How do I calculate the value of the gas constant in units of Pa m3/ mol K? I'm supposed to use a factor label?

The gas constant is, indeed, a constant. Wikipedia shows the constant in various units: Gas constant - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Gas_constant)

If you only have the gas constant in one set of units and wish to convert to another set of units, it's fairly simple to use "dimensional analysis" to do this.

For example, let's say you have R in Liter  Torr/ mol K

and wish to go to Pa M3 / mol K

In this case, the denominator is correct. To convert Torr to Pa:

1 Pa (N/m2) = 7.50062 Micron of mercury (millitorr)

So multiply by 1 Pa / 7.50062 E-3 Torr
(if you do the algebra, you'll see that this is simply 1 and you can multiply anything by 1 and not change it)

Note that the Torr will cancel out and you're left with Pa. Do the same thing with the Liter

1 Liter = 0.001 m3

So multiply by 1 L / 0.001 m3and viola, you have change the constant to a new set of units.