## Derivation of Arrhenius Equation

Arrhenius Equation: $\ln k = - \frac{E_{a}}{RT} + \ln A$

Jason Wu 1E
Posts: 101
Joined: Thu Jul 25, 2019 12:15 am

### Derivation of Arrhenius Equation

I was wondering how the ln(k') - ln(k) = Ea/R ((1/T)-(1/T')) is derived? What was the starting equation for this? I'm curious because this equation is not on the equation sheet.

jisulee1C
Posts: 149
Joined: Thu Jul 25, 2019 12:17 am

### Re: Derivation of Arrhenius Equation

I think this equation is derived using the Arrhenius equation for two different temperatures but it is not on the objectives sheet as something we need to do. Instead, I would memorize the equation because it is useful and not on the equations sheet.

WYacob_2C
Posts: 102
Joined: Sat Jul 20, 2019 12:16 am

### Re: Derivation of Arrhenius Equation

If the original equation is the Arrhenius equation, what happens to the lnA when you derive the equation used to calculate rate constants at different temperatures (the one written in the original question)?

alex_4l
Posts: 109
Joined: Thu Sep 26, 2019 12:18 am

### Re: Derivation of Arrhenius Equation

Could someone give an example of when the Arrhenius Equation would have to be used?

Ashley Tran 2I
Posts: 108
Joined: Thu Jul 11, 2019 12:17 am

### Re: Derivation of Arrhenius Equation

When the prompt talks about temperature, activation energy, and/or the rate constant, it is indicating the use of the Arrhenius equation.

Tyler Angtuaco 1G
Posts: 130
Joined: Wed Sep 11, 2019 12:16 am

### Re: Derivation of Arrhenius Equation

The Arrhenius equation can be re-written as ln k = -Ea/RT + ln A if you take its natural log. In this new form, you can compare the rate constants at two different temperatures using the equation you listed since subtracting lnk of one temperature and lnk of another cancels the term lnA.

Shail Avasthi 2C
Posts: 101
Joined: Fri Aug 30, 2019 12:17 am

### Re: Derivation of Arrhenius Equation

This is done using two different symbolic temperature values, plugging them into the Arrhenius Equation, and subtracting these equations to solve for the rate constants. Pretty much the same as what we did for the Van't Hoff equation (relating temperature changes to a change in K)