Activation Energy and Temperature Dependence of Rates:

According to collision theory, molecules must collide to react. At a higher temperature, molecules move faster, and will collide more often. Also at a higher temperature, the reactant molecules carry more energy and there is a greater proportions of the collisions will have enough energy to lead to product. The Activation Energy (Ea) is the minimum energy that must be overcome for the reactant to proceed to products. See the reaction coordinate diagram below.

The Arrhenius equation relates the rate constant to temperature.

    (eqn 15)

where k is the rate constant

A is the total number of collisions
Ea is the activation energy
R is the gas constant (8.314 J/mol)
T is temperature in Kelvins ( °C + 273.15)

If we take the natural log (ln) of both sides of the Arrhenius equation we get

    (eqn 16)

and since the natural log of e is 1, eqn 16 simplifies to

    or       (eqn 17)

This is an equation for a straight line. A plot of ln k on the y-axis vs 1/T on the x axis will have a slope = -Ea/R and a y-intercept of ln A. We are interested in determining the Ea for the reaction.

For Runs 6-9 the [S2O82-] and [I-] are constant and only the temperature changes. From this data you will calculate the rate

    (eqn 10)

and rate constant, k.

(eqn 14)

Again it is best to summarize the data in a table. For example

Table III: Summary of Rates vs Temperature
Run Rate Rate Constant (k) ln k Temperature (°C) 1/T (K)
6          
7          
8          
9          

Draw a graph of ln k vs 1/T following these basic guidelines:

1. use a graphing program (Excel, KaleidiaGraph, Cricket graph....) or use good graph paper. (see http://www.ncsu.edu/labwrite/res/gt/graphtut-home.html for a brief into to graphing with Excel)
2. axis should be labeled. Plot the dependent variable on the y-axis, and the independent variable on the x-axis.
3. a caption or title explaining what the graph means.

Determine the value for Ea from the slope of the line through your data. One method for determining the slope and y-intercept is to perform a Least Squared Analysis. This is also referred to as a Linear Regression Analysis. Most graphical calculators or graphing programs are capable of this analysis. Otherwise you will determine these values from the graph.

  and     (eqn 18)

You do not have to do an uncertainty analysis for any data in this experiment.

You also need to answer the discussion questions.