What to use each value of R

[GraceChen2A]

I'm confused on what values of the gas constant to use for different equations, particularly 8.314 J/Kmol and 8.206x10^-2 Latm/Kmol. What is the difference between them?

[Niharika Reddy 1D]

Those gas constant values are equivalent, but given in different units. 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(V_final/V_initial). 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).