I am having some trouble in figuring out how units can be used when writing reaction quotients/ equilibrium constants / Nernst Equation. This discussion started in another forum (http://www.physicsforums.com/showthread.php?t=610792
) but it seems I've reached a dead end there, so any help is welcome.
Essentially, I'm puzzled by how we can use apparently arbitrary units when writing the reaction quotient. Suppose we have a very simple reaction, so that its ΔG can be written as
ΔG = - RT ln p0
So far so good. But what if we change the units? Suppose instead of using atm to measure pressure, we choose another unit, mta, such that 1 mta = 2atm. Well, this means that the new value of pressure p will be p = p0
/2. But R also changes when going from atms to mtas, and to fix it, we may use the ideal gas law. Then we get that the new value for R, that I will call R' is half of the original R.
Now, lets restate equation one using our new set of units:
ΔG = - R'T ln p
And, by changing the back to the commonly using atm we get another expression of ΔG:
ΔG = - 0.5 R ln(p0
/2) (equation 2)
Now, we are still talking about the same reaction, so the value of ΔG should NOT change regardless of what units we choose. But clearly, equations 1 and 2 give different values. Why?
(if you check the link above, you'll see that the discussion started somewhat differently there. I began by inquiring how we could simply mix pressures and concentrations in the same reaction quotient when using Nernst's equation, without doing some rescaling. It appears bizarre to me that one can use mol/L and atmospheres in the same reaction quotient and get the correct result. If you do some math using the ideal gas law to find the "concentration" of gas molecules in an ideal gas under 1 atm, you find that it is FAR from being 1 mol/L so it doesn't make sense that one can plug values in such different units into the same equation and still get meaningful results).