Andrew's Experiment on Carbon Dioxide

Andrew's experiment on carbon dioxide

Andrews made a systematic study of the effect of pressure on the volume of gases at different temperatures. He measured the volume of a given mass of the gas at various pressures at a constant temperature and then plotted graphs connecting pressure and volume at different temperatures. These graphs are called isothermals. Obtaining isothermals for different fixed temperatures, it is possible to see when and how the gas deviates from Boyle’s law.

Procedure

The experiment is performed by maintaining a given mass of carbon dioxide at any desired temperature. Pressure of CO₂ is gradually increased from a small value to a very high value and the corresponding volumes of carbon dioxide are noted. A graph is plotted with pressure P along the Y-axis and the volume V along the X-axis. The experiment is done maintaining carbon dioxide at different constant temperature, 13° C, 21°C, 31.1°C, 35.5°C, 48°C... etc.

The isothermals of carbon dioxide at various temperatures are shown in the figure.

Explanation of the Isothermals

Consider the isothermal ABCD at 13°C.

At 13°C, the portion A B represents the gaseous state of carbon dioxide. The curve AB is a parabola. So up to the point B the gas obeys Boyle's law. From B to C it shows an, enormous decrease in volume with a slight increase in pressure. The portion BC represents the-change of state of carbon dioxide from gaseous state to the liquid state.  At C, the whole of the gas has been liquefied. The portion CD represents the liquid state of carbon dioxide because there is no appreciable decrease in volume with increase in pressure.

At 21°C, the curve is similar to that at 13°C; but the horizontal portion has decreased. As the temperature is further raised the horizontal portion of the graph becomes smaller and smaller and finally becomes a point O at 31.1°C. Above this temperature the horizontal part is absent from all isothermals. It shows that the gas cannot be liquefied any more.

Andrews found that the liquefaction of carbon dioxide occurred only below 31.1°C. This temperature is called the critical temperature (T_c) of carbon dioxide. The isothermal corresponding to 31.1°C, the critical temperature is called the critical isothermal. The point of inflexion O, where the horizontal portion of the isothermal is reduced to a point is called the critical point.

Isothermals for water vapour at different temperature are given below.

The pressure-volume relation for a mole of H₂0 is plotted as a set of curves, one for each temperature. At 350°C the portion A B represents the gaseous state. Upto B it more or less obeys Boyles law. The portion BC represents the change of state from gas to liquid. At C it is completely converted into liquid. The molar volumes of liquid and vapour at C and B are very different. At higher temperature, the horizontal portion of the curve has decreased. At 374°C the horizontal portion has vanished and the gas cannot be liquefied by applying pressure. The temperature corresponding to this curve is called critical temperature T_C.

Results:

Andrews summarized the experimental results as follows:

(i)For every gas, there is a particular temperature below which alone the gas can be liquefied by the mere application of pressure. This temperature is called the critical temperature of the gas. Critical temperature of CO₂ is 31.1°C, O₂ is —118.8°C, nitrogen is —147.1°C, hydrogen is —240°C and helium is —268°C.

(ii) There is no essential difference between easily liquefiable and permanent gases. All gases can be liquefied below their critical temperatures by the mere application of pressure.

(iii) There exists a continuity of the liquid and gaseous states. This means that there is no physical distinction between the liquid and gaseous state of a substance. In other words, the two states are only two stages in a series of physical operations.

(iv) All gases equally remote from the critical temperature behave similarly to Boyle's law.

(v) At critical point (a) the densities of the liquid and the vapour gradually merge into one, (b) the boundary between liquid and gas disappears, and (c) compressibility of vapour becomes infinite.

Critical temperature (T_c)

Critical temperature of a substance is that particular temperature below which alone the gas can be liquefied by the mere application of pressure.

Critical pressure (P_c)

Critical pressure of a gas is the pressure that should be applied to the gas at its critical temperature in order to liquefy it.

Critical volume (V_c)

Critical volume of a gas is the specific volume ( i.e the volume of the gas per unit mass) of the gas at critical temperature and pressure. The critical temperature (T_c), the critical pressure (P_c) and the critical volume (V_c) of a gas are called the critical constants of the gas.