How do you plot the Arrhenius equation?

1 Answer
Mar 26, 2016

Answer:

You draw a graph of #lnk# vs. #1/T#.

Explanation:

The Arrhenius equation is

#k = Ae^(-E_a//RT)#

where

  • #k# is the rate constant
  • #A# is the pre-exponential factor
  • #E_a# is the activation energy
  • #R# is the universal gas constant
  • #T# is the temperature

If we take the logarithms of both sides, we get

#lnk = lnA color(white)(l)–E_a/(RT)#

or

#lnk = -(E_a/R)1/T + lnA#

This is the equation of a straight line

#y = mx + b#

where #m# is the slope and #b# is the slope of a plot of #y# vs #x#.

#lnk = ("-"E_a/R)1/T + lnA#
#color(white)(ll)y =color(white)(mm) mcolor(white)(mll)xcolor(white)(ll) + color(white)(ll) b#

By comparing the equations, we see that the slope of the line is #"-"E_a/R# and the #y# intercept is #lnA#

Hence, if we draw a graph of #lnk# vs. #1//T# at various temperatures, we should get a straight line.

Example

For a certain reaction, the data were:

#bbTbb"/°C" color(white)(ml)bb"k/s"^"-1"#
#color(white)(ll)477 color(white)(mll) 0.00018#
#color(white)(ll)523color(white)(mll)0.0027#
#color(white)(ll)577color(white)(mll)0.030#
#color(white)(ll)623 color(white)(mll)0.26#

Plot the Arrhenius equation using the above values.

Solution

We have to plot #lnk# vs #1//T#.

We must convert the temperatures to kelvins and take their reciprocals.

We must also take the natural logarithms of the rate constants.

Although we could do this by hand, I find it easier to do the calculations and the plot in Excel.

Here's are my results.

Arrhenius Plot