Rate of reaction, rate constants, and Arrhenius' Equation

In summary, the effect of temperature on the rate of a reaction was studied using the Arrhenius equation. By plotting ln k versus 1/T, the slope can be calculated using linear regression to determine the activation energy.
  • #1
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Homework Statement



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.


Homework Equations



Relevant equations listed in part 1

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 don't 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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  • #2
Strictly speaking, logarithms are unitless (formally, the rate constants are multiplied by a time unit, giving a unitless quantity for the logarithm/exponential to act on). So I wouldn’t worry too much about that. But other than that, yes, plot the data and take the slope to get the activation energy (pay attention to the negative sign).
 

1. What is the rate of a chemical reaction?

The rate of a chemical reaction is the speed at which reactants are converted into products. It is typically measured in terms of the change in concentration of a reactant or product per unit time.

2. What is a rate constant?

A rate constant, denoted by k, is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants. It is specific to each reaction and is affected by factors such as temperature, pressure, and catalysts.

3. How is the rate constant related to the rate of reaction?

The rate constant is directly proportional to the rate of reaction. This means that as the rate constant increases, the rate of reaction also increases. Conversely, a decrease in the rate constant results in a slower rate of reaction.

4. What is Arrhenius' Equation?

Arrhenius' Equation is a mathematical formula that relates the rate constant of a reaction to the temperature and the activation energy of the reaction. It is given by k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

5. How does temperature affect the rate of reaction?

An increase in temperature generally leads to an increase in the rate of reaction. This is because higher temperatures provide more energy to the reactant molecules, increasing their kinetic energy and thus the frequency of successful collisions. This relationship is described by the Arrhenius Equation.

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