# Van der Waals Equation of State

Van der Walls is the name of a Dutch physicist, J. D. van der Waals (1837-1923). The Van der Waals Equation of State is an equation of state of gas, similar to The equation of state of an ideal gas. The difference is, The equation of state of an ideal gas cannot provide accurate results if the pressure and density of real gas are large enough. Whereas The Van der Waals Equation of State can produce more accurate results.

The existence of this equation originated from Van der Waals who realized the limitations of the equation of state of an ideal. Waals modify the equation of state of the ideal gas, by adding several factors that also influence the real gas condition, when the pressure and density of the real gas are large.

Gas pressure is inversely proportional to volume. If the gas pressure increases, the gas volume decreases. Conversely, if the gas volume decreases, the gas pressure increases. When gas volume decreases, gas density increases (density = mass / volume). It can be said that the pressure is directly proportional to density. If the gas pressure is large, the gas density is also large. Conversely, if the gas pressure is small, the gas density is also small. Gas pressure is also directly proportional to temperature. If gas pressure increases, gas temperature increases. We can conclude that if the gas pressure increases, the temperature, and density of the gas, while the gas volume decreases.

When the gas volume decreases, the distance between molecules becomes closer. When the distance between molecules becomes closer, the molecules attract each other. It’s like when a piece of iron is brought close to a magnet. If the distance between the magnet and iron is far enough, the magnet cannot pull iron. But if the distance between the magnet and iron is close, the iron is pulled closer. When the molecules are about to collide, the electrons on the outside of the molecule repel each other (electrical repulsion). As a result, molecules cannot stick together. From this brief description, it can be said that the pulling force between molecules influences the gas condition.

When the gas pressure is large enough, and the gas volume becomes small, the distance between molecules becomes closer. Because molecules also have a size (atomic diameter = 10^{-10} m), then we also need to take into account the volume of these molecules.

Van der Waals decreases an equation of state, taking into account the molecular volume and the interactions that occur between molecules. The equation derived by Van der Waals is the result of the modification of the ideal gas state equation P V = n R T. Van der Waals Equation of State:

P = gas pressure (N / m^{2} = Pa)

V = gas volume (m^{3})

R = universal gas constant (R = 8.315 J / mol. K = 8315 kJ / kmol.K)

T = temperature (K)

a = empirical constant (the value depends on the force of attraction between the gas molecules)

b = empirical constant (representing the volume of one mole of gas molecules)

n = Number of moles (mol)

bn = total volume of gas molecules

Constants a and b are obtained through experiments. The constant values a and b depend on the type of gas.

n^{2} / V^{2 }= quadratic ratio of the number of moles (n) with the square of the volume of gas (V). The value of n^{2 }/ V^{2} depends on the pressure and density of the gas. If the gas pressure (P) is large, then the volume of gas (V) is small. The smaller V, the greater is n^{2} / V^{2}. When the gas volume is small (n^{2} / V^{2 }is large) the distance between molecules is closer. The closer the distance between molecules, the greater the interactions between these molecules (colliding, pulling together). Therefore n^{2 }/ V^{2} is directly proportional to a constant (compare with van der Waals equation). The greater the value of n^{2} / V^{2}, the greater the attraction between molecules (a).

Conversely, if the gas pressure (P) is small, then the volume of gas (V) becomes large. The more prominent V, the smaller n^{2} / V^{2}. The lower the n^{2 }/ V^{2}, the lower the attraction force between the molecules.

(V – bn) = Difference between gas volume and the total volume of gas molecules. The constant b represents the volume of one mole of gas molecules. n = number of moles. The product of the time between b and n (bn) = the total volume of gas molecules. If the gas pressure (P) gets more significant, then the volume of gas (V) gets smaller.

The smaller V, the smaller (V – bn). This means that the distance between molecules increases and, of course, the attraction between molecules increases. Conversely, if the gas pressure gets smaller, the gas volume gets bigger. The significant the volume of gas, the higher (V – bn). The larger (V – bn), the smaller the attraction between the gas molecules.

We can say that the equation of the van der Waals state describes the real gas state more accurately than the ideal gas equation. When the pressure and gas density are large enough, the van der Waals equation gives more accurate results. If the gas pressure is not too large, then (an^{2} / V^{2}) and (V-bn) can be ignored, so that the Van der Waals state equation changes to an ideal gas state equation.