Question

A sample of methane gas \(\left(\mathrm{CH}_{4}\right)\) is at \(50^{\circ} \mathrm{C}\) and 20 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: The methane gas (CH₄) sample will behave more ideally in scenario (a) when the pressure is reduced to 1 atm.

Step-by-step solution

Write down the Ideal Gas Law equation

The Ideal Gas Law equation is PV = nRT, where P is the pressure, V is the volume, n is the amount of substance in moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Convert the given temperatures to Kelvin

We will convert the temperatures from Celsius to Kelvin: 50°C + 273.15 = 323.15 K, -50°C + 273.15 = 223.15 K.

Compare the initial conditions with Scenario (a) and (b)

The behavior of an ideal gas is dependent on the deviation from the ideal gas law, which is affected mainly by pressure and temperature. High pressure generally leads to less ideal behavior, while a low pressure is associated with more ideal behavior. Similarly, high temperatures lead to more ideal behavior, while low temperatures result in less ideal behavior. (a) The pressure is reduced from 20 atm to 1 atm, which means lower pressure, leading to more ideal gas behavior. Therefore, we can expect the methane gas to behave more ideally when the pressure is reduced to 1 atm. (b) The temperature is reduced from 323.15 K to 223.15 K. This means that the gas is now at a lower temperature, which would generally lead to less ideal behavior as the attractive forces between the gas particles become more significant. Therefore, we can expect the methane gas to behave less ideally when the temperature is reduced to -50°C.