Suggested Reading: Sec 14.3 of your lecture text.
The reaction under study here is
The rate law has the general form
Since [OH-] >> [CV+], the OH- concentration is essentially constant, and the rate law is written as
Your goals here are threefold: you will determine m, the kinetic order of this reaction, the kinetic rate constant k, and the half-life of the reaction.
In terms of absorbance (Abs), areaction that is zero-order in a given reactant has a rate law
Rate = k(Abs)0 = k
In integrated form this rate law looks like
Abs = -kt + Abs0, where Abs0 is the absorbance at time = 0. Thus, if a reaction is zero-order, a plot of Abs vs time will be linear with slope = -k.
A reaction that is first order has a rate law of the form
Rate = k(Abs)
In integrated form this rate law is
ln(Abs) = -k*t + ln(Abs)0
Therefore, for a first-order reaction, a plot of ln(Abs) vs time (t) will be linear, with slope = -k and y-intercept = ln(Abs)0.
A second-order reaction has as its rate law
Rate = k(Abs)2
A second-order reaction will obey the integrated rate law
1/Abs = k*t + 1/Abs0
For a second-order reaction, a plot of 1/Abs vs time will be linear with slope = k and y-intercept = 1/Abs0.
You will deduce the reaction order and rate constant k by making the plots above. Import your data into excel, and plot both runs (where the crystal violet concentration was varied) on the same graph.
First, plot the data in zero-order form (Abs vs t):
This plot (note that all plots should show the results from both runs) doesn't appear to be linear. We plot the data in first-order form (ln(Abs) vs time):
That looks a little better in terms of being linear, but we can't be certain until we plot the data in second order form:
Find the plot (zero, first, or second-order form) which best linearizes the data, and have excel fit a trendline. This gives the reaction order (whichever plot was linear), and from the slope of the trendline on the linear plot, we get the kinetic rate constant (don't forget that this quantity has units!!)
Your final chore is to determine the half-life from the kinetic plots. This can be done in one of two ways:
