The vapor-liquid phase change of a refrigerant is used for cooling. A generic pressure-temperature phase diagram is shown below.pressure-tempt phase diag
According to the phase diagram, the vapor and liquid phases of the refrigerant must coexist along a pressure-temperature phase boundary, shown by the blue line between the vapor and liquid phases. This line only exists between the triple point and the critical point.
A simple explanation of refrigeration is as follows: vaporizing the liquid (which occurs in a cooling systems evaporator) consumes heat in order to cross the phase boundary, so the surrounding air is cooled. Condensing liquid (which occurs in a cooling systems condenser) releases heat in order to cross the phase boundary, so the surrounding air is heated. Essentially, the cooling system removes heat from one area and transfers it to another but repeatedly vaporizing and condensing the refrigerant.
In order for these processes necessary for refrigeration to take place, the refrigerant must be between Ttp and Tcr on the temperature axis and Ptp and Pcr on the pressure axis, as shown on the phase diagram. Each refrigerants pressure-temperature phase diagram has different triple point and critical point temperature and pressure values, resulting from different interactions between the molecules.
Phase diagram from
Since different refrigerants have different pressures and temperatures at which vapor and liquid can coexist, different operating conditions are required. The following chart, known as a Pressure-Temperature (PT) Chart shows the pressure in Psig for each refrigerant at a given temperature.click here
Essentially the PT chart lists the numerical values for the location of the blue line on the phase diagrams. If we want to operate R22 and R410a at the same temperature, then different pressures are required. For instance, if we look at room temperature, ~70F, then we see that R22 is operated at 121.5 Psig, but R410a must be operated at a much higher pressure, 201.5 Psig. Although I am not sure exactly what temperatures and pressures real refrigerant systems operate at, this gives you an idea of why R410a needs a higher pressure than R22 for comparable temperatures.
Therefore, the property responsible for the difference in operating pressures of R22 and R410a is the location of the liquid-vapor coexistence line on the pressure-temperature phase diagram.
Note: A complete understanding of how refrigeration and refrigerants work requires additional understanding of thermodynamics, heat engines, and the refrigeration cycle. The explanation given in the second paragraph is a simplified version of the whole story.