# Redlich-Kwong Equation of State

on . Posted in Thermodynamics

The Redlich-Kwong equation of state is a mathematical model used in thermodynamics and fluid dynamics to describe the behavior of real gases.  It is an improvement over the ideal gas law, which assumes that gases behave ideally (there are no intermolecular forces and the gas particles have zero volume).  This equation takes into account the finite size of gas molecules and the attractive forces between them, making it more accurate for describing the behavior of real gases, especially at higher pressures and lower temperatures.

The constants a and b are known as the Redlich-Kwong parameters and are determined experimentally for each gas.  They characterize the strength of intermolecular forces (through a) and the finite size of the gas molecules (through b).

### Key Points about Redlich-Kwong Equation of State

• It provides a more accurate representation of real gas behavior compared to the ideal gas law, especially at high pressures and low temperatures.
• It accounts for both attractive forces (through a) and finite molecular volume (through b) in the equation.
• It can be used to calculate various thermodynamic properties of real gases, such as compressibility factors, fugacity coefficients, and phase equilibria.

However, it's important to note that while the Redlich-Kwong equation of state is an improvement over the ideal gas law, it is still an empirical model and may not always accurately predict the behavior of all gases across a wide range of conditions.  For gases that exhibit highly non-ideal behavior, more complex equations of state, such as the Peng-Robinson equation or the Soave-Redlich-Kwong equation, may be used to provide better predictions.

## Redlich-Kwong Equation of State Formula

$$\large{ p = \frac{R \; T}{ V_m \;-\; b } - \frac{ a }{ \sqrt{T} \; V_m \; \left( V_m \;+\; b \right)' } }$$
Symbol English Metric
$$\large{ p }$$ = pressure of gas $$\large{\frac{lbf}{in^2}}$$   $$Pa$$
$$\large{ a }$$ = correction for the intermolecular forces   $$\large{dimensionless}$$
$$\large{ b }$$ = adjusts for the volume occupied by the gas particles $$\large{in^3}$$ $$\large{mm^3}$$
$$\large{ V_m }$$ = molar volume of gas $$\left( \frac{V}{n} \right)$$ $$\large{\frac{ft^3}{mol}}$$ $$\large{\frac{m^3}{mol}}$$
$$\large{ n }$$ = number of moles of gas   $$\large{dimensionless}$$
$$\large{ R }$$ = specific gas constant (gas constant) $$\large{\frac{lbf-ft}{lbm-R}}$$ $$\large{\frac{J}{kg-K}}$$
$$\large{ T }$$ = temperature of gas $$\large{R}$$ $$\large{K}$$

Tags: Gas Ideal Gas