Problem 22 - General Chemistry: Principles and Modern Applications

Question

A vapor volume of 1.17 L forms when a sample of liquid acetonitrile, \(\mathrm{CH}_{3} \mathrm{CN},\) absorbs \(1.00 \mathrm{kJ}\) of heat at its normal boiling point \(\left(81.6^{\circ} \mathrm{C} \text { and } 1 \mathrm{atm}\right) .\) What is \(\Delta H_{\text {vap }}\) in kilojoules per mole of \(\mathrm{CH}_{3} \mathrm{CN} ?\)

Step-by-Step Solution

Answer

The enthalpy of vaporization (\( \Delta H_{\text {vap }} \)) of acetonitrile is the result obtained by dividing the heat absorbed (1.00 kJ) by the number of moles of acetonitrile calculated in step 1.

Step 1: Calculate the number of moles

First, we need to calculate the number of moles of acetonitrile that produces 1.17L of vapor at 1 atm and 81.6°C. We use the ideal gas law here: \(PV = nRT\). Rearranging the equation, we get \(n=PV/RT\). Substituting the given values (keep in mind to use correct units - temperature should be in Kelvin, volume in liters, and remember R = 0.0821 L.atm/K.mol):\(n = (1 atm)(1.17 L) / ((0.0821 L.atm/K.mol)(81.6°C + 273.15))\)This gives the number of moles of acetonitrile that forms 1.17L vapor.

Step 2: Calculate enthalpy of vaporization

Now we've obtained that the number of moles of acetonitrile is \(n\). We know that 1.00 kJ of heat is absorbed for this many moles to vaporize. Therefore,\(\Delta H_{\text {vap }} = Q/n\)Substitute Q=1.00 kJ and \(n\) from the previous step. This will give us the enthalpy of vaporization of acetonitrile.

Key Concepts

Ideal Gas Law

The ideal gas law is an essential equation for chemists. It relates pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas using the equation \( PV = nRT \), where \( R \) is the ideal gas constant. This law is handy when you need to convert between different states of a gas. For example, when liquid acetonitrile turns into vapor, it behaves like an ideal gas under specific conditions.
To use this equation correctly, remember:

• Pressure must be in atmospheres (atm).
• Volume is usually in liters (L).
• Temperature is in Kelvin (K) (convert from Celsius by adding 273.15).
• The ideal gas constant \( R \) is 0.0821 L.atm/K.mol.

By rearranging the equation to \( n = \frac{PV}{RT} \), you can calculate the moles of gas present, which is vital for understanding reactions and properties like the enthalpy of vaporization.

Acetonitrile

Acetonitrile, with the chemical formula \( \mathrm{CH}_3 \mathrm{CN} \), is a colorless, volatile liquid. It's often used as a solvent in laboratories due to its ability to dissolve a variety of substances. In chemical processes, its volatility means it easily transitions from a liquid to a vapor.
Understanding acetonitrile's behavior as a gas is crucial when calculating its enthalpy of vaporization. This is because when it vaporizes, it needs to be treated as an ideal gas to perform calculations using the ideal gas law. Remember, the characteristics of acetonitrile, such as its boiling point and interactions with heat energy, are key to these transformations.

Boiling Point

The boiling point of a substance, such as acetonitrile, is the temperature at which it moves from the liquid phase to the vapor phase. For acetonitrile, this happens at \( 81.6^{\circ} \mathrm{C} \) at 1 atm pressure. At this temperature, the energy added to the liquid exceeds the intermolecular forces holding its molecules together, allowing it to form vapor.
This concept is important in the study of thermochemistry because the boiling point not only provides information about the temperature of phase change but also helps in calculating the enthalpy of vaporization. During the boiling process at standard atmospheric pressure, a constant quantity of heat is absorbed, which relates directly to the energy required to vaporize the substance.

Thermochemistry

Thermochemistry is the study of heat energy involved in chemical reactions and phase changes. When acetonitrile absorbs heat at its boiling point, it undergoes a phase change from liquid to vapor, which involves energy known as the enthalpy of vaporization \( \Delta H_{\text{vap}} \).
The enthalpy of vaporization is the heat required to convert one mole of a liquid into vapor without changing its temperature. This process requires breaking intermolecular forces within the liquid; thus, studying thermochemistry helps us understand energy changes. For acetonitrile, the amount of heat absorbed during vaporization can be calculated using the formula \( \Delta H_{\text{vap}} = \frac{Q}{n} \), where \( Q \) is the heat energy absorbed and \( n \) is the number of moles vaporized, as calculated by the ideal gas law.
Thermochemical calculations are central in laboratory settings, industry, and various applications where the energy efficiency of transformations is critical.