Question

The temperature at which real gases obey the ideal gas laws over a wide range of pressure? 

Answer 1

The temperature at which a real gas obeys ideal gas law over an appreciable range of pressure is called Boyle Temperature or Boyle Point.

For an Ideal gas:

$P\ V\ =\ n\ R\ T\\ \\Let\ \ Z = \frac{P\ V_{real}}{n\ R\ T}$

For an ideal gas, Z = 1 at any temperature or pressure.  

Boyle point depends on the nature of the real gas. Above the Boyle point Z is greater than 1.

At low pressures and high temperatures much above the critical point of the substance, the real gases can be taken to behave like ideal gases.  Gases like O₂, N₂, H₂, He, mono-atomic gases and inert gases behave NEARLY ideal at standard temperature (0⁰C) and pressure (1 standard atmosphere).

Ideal gas law does not take into account the molecular size, and inter-molecular attraction or repulsion forces. It assumes that those factors are zero.  In mono-atomic gases this assumption is valid over a wide range of pressures and temperatures. But in other real gases, inter-molecular forces are weak at high temperatures and low pressures. The reason is high kinetic energy overcomes small inter-molecular forces as the molecules are separated by large distances. The molecules occupy very little space compared to the total volume of the gas.

Boyle point or temperature $T_b = \frac{a}{R b},$  where a and b are Vander Waal's parameters that appear in Vander Waals gas equation and R is the universal gas constant.

Answer 2

The temperature at which a real gas obeys ideal gas law over an appreciable range of pressure is called Boyle Temperature or Boyle Point.

For an Ideal gas:

\begin{gathered}P\ V\ =\ n\ R\ T\\ \\Let\ \ Z = \frac{P\ V_{real}}{n\ R\ T}\end{gathered}

P V = n R T

Let \ Z=

n R T

P V

real

For an ideal gas, Z = 1 at any temperature or pressure.

Boyle point depends on the nature of the real gas. Above the Boyle point Z is greater than 1.

At low pressures and high temperatures much above the critical point of the substance, the real gases can be taken to behave like ideal gases. Gases like O₂, N₂, H₂, He, mono-atomic gases and inert gases behave NEARLY ideal at standard temperature (0⁰C) and pressure (1 standard atmosphere).

Ideal gas law does not take into account the molecular size, and inter-molecular attraction or repulsion forces. It assumes that those factors are zero. In mono-atomic gases this assumption is valid over a wide range of pressures and temperatures. But in other real gases, inter-molecular forces are weak at high temperatures and low pressures. The reason is high kinetic energy overcomes small inter-molecular forces as the molecules are separated by large distances. The molecules occupy very little space compared to the total volume of the gas.

Boyle point or temperature T_b = \frac{a}{R b},T

b

=

Rb

a

, where a and b are Vander Waal's parameters that appear in Vander Waals gas equation and R is the universal gas constant.