0.15 Phase transitions and phase equilibrium  (Page 2/7)

Observation 1: Gas-Liquid Phase Transitions

We begin by returning to our observations of Charles’ Law, which states that the volume of a fixed sample of a gas is proportional to the absolute temperature of the gas, provided that the pressure is held constant. Remember that we observed Charles’ Law by trapping an amount of gas in a cylinder fitted with a piston and applying a fixed pressure to the piston. When we vary the temperature of the gas, the piston moves to maintain a constant pressure of the trapped gas, since the pressure applied to the piston is constant. At each temperature, the piston moves to a new point with a new total volume inside the cylinder, and we can then measure the volume of the gas. Our measurements showed that the gas volume is proportional to the absolute temperature in Kelvin. Thus, in Figure 1, a graph of the volume of 1.00 mol of butane gas (C ₄ H ₁₀ ) versus its absolute temperature is a straight line, and that straight line could be extrapolated to a zero volume at 0 K.

What if we keep lowering the temperature? Do we observe the extrapolated straight line in Figure 1? To find out, we take exactly 1.00 mol of butane gas at 1 atm pressure inside our cylinder. When we start at a temperature of 400 K and slowly lower it to 300 K, we observe the expected proportional decrease in the volume from 32.8 L to 24.6 L. We also observe that this proportionality works very well for temperatures just slightly above 272.6 K, where the volume is 22.4 L. However, as shown in Figure 1, when we reach 272.6 K, the volume of the butane drops very abruptly, falling to about 0.097 L at temperatures just slightly below 272.6K. This is less than one-half of one percent of the previous volume! This striking change in volume is shown in Figure 1 as a vertical line at 272.6 K. The new volume is so small that it looks like a zero volume on the graph. Actually, the volume is non-zero, just very small in comparison to the previously measured volumes.

This dramatic change in physical properties at one temperature is referred to as a “phase transition.” When cooling butane through the temperature 272.6 K, the butane is abruptly converted at that temperature from one phase, gas, to another phase, liquid, with very different physical properties.

If we reverse the process, starting with liquid butane at 1 atm pressure and a temperature below 272.6 K and heat it, we find that the butane remains entirely liquid for temperatures below 272.6 K and then becomes entirely gaseous for temperatures above 272.6 K. We refer to the temperature of the phase transition by the familiar name “boiling point temperature.” (We will discuss the phases present at the boiling point, rather than above and below that temperature, in the next section.)

We now consider how the phase transition between solid and liquid depends on a variety of factors, including the amount of substance, the type of substance, and the pressure we apply. We first look at changing the amount of the substance by capturing 2.00 mol of butane in the cylinder, still at 1 atm pressure. The volume of 2.00 mol of butane is twice than that of 1.00 mol, by Avogadro’s Law. The proportional volume decrease of 2.00 mol of gas is shown in Figure 2 along with the previous result for 1.00 mol. Note that the phase transition is observed to occur at exactly the same temperature, 272.6 K, even though there is double the mass of butane. Apparently, the boiling point does not depend on how much liquid or gas there is in a sample.