Ap chem question I cannot figure out

Question

The reaction between crystal violet (a complex organic molecule represented by CV+) and sodium hydroxide is as follows:

CV+ + OH- → CVOH

                (violet)  (colorless)   (colorless)

(a) Identify a method a chemist could use to determine the rate of this reaction. Explain why this would be an effective method.

(b) The following data were gathered from the reaction as it was studied over time. Identify the order of the 

       reaction. On the provided axes, graph the function of [CV+] vs time that would generate a straight line.  

       Label the axes.

Time (sec)	[CV+] (M)
0	5.5 x 10-5
60	3.8 x 10-5
120	2.6 x 10-5
180	1.8 x 10-5

(c) Write the integrated rate law for this reaction. Identify the value of the rate constant, to three significant figures, and include proper units.

     

(d) Calculate the half-life of the reaction.

Answer 1

Hello Ben,

One obvious (to a chemist, anyway) method that could be used to measure the rate of this reaction is spectrophotometry, monitoring the absorbance of light by the CV+. Under suitable conditions, Beer's law can be used to obtain the concentration of [CV+] vs. time. There are also ways that this could be done w/out an instrument, such as setting up a number of standard solutions and monitoring the time required for test sample to change form the color intensity of one standard sample to another.

Something to notice immediately in the data table is that for the times 0 and 120, and for 60 and 180, both of which are 120 seconds apart, the concentration of [CV+] falls by roughly half. This strongly suggests that the reaction is first order in [CV] (which could easily be the case, for instance if [OH-] is present in large excess so it is effectively constant during the reaction).

That suggests a rate law like d[CV+]/dt = -k[CV+].

Because the integrated rate law for a first order reaction would be ln([CV+]) = -kt +ln([CV+]₀) you can plot ln([CV+]) vs. t to check for first order behavior, and obtain the rate constant k. The data should closely fit a straight line, and the slope of a fitted line would correspond to -k.

You actually already roughly know the half-life from the data table, but it can also be calculated from k. There's a simple formula for that, which I'm sure you can find online if you look. It should be in your text or course materials also.

Good luck!

Answer 2

Hi Ben T.,

What specifically are you stuck on here?

If stuck on the general approach: assume pseudo-first order in CV+; graph as for an exponential decay (take ln(CV+) vs. t), negative of slope is rate constant IFF a straight line! You should use a spreadsheet, or graphing calculator, to graph and test for the exact (linear regression) slope.

Else, assume 2nd order, first order in both CV+ and OH-. You may have to adjust the assumed initial OH- concentration, to get a second-order graphical behavior. (Hint: integrated form is linear 1/[CV+] vs. t)

If neither of those work out, you may have to get quite ingenious (e.g., assume intermediate reactions).

C'mon, how would you follow a violet species reacting to make a colorless one, in solution?

-- Cheers, -- Mr. d.