# What is Compressibility Factor? Explain the Factors which affects Z-value.

## Compressibility Factor (Z)

Compressibility factor is a measure of deviation of a gas from ideal gas behavior when pressure and temperature changes. It is also called Z-factor and helps to understand how gases behave under different conditions. It is a dimensionless quantity that relates the actual behavior of a real gas to that of an ideal gas.

Compressibility factor is the ratio of the actual volume (V) to the ideal volume (V_{ideal}) of a gas .

Mathematically, it can be written as-

Z = V / V_{ideal}

Compressibility factor (Z) can be calculated by using the ideal gas law equation i.e. PV = ZnRT

or, Z = PV / nRT

where P, V, n, R and T represents pressure, volume, no. of moles, gas constant and temperature respectively.

By knowing the pressure, volume, temperature and the number of moles of a gas, we can easily determine its compressibility factor and compare how closely it behaves like an ideal gas.

From the graph, we can say that If the compressibility factor(Z) is greater than 1 is considered to be more compressible than an ideal gas, while a gas with a Z-factor less than 1 is considered to be less compressible. If the z-factor is equal to 1 is considered to be the gas behaves ideally, similar to what we would expect in an ideal gas.

## Factors Affecting Compressibility Factor

Ther are number of factors that affect the Z-value, some of them are discussed below-

### Pressure and Temperature

The compressibility factor depends on both pressure and temperature. As pressure increases, gas molecules come close to each-other, leading to stronger intermolecular forces and higher compressibility factors. Similarly, as temperature decreases, the kinetic energy of gas molecules decreases. Thus, the movement of molecules decreases and compressibility increases.

From the graph, it is observed that the deviation from Ideal behaviour is quite large at low temperatures. But as the temperatures is increased, the dip in the curve becomes lesser and lesser. In other words, the deviation goes on decreasing as temperature increases. However, at a particular temperature the value of 'z' remains close to one over an appreciable range of pressure i.e. the gas shows Ideal behaviour.

### Molecular Shape and Size

The shape and size of gas molecules affect their ability to be compressed. Larger molecules with complex shapes tend to have lower compressibility factors since their molecular interactions impede compression more effectively.

### Intermolecular Forces

Intermolecular forces, such as van der Waals forces, play a significant role in determining the compressibility factor. Strong intermolecular forces result in a higher compressibility factor.

### Compressibility factor for almost all the gases are approximately same at the same

A. Pressure and temperature

B. Reduced pressure and reduced temperature

C. Critical pressure and critical temperature

D. None of these

## Answer

Option B is correct

Compressibility factor (Z) is an function of reduced temperature and reduced pressure

i.e. Z = f_{n}(P_{r},T_{r}).

At same P_{r} and T_{r} the compressibility factor remains constant.

### Which of the following statements is/are incorrect?

A. All real gases are less compressible than ideal gases at high pressure.

B. Hydrogen and helium are more compressible than ideal gases for all values of pressure.

C. Except H_{2} and He, the compressibility factor Z = [PV/nRT] < 1 for all gases at low pressure.

D. The compressibility factor of real gases is independent of temperature.

## Answer

Option B and D are the answer.

H_{2} and He are less compressible than ideal gas because of their small size, the intermolecular force of attraction is negligible. Therefore, even at low pressure the volume factor is high so the compressibility factor Z > 1.

The compressibility factor, Z is inversely proportional to temperature. Higher the temperature, lower the deviation from ideal gas.