Question

A sample of methane gas \(\left(\mathrm{CH}_{4}\right)\) is at \(50^{\circ} \mathrm{C}\) and \(20 \mathrm{~atm}\). Would you expect it to behave more or less ideally if (a) the pressure were reduced to 1 atm? (b) the temperature were reduced to \(-50^{\circ} \mathrm{C}\) ?

Short answer

Answer: (a) When the pressure is reduced from 20 atm to 1 atm, the methane gas would behave more ideally. (b) When the temperature is reduced from 50°C to -50°C, the methane gas would behave less ideally.

Step-by-step solution

(a) Change in Pressure (from 20 atm to 1 atm)

Since the methane gas is at 20 atm and 50°C initially, reducing the pressure from 20 atm to 1 atm is an example of a decrease in pressure. In general, gases tend to behave more like ideal gases when the pressure is low because molecules are farther apart which reduces the strength of intermolecular forces and the volume of the individual molecules becomes less significant compared to the volume of the container. So, when we decrease the pressure, the methane gas will behave more ideally. Thus, yes, we would expect the methane gas to behave more ideally if the pressure were reduced to 1 atm.

(b) Change in Temperature (from 50°C to -50°C)

In this case, the temperature is being reduced from 50°C to -50°C. Gases behave more ideally at high temperatures because the high kinetic energy at high temperatures overcomes the intermolecular forces and as a consequence the gas molecules hardly interact with each other. When the temperature is reduced, the kinetic energy of the gas molecules decreases, and the intermolecular forces between them become more significant. As a result, the gas behaves less ideally. So, the methane gas will behave less like an ideal gas if the temperature were reduced to -50°C.

Key concepts

Methane Gas

Methane gas, with the chemical formula \(\mathrm{CH}_4\), is an important component in natural gas. It is the simplest alkane and consists of one carbon atom bonded to four hydrogen atoms. This configuration gives methane its relatively high stability as a small molecule.
It's a greenhouse gas that's highly studied due to its effects on the environment. Methane is colorless and odorless, and is typically found in gaseous form at room temperature. Its behavior as a gas can offer insights into the fundamental behavior of gases when studied under different conditions of pressure and temperature.
In the lab, pure samples of methane are used to study how gases like methane follow or deviate from ideal behavior in compliance with the gas laws.

Pressure and Temperature Effects

The behavior of gases, such as methane, is significantly influenced by changes in pressure and temperature. These factors determine how closely a gas can be approximated by the ideal gas law.
When a gas like methane is subjected to decreased pressure, from 20 atm to 1 atm, for instance, molecules move further apart, reducing the intermolecular force impacts. This allows it to behave more ideally under low-pressure conditions.
Conversely, reducing the temperature of methane can lead to less ideal behavior. At lower temperatures, gas molecules have reduced kinetic energy, making intermolecular forces more prominent. For example, cooling methane from 50°C to -50°C can increase interactions among molecules, causing deviation from ideal gas behavior.

Intermolecular Forces

Intermolecular forces are the attractions between molecules that affect a gas's behavior. In gases, these forces are significantly weaker compared to solids and liquids due to the larger distances between molecules.
For methane, a non-polar molecule, the predominant intermolecular force is the London dispersion force, which is relatively weak. As such, when conditions change in a way that affects these forces — such as increased pressure or decreased temperature, the forces become more significant, and the gas deviates from ideal behavior.
In ideal gas behavior, intermolecular forces are considered negligible, which is more achievable at high temperatures and low pressures, where the kinetic energy of molecules overcomes these attractions.

Gas Laws

Gas laws describe the behavior of gases under various conditions, and they often assume ideal behavior. This means that the gas has negligible volume and no intermolecular forces. The most commonly used gas laws include Boyle's Law, Charles's Law, and the Ideal Gas Law.
The Ideal Gas Law, given by the equation \(PV = nRT\), relates pressure \(P\), volume \(V\), temperature \(T\), and the amount of gas in moles \(n\), with \(R\) being the gas constant.
For gases like methane, these laws suggest that

• Lower pressure allows gases to expand, becoming less dense and more ideal in behavior.
• Higher temperatures result in increased kinetic energy, which also supports ideal behavior because energy overcomes any intermolecular attractions.

By understanding these principles, we can predict and explain how gases such as methane will behave under different conditions.