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Rate of reaction, rate constants, and Arrhenius' Equation

  1. Sep 25, 2009 #1
    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)
    3.06×10-4 10
    4.84×10-4 16
    6.50×10-4 20
    1.40×10-3 31
    2.87×10-3 42
    4.16×10-3 48
    5.94×10-3 54
    7.92×10-3 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.

  2. jcsd
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