.26 \mathrm{g}\) is heated in boiling water to \(98.3^{\circ} \mathrm{C}\) and then dropped into a coffee-cup calorimeter containing \(82.3 \mathrm{g}\) of water at \(23.3^{\circ} \mathrm{C} .\) When thermal equilibrium is reached, the final temperature is \(25.6^{\circ} \mathrm{C} .\) Calculate the specific heat capacity of chromium.

Which of the following are state functions? (a) the volume of a balloon (b) the time it takes to drive from your home to your college or university (c) the temperature of the water in a coffee cup (d) the potential energy of a ball held in your hand

You want to heat the air in your house with natural gas \(\left(\mathrm{CH}_{4}\right) .\) Assume your house has \(275 \mathrm{m}^{2}\) (about \(2800 \mathrm{ft}^{2}\) ) of floor area and that the ceilings are 2.50 m from the floors. The air in the house has a molar heat capacity of \(29.1 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K} .\) (The number of moles of air in the house can be found by assuming that the average molar mass of air is \(28.9 \mathrm{g} / \mathrm{mol}\) and that the density of air at these temperatures is \(1.22 \mathrm{g} / \mathrm{L} .\). What mass of methane do you have to burn to heat the air from \(15.0^{\circ} \mathrm{C}\) to \(22.0^{\circ} \mathrm{C} ?\)

What quantity of energy, in joules, is required to raise the temperature of \(454 \mathrm{g}\) of tin from room temperature, \(25.0^{\circ} \mathrm{C},\) to its melting point, \(231.9^{\circ} \mathrm{C},\) and then melt the tin at that temperature? (The specific heat capacity of tin is \(0.227 \mathrm{J} / \mathrm{g} \cdot \mathrm{K},\) and the heat of fusion of this metal is \(59.2 \mathrm{J} / \mathrm{g} .\) )

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