Equation


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Bella Townsend
Posts: 50
Joined: Wed Feb 20, 2019 12:18 am

Equation

Postby Bella Townsend » Fri Feb 21, 2020 9:25 pm

What is the original equation that lnK2/lnK1=-dH/R * (1/T2-1/T1) is derived from?

Chris Tai 1B
Posts: 102
Joined: Sat Aug 24, 2019 12:16 am

Re: Equation

Postby Chris Tai 1B » 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)


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