Although the ideal gas model is very useful, it is only an approximation of the real nature of gases, and the equations derived from its assumptions are not entirely dependable. As a consequence, the measured properties of a real gas will very often differ from the properties predicted by our calculations. Let’s look at some of the reasons for these discrepancies.  

 

Decreased Temperature and Real Gas Pressure

Picture yourself riding on an H₂O molecule in water vapor heated to a relatively high temperature. (The term vapor is commonly used to describe a gas that is derived from a substance that is a liquid at normal temperatures and pressures.) As your H₂O molecule passes close to another one, the two particles may experience a mutual attraction. As long as the temperature remains high, however, the rapidly moving water molecules break the attraction almost immediately and continue on their separate paths. Because, the particles in a gas at high temperature spend only a small fraction of their time experiencing these short-lived attractions, the effect of the attractions on the properties of the gas is negligible. We can therefore consider a gas at high temperature to be an ideal gas, with no attractions between the particles.

When the temperature of the water vapor decreases, the water molecules move more slowly, and it becomes more difficult for them to break the attractions that form between them. Thus the particles of a gas at a lower temperature spend a greater portion of their time attracted to other particles. The ideal gas model is based on the assumption that there are no significant attractions between the particles. Therefore, the lower the temperature, the less a gas behaves like an ideal gas.

When the attractions between its particles are significant, the measured pressure of a real gas is less than the pressure predicted by the ideal gas equation.

P_real = measured pressure

P_ideal = pressure calculated from the ideal gas equation and measured n, T, and V

P_real < P_ideal

To understand why the real pressure is less than the predicted ideal pressure, picture yourself riding on a gas particle at the instant before it hits a wall of its container. At that instant, there are more particles behind your particle than in front of it. In an ideal gas with no attractions between the particles, your particle would hit the wall with a force that depends only on the particle’s mass and velocity. In a real gas, however, the attractions between the particles will pull your particle back toward the center of the container, slow it down, and decrease the force of its collision with the wall (Figure 1). If the force of the collisions of gas particles against the walls is diminished, the pressure of the gas will be decreased. Thus the pressure of a real gas, with attractions between the particles, will be less than the pressure predicted for an ideal gas, with no attractions between the particles.

The lower the temperature of a gas is, the more attractions there are between the particles, and the more the real or measured pressure deviates from the pressure predicted by the ideal gas equation.

 

Figure 1:   Preal is less than Pideal   In a real gas there are attractions between the particles. At the instant before a particle collides with a wall of its container, the particles behind it pull it back, decreasing its velocity and decreasing the force of its collision.

 

Increased Concentration and Real Gas Pressure

The concentration of a gas (moles of gas per unit volume) can be increased in two ways: (1) by decreasing the volume or (2) by adding more gas to a given volume. The higher the concentration of the gas is, the shorter the average distance between the particles; and if the particles are closer together, more of them will be close enough to feel significant mutual attractions (Figure 2). Therefore, although the pressure of a real gas increases as the concentration increases, it does not increase as much as it would if there were no attractions between the particles. With a greater concentration of gas, there are more particles pulling a particle back to the center of the container at the instant before it hits the wall. This greater attraction in the direction away from the wall decreases the pressure against the walls compared to what it would be if there were fewer attractions between the particles (Figure 13.3).

Figure 2:   Increased Concentration of Gas Leads to a Greater Difference between Real and Ideal Pressures   The greater the number of particles per unit volume, the greater the number of significant attractions between a particle just before it hits the wall and the particles behind it. This leads to a greater pull toward the center of the container and a greater difference between the real, measured pressure and the ideal, calculated pressure.

 

Figure 3:    Why Real Pressure Deviates from Ideal Pressure

 

Increased Concentration and Real Gas Volume

When a gas behaves like an ideal gas, we can calculate its volume by measuring its temperature, pressure, and moles and plugging them into the ideal gas equation. When the concentration of a gas is very high, however, the real or measured volume is greater than the volume that would be calculated from the ideal gas equation. The reason is that small as the particles of a gas are, they do constitute part of its volume. In other words, the real volume of a gas is equal to the volume that the particles themselves occupy plus the volume of the empty space between the particles.

V_real = V_particles + V_empty

One of the assumptions of the ideal gas model is that the volume occupied by the particles is negligible, so the ideal volume is equal to the volume of the empty space. However, because the particles of a real gas do occupy a finite volume, the real or measured volume of a gas is larger than the ideal volume calculated from the ideal gas equation.

V_ideal = V_empty

V_real = V_particles + V_empty = V_particles + V_ideal

V_real > V_ideal

As the concentration of a gas increases-either because more gas has been added to the same volume or because the gas has been compressed into a smaller volume-the percentage of the volume occupied by the particles increases. This leads to a greater difference between the real, measured volume and the calculated, ideal volume (Figure 4).

 

Figure 4:  Effect of Concentration on Real Volume Compared to Ideal Volume