Problem 20 - Chemistry and Chemical Reactivity

Question

Chloromethane, \(\mathrm{CH}_{3} \mathrm{Cl},\) arises from microbial fermentation and is found throughout the environment. It is also produced industrially, is used in the manufacture of various chemicals, and has been used as a topical anesthetic. How much energy is required to convert \(92.5 \mathrm{g}\) of liquid to a vapor at its boiling point, \(-24.09^{\circ} \mathrm{C} ?\) (The heat of vaporization of \(\mathrm{CH}_{3} \mathrm{Cl}\) is \(21.40 \mathrm{kJ} / \mathrm{mol} .\) )

Step-by-Step Solution

Answer

39.22 kJ of energy is required.

Step 1: Calculate Moles of Chloromethane

First, we need to determine how many moles of chloromethane are present in the given mass. Use the molar mass of chloromethane, \( \mathrm{CH}_{3}\mathrm{Cl} \), which is approximately 50.49 g/mol. Convert grams to moles using the formula: \[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \]. For the given 92.5 g, it calculates to: \[ \text{Moles} = \frac{92.5 \text{ g}}{50.49 \text{ g/mol}} \approx 1.832 \text{ mol} \].

Step 2: Use Heat of Vaporization

Chloromethane's heat of vaporization is given as \( 21.40 \text{ kJ/mol} \). This value indicates the energy required to convert 1 mole of liquid chloromethane to vapor at its boiling point. To find the total energy required for 1.832 moles, multiply the number of moles by the heat of vaporization: \[ \text{Energy} = 1.832 \text{ mol} \times 21.40 \text{ kJ/mol} = 39.22 \text{ kJ} \].

Key Concepts

Moles and Molar Mass

In the world of chemistry, understanding the concept of moles and molar mass is essential for quantifying substances. A mole is a unit that measures the amount of a substance based on the number of atoms or molecules present. It's similar to how you would use a dozen to count twelve eggs. The molar mass, on the other hand, represents the mass of one mole of a substance. For any given chemical compound, the molar mass can be found by summing the atomic masses of its elements, which are listed on the periodic table.
For example, the molar mass of chloromethane (\(\mathrm{CH}_3\mathrm{Cl}\)) is calculated by adding the atomic masses of carbon, hydrogen, and chlorine. This turns out to be approximately 50.49 g/mol. With this value, you can convert from grams to moles— a crucial step in many chemical calculations.

• To find how many moles are in a given mass of a substance, use the formula: \(\text{Moles} = \frac{\text{mass}}{\text{molar mass}}\).
• In our example problem, for 92.5 g of chloromethane, the calculation shows it contains around 1.832 moles.

This calculation is vital in predicting reactions, where the quantity of reactants and products is usually expressed in moles.

Heat of Vaporization

The heat of vaporization refers to the amount of energy needed to convert a substance from a liquid to a gas at its boiling point. It's expressed in kJ/mol and indicates how much energy is needed per mole for this phase transition.
Chloromethane, with a boiling point around \(-24.09^{\circ}\)C, has a heat of vaporization of 21.40 kJ/mol. This means, to vaporize one mole of liquid chloromethane, you need 21.40 kJ of energy.

• The heat of vaporization is essential for calculations involving phase changes.
• It helps in designing processes like distillation where boiling and condensation cycles are repeatedly used.

Understanding the heat of vaporization allows chemists to estimate the energy requirements of processes and provides insights into the intermolecular forces present in a liquid.

Phase Change Energy

Energy is either absorbed or released during phase changes and knowing how to calculate this is crucial in many practical applications. Phase change energy refers to the amount of energy needed to change the phase of a substance, such as from liquid to gas, without changing its temperature.
For our given problem, once we know the moles of chloromethane, calculating the energy required for all of it to vaporize means multiplying this quantity by the heat of vaporization. This gives the total phase change energy needed. For the breakdown:

• Multiply the moles (1.832 mol) by the heat of vaporization (21.40 kJ/mol).
• You obtain the total energy needed: 39.22 kJ.

Understanding how much energy is exchanged during these transitions not only helps in chemical processing but also in fields like meteorology, where the phase changes of water are of strategic importance, or engineering, where energy efficiency is crucial.