Which of the following relationships are consistent with the ideal gas law?

Question: Which of the following relationships are consistent with the ideal gas law?

The ideal gas law is a mathematical equation that relates the pressure, volume, temperature and amount of gas in a system. It is often written as PV = nRT, where P is the pressure, V is the volume, n is the amount of gas in moles, R is the universal gas constant and T is the temperature in kelvins.

The ideal gas law can be used to describe the behavior of gases under various conditions, such as changes in pressure, volume or temperature. However, it is important to note that the ideal gas law is based on some assumptions that may not always be valid for real gases. For example, the ideal gas law assumes that the gas molecules have negligible size and do not interact with each other. These assumptions are more likely to hold true when the gas is at low pressure and high temperature.

One way to test the validity of the ideal gas law is to compare it with other equations of state that account for the deviations of real gases from ideal behavior. For example, the van der Waals equation of state modifies the ideal gas law by introducing two correction factors: a term that reduces the pressure to account for the attractive forces between gas molecules, and a term that reduces the volume to account for the finite size of gas molecules. The van der Waals equation of state can be written as (P + a(n/V)^2)(V - nb) = nRT, where a and b are constants that depend on the type of gas.

So, which of the following relationships are consistent with the ideal gas law?

- The pressure of a gas increases as its volume decreases at constant temperature and amount. This relationship is consistent with the ideal gas law, as it follows from the inverse proportionality between pressure and volume in PV = nRT.

- The volume of a gas increases as its temperature increases at constant pressure and amount. This relationship is also consistent with the ideal gas law, as it follows from the direct proportionality between volume and temperature in PV = nRT.

- The amount of a gas decreases as its pressure increases at constant volume and temperature. This relationship is not consistent with the ideal gas law, as it contradicts the direct proportionality between amount and pressure in PV = nRT.

- The temperature of a gas decreases as its pressure decreases at constant volume and amount. This relationship is not consistent with the ideal gas law, as it contradicts the direct proportionality between temperature and pressure in PV = nRT.

Therefore, only the first two relationships are consistent with the ideal gas law, while the last two are not.