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

## 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

Jun 23, 2018

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.

The straight-line version of the Arrhenius equation is:

${\overbrace{\ln k}}^{y} = {\overbrace{- {E}_{a} / R}}^{m} {\overbrace{\frac{1}{T}}}^{x} + {\overbrace{\ln A}}^{b}$

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:

$\implies \text{slope} = \frac{\Delta \left(\ln k\right)}{\Delta \left(1 / T\right)} = \frac{- 26.7639 - \left(- 27.361\right)}{0.002681 - 0.004348}$

$\approx$ $- {\text{358.19 K}}^{- 1}$

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

$- {\text{358.19 K}}^{- 1} = \frac{\ln A - \left(- 27.361\right)}{0 - 0.004348}$

$\implies \text{y-intercept} = \ln A = - 25.804$

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

$\ln k = - {E}_{a} / R \frac{1}{T} + \ln A$

The slope then allows us to find the activation energy:

$\textcolor{b l u e}{{E}_{a}} = - R \cdot \text{slope}$

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

$=$ $\textcolor{b l u e}{\text{2.98 kJ/mol}}$

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

$\textcolor{b l u e}{A} = {e}^{\text{y-intercept}}$

$= {e}^{- 25.800}$

$= \textcolor{b l u e}{6.24 \times {10}^{- 12} \text{cm"^3"/molecule"cdot"s}}$

or perhaps in units we are more familiar with... this is equal to $3.76 \times {10}^{9} {\text{M"^(-1)cdot"s}}^{- 1}$.

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:

$\ln k = - {E}_{a} / R \frac{1}{T} + \ln A$

From this, the example slope is

$- {E}_{a} / R = - {\text{359.78 K}}^{- 1}$

and the example y-intercept is

$\ln A = - 25.798$

Therefore, the activation energy is:

$\textcolor{b l u e}{{E}_{a}} = - R \cdot \text{slope}$

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

$=$ $\textcolor{b l u e}{\text{2.99 kJ/mol}}$

and the frequency factor is:

$\textcolor{b l u e}{A} = {e}^{\text{y-intercept}}$

$= {e}^{- 25.798}$

$= \textcolor{b l u e}{6.25 \times {10}^{- 12} \text{cm"^3"/molecule"cdot"s}}$

or perhaps in units we are more familiar with... this is equal to $3.77 \times {10}^{9} {\text{M"^(-1)cdot"s}}^{- 1}$.

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