Posted: Fri Feb 21, 2020 9:25 pm
What is the original equation that lnK2/lnK1=-dH/R * (1/T2-1/T1) is derived from?
Posted: Fri Feb 21, 2020 9:39 pm
This equation is derived from a litany of other steps and equations.
First, we know that deltaGknot = -RTlnK, and that deltaGknot = deltaHknot - TdeltaSknot. So, substituting each equation in for deltaGknot, we get that
-RTlnK = deltaHknot - TdeltaSknot.
Next, if we know that deltaHknot is some specific value, we can divide both sides by -RT to get lnK = (deltaHknot/-RT) + (deltaSknot/R).
We know that a given temperature T1, there is a specific equilibrium constant K1, so lnK1 = (deltaHknot/-RT1) + (deltaSknot/R)
Similarly, at a given temperature T2, there is a specific equilibrium constant K2, so lnK2 = (deltaHknot/-RT2) + (deltaSknot/R).
lnK2 - lnK1 = ln(K2/K1), by the properties of logarithms.
ln(K2/K1) = (deltaHknot/-RT2) + (deltaHknot/RT1), assuming that deltaSknot is constant in regards to temperature.
Hence, we can take out a -deltaHknot/R value from the equation via the inverse distributive property to get
ln(K2/K1)=-dH/R * (1/T2-1/T1)