## R Constants

Ishkhan 3O
Posts: 24
Joined: Fri Sep 26, 2014 2:02 pm

### R Constants

How do we know which constant to use for R? Or do we just need to look at the units and see which one the units match?

Niharika Reddy 1D
Posts: 127
Joined: Fri Sep 26, 2014 2:02 pm

### Re: R Constants

Yes, as you said, you essentially just look at units to see which form of the gas constant you should use. The conversion factor between joules and (L atm) is 101.325 J=1 (L atm). If you take 0.08206 (L atm)/(K mol) and multiply it by 101.325 J/(L atm), you are left with another equivalent version of the gas constant: 8.3145 J/(K mol). Which one we use depends on what we are trying to find for that particular problem to make it easier at the end.

For instance, if we were trying to find volume (L) and we know pressure (atm), amount of gas (mol), and temperature (K), we use R=0.08206 (L atm)/(K mol) and the ideal gas law PV=nRT, because all the units would cancel except for "L", which is what we are solving for.

When calculating work for an isothermal, reversible expansion, w=-nRTln(Vfinal/Vinitial). In this case, we want our final answer in J, so instead of using the gas constant in terms of (L atm)/(K mol), we use the one in terms of J/(K mol) to save the step of converting into J at the end. You could use the first one and still end up with the same answer if you just convert from (L atm) to J using the following conversion factor: 101.325 J=1 (L atm).