Problem 16 - Chemistry The Molecular Science

Question

The molar vaporization enthalpy of methanol is \(38.0 \mathrm{~kJ} / \mathrm{mol}\) at \(25^{\circ} \mathrm{C} .\) Calculate the heat energy transfer required to convert \(250 . \mathrm{mL}\) of the alcohol from liquid to vapor. The density of \(\mathrm{CH}_{3} \mathrm{OH}\) is \(0.787 \mathrm{~g} / \mathrm{mL}\) at \(25^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

The heat energy required is 233.32 kJ.

Step 1: Determine the Mass of Methanol

First, calculate the mass of methanol using its volume and density. The given density \( \rho \) is 0.787 g/mL, and the volume \( V \) is 250 mL. Use the formula: \( \text{mass} = \text{density} \times \text{volume} \). Thus, the mass \( m \) of methanol is \( 0.787 \times 250 = 196.75 \) grams.

Step 2: Convert Mass to Moles

Now, convert the mass of methanol to moles. The molar mass of methanol \( \text{CH}_3\text{OH} \) is 32.04 g/mol. Use the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). Therefore, the number of moles \( n \) is \( \frac{196.75}{32.04} \approx 6.14 \) moles.

Step 3: Calculate Heat Energy Required

Finally, calculate the heat energy required using the molar vaporization enthalpy, which is 38.0 kJ/mol. Use the formula: \( Q = n \times \Delta H_{\text{vap}} \). Substituting the values, \( Q = 6.14 \times 38.0 = 233.32 \) kJ. This is the heat energy needed to vaporize the methanol.

Key Concepts

Methanol

Methanol, often denoted as \( \text{CH}_3\text{OH} \), is a simple form of alcohol. It serves as both a valuable industrial solvent and a key component in antifreeze and fuel. Unlike ethanol, which is found in alcoholic beverages, methanol is not safe for consumption. Its clear, colorless appearance and slightly sweet odor make it easy to confuse with other liquids if not properly labeled. Methanol's notable feature is its ability to vaporize at a relatively low temperature, which makes understanding its properties essential when calculating energy requirements for phase changes.

Heat Energy Transfer

Heat energy transfer refers to the movement of thermal energy from one body or substance to another. In the context of methanol's vaporization, this process involves supplying the necessary energy to change methanol from its liquid form to its gaseous form. This energy is measured in kilojoules (kJ). The amount of energy required is calculated by multiplying the number of moles of methanol by its molar vaporization enthalpy. Understanding energy transfer is crucial in various scientific fields, including chemistry and engineering.

Density of Liquids

The density of liquids is an important property that relates a liquid's mass to its volume, expressed as grams per milliliter (g/mL). For methanol, given a density of 0.787 g/mL, you can calculate its mass by multiplying its density by the volume of the liquid. This relationship allows you to convert volume measurements into mass, a vital step when preparing to calculate moles. Understanding density helps in practical applications like mixing solutions and ensuring measurements are accurate across various chemical processes.

Calculation of Moles

Calculating moles involves converting a substance's mass into an amount of substance expressed in 'moles'. A mole is a standard scientific unit for measuring large quantities of very small entities, such as atoms or molecules. For methanol, the number of moles is calculated by dividing the mass by its molar mass (32.04 g/mol for methanol). This conversion is essential because it allows chemists to relate mass measurements to substance quantities in chemical reactions, drills, and experiments.

Enthalpy

Enthalpy is a measure of the total heat content in a system. For methanol's phase transition from liquid to gas, we use molar vaporization enthalpy, which is the heat required to vaporize one mole of a liquid. Methanol's molar vaporization enthalpy at 25°C is 38.0 kJ/mol. To calculate the total heat energy required for vaporization, you multiply the moles of methanol by this enthalpy value. Enthalpy calculations are not only limited to phase changes but also apply to chemical reactions and processes, contributing to a deeper understanding of thermodynamic systems.