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 \(21.40 \mathrm{kJ} / \mathrm{mol}\).)

Short answer

The energy required is approximately 39.21 kJ.

Step-by-step solution

Determine Molar Mass of Chloromethane

To calculate the amount of energy required, we first need to determine the molar mass of chloromethane (\(\mathrm{CH}_{3} \mathrm{Cl}\)). The atomic masses are approximately: C = 12.01 g/mol, H = 1.01 g/mol each, and Cl = 35.45 g/mol. The molar mass is calculated as follows: \[\text{Molar mass of } \mathrm{CH}_{3} \mathrm{Cl} = 12.01 + (3 \times 1.01) + 35.45 = 50.49\, \mathrm{g/mol}.\]

Calculate Moles of Chloromethane

Now that we have the molar mass, we can calculate the number of moles in 92.5 grams of chloromethane using the formula:\[\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{92.5\, \mathrm{g}}{50.49\, \mathrm{g/mol}}.\]This gives us approximately 1.832 moles of \(\mathrm{CH}_{3} \mathrm{Cl}\).

Calculate Energy Required for Vaporization

Once we know the number of moles, we can calculate the energy required to vaporize the chloromethane using the heat of vaporization. The formula is:\[\text{Energy} = \text{Moles} \times \text{Heat of Vaporization} = 1.832\, \mathrm{mol} \times 21.40\, \mathrm{kJ/mol}.\] This equals approximately 39.21 kJ.

Key concepts

Understanding Molar Mass Calculation

To determine how much energy is needed to convert a liquid to its vapor form, it's important to understand the concept of molar mass. Molar mass is simply the mass of one mole of a given substance, expressed in grams per mole. Knowing this helps us figure out how many moles are in a given mass of material. For chloromethane (\( \mathrm{CH}_{3} \mathrm{Cl} \)), we start by finding the atomic masses of its components:

• Carbon (C) = 12.01 g/mol
• Hydrogen (H) = 1.01 g/mol
• Chlorine (Cl) = 35.45 g/mol

Next, you sum up these masses according to \( \mathrm{CH}_{3} \mathrm{Cl} \)'s molecular structure:\[\text{Molar mass of } \mathrm{CH}_{3} \mathrm{Cl} = 12.01 + (3 \times 1.01) + 35.45 = 50.49 \, \mathrm{g/mol}.\]This calculation is essential as it allows us to calculate the number of moles when given a specific quantity of chloromethane. Molar mass acts like a bridge between the mass of the molecules you have and their quantity in moles, which are the key entities when calculating energy changes.

Effective Energy Calculation Process

After determining the molar mass, the next step is to calculate how much energy is required to vaporize our sample. Here, we use the concept of moles to connect mass with energy needs. Let's break it down:First, compute the moles of the substance using:\[\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{92.5 \, \mathrm{g}}{50.49 \, \mathrm{g/mol}}\]which results in approximately 1.832 moles of chloromethane. Knowing the moles, we can apply the heat of vaporization, which quantifies how much energy is needed to convert one mole of liquid chloromethane to a gas. It is given as 21.40 kJ/mol.Finally, calculate the total energy by multiplying moles by the heat of vaporization:\[\text{Energy} = \text{Moles} \times \text{Heat of Vaporization} = 1.832 \, \mathrm{mol} \times 21.40 \, \mathrm{kJ/mol} \approx 39.21 \, \mathrm{kJ}.\]This energy value tells us how much heat is needed to change all 92.5 grams of chloromethane from liquid to vapor at its boiling point.

Examining the Phase Change

A phase change refers to the transition of a substance from one state of matter to another. Here, we are looking at chloromethane, changing from a liquid to a vapor. This transformation is essential since it involves breaking intermolecular forces, which requires energy input. The specific quantity needed for chloromethane is defined by its heat of vaporization, which is 21.40 kJ per mole.The boiling point of chloromethane is \(-24.09^{\circ} \mathrm{C} \), meaning that at this temperature, chloromethane in liquid form starts to convert into vapor when energy is continuously applied. Each molecule in the liquid gains enough energy to overcome intermolecular attractions, allowing it to enter the gas phase.Understanding the phase change is crucial, especially in chemical processes and industrial applications where precise control over energy and material states is required. This concept is used regularly in manufacturing, where substances often need to be changed into vapors or liquids as part of product formulation. So, the heat of vaporization not only helps calculate the energy required but also guides how energy is used efficiently during such transitions.