# How do you calculate the pre-exponential factor from the Arrhenius equation?

##### 1 Answer

By graphing.

The Arrhenius equation is

#\mathbf(k = Ae^(-E_a"/"RT))# ,where:

#k# is therate constant, in units of#1/("M"^(1 - m - n)cdot s)# , where#m# and#n# are the order of reactant#A# and#B# in the reaction, respectively.#A# is thepre-exponential factor, correlating with the number of properly-oriented collisions.#E_a# is theactivation energyin, say,#"J"# .#R# is theuniversal gas constant,#"8.314472 J/mol"cdot"K"# .#T# is thetemperaturein#"K"# .

So by taking the natural log, we can solve for

#ln k = lnAe^(-(E_a)/(RT))#

#= lnA - (E_a)/(RT)#

Thus, we have

#color(blue)(stackrel(y)overbrace(ln k) = stackrel(m)overbrace(-(E_a)/(R))stackrel(x)overbrace(1/T) + stackrel(b)overbrace(lnA))#

Therefore, simply graph multiple values of

**can be gotten experimentally**; just know your initial concentrations and reactant orders, and time the reaction accurately. Then determine the rate based on a particular reactant (

However, *can't be obtained by observation*, and neither can **experimentally possible** to determine

The less foolproof way that doesn't require multiple data points is to simply divide.

#color(green)(A = k/(e^(-E_a"/"RT)))#

For this you would have to know the activation energy, rate constant, and temperature ahead of time, which you normally don't. Normally