I need to solve an equation i'm very stuck help :/

Hi,
Im super stuck on this:

rate=Ae^(-(Ea/RT))

I need to solve this for Ea, knowing that A, e and R are constants, T is temperature.
thank you so much to anyone who can help

Reply 1

shrey19

Hey!

The equation if I'm not mistaken is k=Ae^(-Ea/RT)

Where k is the rate constant, A is the arrhenius constant, T is the absolute temperature in Kelvin, R is the gas constant= 8.31 J/(Kmol) and Ea is the activation energy.

So how it's done is by applying the logarithm base e on either side.

This gives You-
ln(k)= ln(Ae^(-Ea/RT))

This can be simplified using log rules to-
ln(k)= ln(A) + ln(e^(-Ea/RT)
ln(k)= ln(A) - Ea/R (1/T)
ln(k)= (-Ea/R)(1/T) + ln(A)

This looks just like the general line equationy=mx+c where
m=-Ea/R
x= 1/T
y= ln(k)
And c=ln(A)
If you plot a graph of ln k against 1/T you get a straight line with a negative slope. You can find this slope using m=(y2-y1)/(x2-x1)
Equate this m value to -Ea/R
So if m=-Ea/R
Then Ea= -mR
That's how you get Ea since you already know what R is and have calculated m.

NOTE: Ea should always be positive. In case you get a negative answer you know you messed up somewhere.