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Rate of reaction, rate constants, and Arrhenius' Equation

by physics120
Tags: arrhenius, constants, equation, rate, reaction
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physics120
#1
Sep25-09, 06:39 PM
P: 34
1. The problem statement, all variables and given/known data

The effect of temperature on the rate of a reaction was studied and the following data obtained:

k (s-1) T (C)
3.0610-4 10
4.8410-4 16
6.5010-4 20
1.4010-3 31
2.8710-3 42
4.1610-3 48
5.9410-3 54
7.9210-3 59


It is known that the variation of the rate constant k with the absolute temperature T is described by the Arrhenius equation:


k = A exp^[( -Ea )/(RT)]


where Ea is the activation energy, R is the universal gas constant and A is the pre-exponential factor (units of the rate constant). Taking the natural logarithm of both sides affords:


ln k = ln A - Ea/RT


a) For a plot of y = ln k versus x = 1/T, calculate the slope of the best straight line using linear regression.

b) Calculate the activation energy Ea.


2. Relevant equations

Relevant equations listed in part 1

3. The attempt at a solution

Do I need to plot this data? Is there any way to do this without using excel or a graphing calculator? If there isn't, I tried putting these in a spreadsheet, then plot ln k in the y axis and 1/T on the x axis and then use Excel's "trendline" to get the slope. (The slope is Ea/R. So Ea is R x slope for part 2). However, I got -38.619 for the slope.. although, I dont know if this is right or wrong as I seem to keep getting the units wrong, are the not the units for (ln k)/(1/T), which is s^(-1)/degC^(-1), or degC/s??? (where degC = degrees celcius)

If there is another way to figure this out, and if you know why I am getting the wrong units, help would be greatly appreciated! Once I know the first part, part b is a cinch.

Thank-you!
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