Problem 28 - Chemistry The Molecular Science

Question

The specific heat capacity of carbon tetrachloride, \(\mathrm{CCl}_{4}\), is \(0.861 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\). Calculate its molar heat capacity.

Step-by-Step Solution

Answer

The molar heat capacity of \(\mathrm{CCl}_4\) is \(132.48 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\).

Step 1: Understand the Problem

We are given the specific heat capacity of carbon tetrachloride, \(\mathrm{CCl}_4\), as \(0.861 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\) and need to find the molar heat capacity.

Step 2: Find the Molar Mass of \(\mathrm{CCl}_4\)

To find the molar heat capacity, first determine the molar mass of \(\mathrm{CCl}_4\). The atomic masses are: C = 12.01 g/mol, Cl = 35.45 g/mol. Thus, \(\mathrm{CCl}_4\) has a molar mass of \(12.01 + 4 \times 35.45 = 153.81\) g/mol.

Step 3: Use Conversion Formula

The molar heat capacity \(C_m\) is calculated using the formula \(C_m = C_s \times M\), where \(C_s\) is the specific heat capacity, and \(M\) is the molar mass. Substitute the values: \(C_m = 0.861 \times 153.81\).

Step 4: Calculate the Molar Heat Capacity

Perform the multiplication: \(C_m = 0.861 \times 153.81 = 132.47541\). Thus the molar heat capacity is \(132.48 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) (rounded to two decimal places).

Key Concepts

Specific Heat Capacity

Specific heat capacity is a fundamental property of materials, indicating how much heat energy is required to raise the temperature of a given mass by one degree Celsius (or Kelvin). In simpler terms, it tells us how easily a substance heats up or cools down.
For carbon tetrachloride, the specific heat capacity is given as \(0.861 \, \mathrm{J} \, \mathrm{g}^{-1} \, \mathrm{K}^{-1}\). This means that each gram of carbon tetrachloride needs 0.861 joules of energy to increase its temperature by 1 Kelvin.
Understanding specific heat capacity is key in thermodynamics and helps us distinguish how substances differ in thermal response. For educational purposes, you can think of it as a weight of heat that varies from one material to another. Materials with high specific heat capacities will take longer to heat up and cool down, as they absorb more energy without a significant change in temperature.

Molar Mass Calculation

Calculating the molar mass is crucial when you need to convert between grams and moles in chemistry problems. The molar mass is essentially the weight of one mole of a substance, usually expressed in grams per mole (g/mol).
In the case of carbon tetrachloride \(\mathrm{CCl}_4\), we calculate its molar mass by adding the atomic masses of its constituent atoms. The atomic mass for carbon (C) is \(12.01 \, \mathrm{g/mol}\) and for chlorine (Cl) it is \(35.45 \, \mathrm{g/mol}\). Since carbon tetrachloride contains one carbon atom and four chlorine atoms, its molar mass is:

• 12.01 (from C) + 4 \(\times\) 35.45 (from 4 Cl) = 12.01 + 141.8 = 153.81 \mathrm{\, g/mol}\

This value, 153.81 \(\mathrm{g/mol}\), represents the mass of one mole of carbon tetrachloride molecules.

Carbon Tetrachloride

Carbon tetrachloride, noted chemically as \(\mathrm{CCl}_4\), is a colorless liquid that was once widely used in fire extinguishers and as a cleaning agent and solvent. It's important to consider some of its properties:

• Carbon tetrachloride is non-flammable.
• It has a sweet smell that can be detected at low concentrations.
• It was historically used in dry cleaning and as a refrigerant.

Despite these uses, its toxicity has led to a decline in its application in households and industries. Carbon tetrachloride can have serious effects on the liver and nervous system if inhaled or ingested. This has prompted tighter regulations around its use.
Knowing about the properties and safe handling of substances like carbon tetrachloride is crucial, especially in chemistry, where such solvents might still be encountered in controlled laboratory settings.