Units and the Ideal Gas Law

Suppose that we had expressed the temperamre in °C rather than in kelvins in the above example It should take you only a little work to convince yourself that the equation we used will not hold true. Changing the temperature of a gas from 10 to 20°C, for example, will not double its volume. The ideal gas law itself is only valid when we use an absolute temperature scale where T= 0 corresponds to absolute zero temperature. Th see why this must be so, notice that putting T= 0 into the gas law implies that either P or For both must also go to zero, meaning that there must be no gas present. This simply can t be correct for T = 0°C or T = 0°F that s obvious because the winter temperature routinely reaches these levels in many areas, and yet the air in the atmosphere obviously does not vanish. Absolute zero (0 K), on the other hand, is a very special temperature, and it is reasonable that there might be peculiar consequences if we actually cooled a gas to this level. 

Although absolute zero is a fairly abstract concept, temperatures well below 1 K can be achieved routinely in the laboratory. 

No degree sign is used when writing Kelvin temperatures. 

If you look at a table like the one in Appendix B of this book, you will find values for R in several combinations of units. 

Students often ask how to decide which of these values is the right R to use in a given situation. The answer is that they are all really the same quantity, just expressed in different units. (If you are curious, you can do unit conversions to verify this for yourself.) If pressure is given in atm and volume in L, then it will be convenient to use R as 0.08206 L atm mol K , for example. But if pressures are given in torr, it might be easier to insert 62.37 L torr mol K for R. Or, if you always prefer to use the same value of R, you could simply convert pressures from any other units into atm before doing any calculations. It doesn t matter which set of units we choose, as long as we are careful to reconcile the units in all of our calculations. 

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