molar mass), the equation for vrms is also often written as follows:
Notice that these last two equations can only determine vrms. It’s important to
realize that the molecules in the container have a wide range of speeds; some are
much slower and others are much faster than vrms. The root-mean-square speed is
important because it gives us a type of average speed that’s easy to calculate from
the temperature of the gas.
- What happens to the rms speed of the molecules in a sample of
helium gas if the temperature is increased from −73°C to 527°C?
Here’s How to Crack It
When we use the ideal gas law or the formulas for vrms, we have to use absolute
temperatures—that is, temperatures expressed in kelvins. The conversion between
degrees Celsius and kelvins is T°C + 273 = T, so −73°C = 200 K and 527°C = 800
K. Therefore, the absolute temperature of the gas is increased by a factor of 4 (from
200 K to 800 K). Since vrms is proportional to , if T increases by a factor of 4,
then vrms increases by a factor of = 2.
- What happens to the pressure of a sample of helium gas if the
temperature is increased from 200 K to 800 K, with no change in
volume?
Here’s How to Crack It
The ideal gas laws, PV = nRT, tells us that if V remains constant, then P is
proportional to T. So, if T increases by a factor of 4, then so will P.