The compressibility of a real gas and an ideal gas at a temperature of 200 K is shown as a function of pressure in the graph below. Compared to the volume of the ideal gas at 350 atm, the volume of an equimolar amount of the real gas under identical conditions is:

Question

The compressibility of a real gas and an ideal gas at a temperature of 200 K is shown as a function of pressure in the graph below.  Compared to the volume of the ideal gas at 350 atm, the volume of an equimolar amount of the real gas under identical conditions is:

Quizplus · Accepted Answer

11ecba2d_124f_6331_a3bf_55b4c9a719a4_MD0008_00 An ideal gas is a hypothetical gas with well-behaved (idealized) characteristics used as a simplified model to approximate the behavior of real gases according to the ideal gas law: 11ecba2d_124f_6332_a3bf_851bdc776683_MD0008_00 The ratio of these gas law terms gives the gas compressibility: 11ecba2d_124f_6333_a3bf_5bb720a22d9b_MD0008_00 For 1 mole of an ideal gas, the compressibility ratio equals 1 at all pressures. However, for real gases under very low temperatures or high pressures, this ratio may be higher or lower than 1 because real gases exhibit characteristics that deviate from the ideal gas model. A real gas with compressibility < 1 indicates attractions between molecules. These attractions decrease the force of the molecular collisions with the container wall, which gives a real gas a lower pressure and a lower compressibility than an ideal gas. A real gas with compressibility > 1 indicates effects from molecular volume. Although the molecular volume of a real gas is very small, it is not zero. The nonzero molecular volume of a real gas diminishes the available container space through which the gas can move. This adds a small amount of non-compressible volume and gives a real gas a higher volume and higher compressibility than an ideal gas. Therefore, in this question, the real gas has a larger volume than the ideal gas at 350 atm because the combined volume of gas molecules is significant compared to the volume of the container. (Choice A) Because the two lines on the graph diverge as pressure increases, the volume of the real gas must be greater than the volume of the ideal gas, even if the pressure and temperature are the same. (Choice B) Under the same P and T as the ideal gas, an equal number of moles of the real gas must have a larger actual V to achieve the higher compressibility seen on the graph. Additionally, Avogadro's law states that volume depends on the moles of the gas (not its molar mass). (Choice D) Intermolecular interactions generally cause a real gas to have a smaller volume than an ideal gas at the same pressure. Educational objective: Deviations from ideal gas behavior occur in real gases when the gas molecules with a non-negligible volume have significant intermolecular interactions and occupy a system at high pressure and low temperature.

The Compressibility of a Real Gas and an Ideal Gas