Question

Assume that all the four liquids in todays experiment are heated to 1000C using a heat chamber; will they behave more ideal or less ideal compared to 100C? Explain

Which of the three gases -HE, N2 and CO2, you will expect to be the most ideal at STP? Explain.

Explain why most gases behave ideally at lower pressures than higher pressures.

Explain what simple adjustments were made by van der Waals to ‘P’ and ‘V’ in the ideal gas law to make it applicable to real gases.

Answer 1

Monatomic helium gas is closer to an ideal gas than either of the others, for two reasons. 1. It has the smallest particles, so the volume of the particles are the smallest compared to the volume of the gas. 2. It has the smallest forces between particles, because the electrons in the atoms are all in very stable orbitals. It only has 2 electrons, tightly bound in the spherically symmetric 1s orbital, with opposite spin. A lot of energy would be needed to disturb these electrons.

The fallacy of an ideal gas arises from the Kinetic Theory of Gases, in particular, two of its postulates that were later found to be incorrect.

• Firstly, it assumed that a gas occupies a volume far larger than that occupied by its molecules. This isn't really a good assumption to make under all possible conditions, especially when the gas is highly compressed. This was the first distinction between a real and ideal gas. The ideal gas molecules occupy a volume negligible in comparison to that occupied by the gas itself, but for a real gas, this is not so. But now, suppose that the pressure is really low. In that case, the volume occupied by the gas must be quite high. Under such circumstances, the assumption is reasonably valid, and indeed, it has been observed that a real gas behaves ideally at low pressure.
• Coming to the second error, which was the assumption that the gas molecules exert no influence whatsoever on each other. Clearly, this cannot be so. Electrostatic forces of interaction play a big role in deciding the velocity of, and the pressure exerted by the gas molecules. Here comes the second distinction between a real and ideal gas. The ideal gas molecules do not interact with each other, but the real gas molecules do. However, if the temperature is quite high, then the velocity of the molecules is also high, and at such high velocities, the interactions are negligible. So it's possible to ignore them, and assume that there are no intermolecular interactions at all. Experimental observations seem to support this, as real gases do behave ideally at very high temperatures.

A compressibility factor of 1 implies ideal behaviour, and so, it's reasonable to assume that a real gas will behave ideally at low pressure and high temperature.

Van der Waals realized that two of the assumptions of the kinetic molecular theory were questionable. The kinetic theory assumes that gas particles occupy a negligible fraction of the total volume of the gas. It also assumes that the force of attraction between gas molecules is zero.

The first assumption works at pressures close to 1 atm. But something happens to the validity of this assumption as the gas is compressed. Imagine for the moment that the atoms or molecules in a gas were all clustered in one corner of a cylinder, as shown in the figure below. At normal pressures, the volume occupied by these particles is a negligibly small fraction of the total volume of the gas. But at high pressures, this is no longer true. As a result, real gases are not as compressible at high pressures as an ideal gas. The volume of a real gas is therefore larger than expected from the ideal gas equation at high pressures.

Van der Waals proposed that we correct for the fact that the volume of a real gas is too large at high pressures by subtracting a term from the volume of the real gas before we substitute it into the ideal gas equation. He therefore introduced a constant

constant (b) into the ideal gas equation that was equal to the volume actually occupied by a mole of gas particles. Because the volume of the gas particles depends on the number of moles of gas in the container, the term that is subtracted from the real volume of the gas is equal to the number of moles of gas times b.

P(V - nb) = nRT

When the pressure is relatively small, and the volume is reasonably large, the nb term is too small to make any difference in the calculation. But at high pressures, when the volume of the gas is small, the nb term corrects for the fact that the volume of a real gas is larger than expected from the ideal gas equation.

The assumption that there is no force of attraction between gas particles cannot be true. If it was, gases would never condense to form liquids. In reality, there is a small force of attraction between gas molecules that tends to hold the molecules together. This force of attraction has two consequences: (1) gases condense to form liquids at low temperatures and (2) the pressure of a real gas is sometimes smaller than expected for an ideal gas.

To correct for the fact that the pressure of a real gas is smaller than expected from the ideal gas equation, van der Waals added a term to the pressure in this equation. This term contained a second constant (a) and has the form: an²/V². The complete van der Waals equation is therefore written as follows.

This equation is something of a mixed blessing. It provides a much better fit with the behavior of a real gas than the ideal gas equation. But it does this at the cost of a loss in generality. The ideal gas equation is equally valid for any gas, whereas the van der Waals equation contains a pair of constants (a and b) that change from gas to gas.