1 answer

Is there a way to calculate values in the Arrhenius equation without a graphing calculator?

Question:

My Chemistry professor never mentioned anything about using graphing apparatuses, so

Just part A This video confuses me, not to mention that I don't own a TI-85. I have a TI-84 Plus


Answers

Well, you can do it on Excel, or by hand... You may want to take a look at this 10-minute video I made, which teaches you how to use Excel for Chemistry:


DISCLAIMER: LONG ANSWER! Lots of images.

Let's try an example... consider the following reaction.

https://kinetics.nist.gov/kinetics/Detail?id=1989NES/PAY5158-5161:1

https://kinetics.nist.gov/kinetics/Detail?id=1989NES/PAY5158-5161:1

The straight-line version of the Arrhenius equation is:

#overbrace(ln k)^(y) = overbrace(-E_a/R)^(m) overbrace(1/T)^(x) + overbrace(ln A)^(b)#

METHOD 1

Since you know that the activation energy is a constant with respect to a small enough temperature range, this should be a straight line if you plot #ln k# vs. #1//T#.

Once you calculate #ln k# and #1//T# by hand... and it is an exercise you should attempt...

You should get:

When doing it by hand, you could pick the first and last data points, as it is a straight line... in doing so, estimate the slope:

#=> "slope" = (Delta(lnk))/(Delta(1//T)) = (-26.7639 - (-27.361))/(0.002681 - 0.004348)#

#~~# #-"358.19 K"^(-1)#

The y-intercept will also be needed, and it is estimated by extrapolating back to #1//T = 0# using the slope:

#-"358.19 K"^(-1) = (ln A - (-27.361))/(0 - 0.004348)#

#=> "y-intercept" = ln A = -25.804#

From here we should compare to the straight-line version of the Arrhenius equation:

#ln k = -E_a/R 1/T + ln A#

The slope then allows us to find the activation energy:

#color(blue)(E_a) = -R cdot "slope"#

#= -8.314 cancel"J""/mol"cdotcancel"K" xx ("1 kJ")/(1000 cancel"J") xx -358.19 cancel("K"^(-1))#

#=# #color(blue)("2.98 kJ/mol")#

The y-intercept allows us to find the frequency factor:

#color(blue)(A) = e^("y-intercept")#

#= e^(-25.800)#

#= color(blue)(6.24 xx 10^(-12) "cm"^3"/molecule"cdot"s")#

or perhaps in units we are more familiar with... this is equal to #3.76 xx 10^9 "M"^(-1)cdot"s"^(-1)#.

METHOD 2

Or, if you aren't that visual... on Excel, simply set up data columns like this:

Then select D3 through E9 and go to Insert > Recommended Charts > All Charts > X Y (Scatter).

You should get this:

With a little bit of formatting, you could get this:

And by right-clicking on the data point, go to Add Trendline, then scroll down to find and click "Display equation on chart" and "Display R-squared value on chart".

What you should end up with is:

From this we should again compare to the straight-line version of the Arrhenius equation:

#ln k = -E_a/R 1/T + ln A#

From this, the example slope is

#-E_a/R = -"359.78 K"^(-1)#

and the example y-intercept is

#ln A = -25.798#

Therefore, the activation energy is:

#color(blue)(E_a) = -R cdot "slope"#

#= -8.314 cancel"J""/mol"cdotcancel"K" xx ("1 kJ")/(1000 cancel"J") xx -359.78 cancel("K"^(-1))#

#=# #color(blue)("2.99 kJ/mol")#

and the frequency factor is:

#color(blue)(A) = e^("y-intercept")#

#= e^(-25.798)#

#= color(blue)(6.25 xx 10^(-12) "cm"^3"/molecule"cdot"s")#

or perhaps in units we are more familiar with... this is equal to #3.77 xx 10^9 "M"^(-1)cdot"s"^(-1)#.

We more-or-less got the same thing either way, so both ways work.

.

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