CEE 670 Fall 2010

# Kinetics Homework #2

1.
 1 Point

The data below are for the decomposition of Dichloroacetonitrile (DCAN) at pH 7, and 20 C.  One column is for and ionic strength of 0.01 M (mostly NaCl), and the other for 0.03 M.  Analyze these data and make any conclusions you can regarding the nature of the hydrolysis reaction of DCAN.

 DCAN Concentration (µg/L) Time (hours) I = 0.01 M I = 0.03 M 0.00 44.49 44.74 0.75 41.10 42.29 1.50 43.73 41.64 2.50 38.84 37.87 3.50 38.27 38.45 6.50 29.22 31.97 9.50 26.94 29.17 19.50 16.25 19.31 24.50 12.66 16.44 29.50 9.52 13.49 41.50 5.42 10.06 69.50 1.55 3.83 116.50 2.05

Solution

This is an ideal data set for use of the integral method of kinetic analysis.  So, I’d prepare 0 order, 1st order and 2nd order graphs based on integral method.  Then you can assess the relative fit of the kinetic order.  It also allows you to calculate rate constants.

·         Conclusion is that 1st order in DCAN fits best, especially when last point in the high ionic strength dataset is ignored.  Why ignore that data point?  Because log transform accentuates its importance in a linear regression (expands the error).  One presumes that error is essentially constant in the un-transformed data

·         Rate constant goes up as ionic strength goes down; 0.035hr-1 to 0.049hr-1.

·         Direction and magnitude of ionic strength effects implies that reaction is between a negative species (hydroxide) and a species with a positive center (maybe the carbon on the nitrile).

2.
 1 Point

Prepare a Hammett Plot for the chlorination of phenol at high pH (i.e., phenate ions).  Use all of the rate constants in Figure 13 from Deborde & von Gunten, 2008 [Water Research 42:13-51].  To help you with this you should number each carbon and treat the attack on different carbon atoms separately even if they result in the same product.  Use the Hammett substituent constants in the attached table.  Compare your results with those obtained by Deborde & von Gunten in their Figure 15.

Solution:

I used benzene as the implicit “reference compound” instead of phenate, because attack on phenate can occur at the ortho, meta or para positions (3 different scenarios, and effectively 3 different reference reactions).  In contrast, attack on benzene is only on one carbon as they are all identical.

This requires that you include the phenoxy (-O-) group explicitly in your Hammett Plots.

Also, I included the last reaction (k6), presuming attack on both open ring positions (identical).  Many chose not to include this reaction, presumably because the exact products are not known.  This is fine, but it give different answers as noted below.

 Compound attack (wrt OH) From figure Overall Rate #sites Rate per site logk2' hydroxy anion chlorine sum σp σm σo σp σm σo Σσ phenol ortho k11 1.75E+04 2 8.75E+03 3.94E+00 -1.10 -1.1 para K12 4.40E+03 1 4.40E+03 3.64E+00 -0.81 -0.81 2-chloro ortho k21 1.78E+03 1 1.78E+03 3.25E+00 -1.10 0.37 -0.73 para k22 6.40E+02 1 6.40E+02 2.81E+00 -0.81 0.37 -0.44 4-chloro ortho k3 2.17E+03 2 1.09E+03 3.04E+00 -1.10 0.37 -0.73 2,6-dichloro para k4 1.94E+02 1 1.94E+02 2.29E+00 -0.81 0.74 -0.07 2,4-dichloro ortho k5 3.03E+02 1 3.03E+02 2.48E+00 -1.10 0.74 -0.36 2,4,6-trichloro meta k6 1.28E+01 2 6.40E+00 8.06E-01 -0.47 0.23 1.36 1.12

Regression Fit:

Logk2 (M-1s-1) = 2.24 -1.39Σσ

And if you didn’t use k6, you would have gotten

Logk2 (M-1s-1) = 1.96 -1.97Σσ

In either case the slope is much less than the one presented by Deborde & vonGunten.

3.
 1 Point

Use the Hammett Plot prepared for #2, and predict the rate constant for the reaction of chlorine with the phenate ion of 2-amino-4-nitro-5-methyl phenol.  Assume that the two unsubsituted carbons (C3 and C6) are the only sites of attack.  Estimate the relative rate of attack on these two carbons.

Solution:

First its important to recognized that you’re working with the following molecule

 2-amino-4-nitro-5-methyl phenol position C3 C6 sigma 0.89 -0.67 log k 1.0029 3.1713 k 10.1 1483.5 M-1s-1

Therefore, the overall 2nd order rate constant is 1494 M-1s-1, or about 1.5 x103 M-1s-1, with slightly more than 99% of the attack at the #6 carbon.

If you had chosen not to use k6, you would have gotten overall 2nd order rate constant of 1.62 M-1s-1, for the C3 attack and about 1.89 x103 M-1s-1 for the C6 attack.

Hammett Substituent Constants

 Substituent σp σm σo σp+ σ+m σ* R F -N(CH3)2 -0.83 -0.16 -0.36 -1.70 -0.98 0.15 -O- -0.81 -0.47 -1.10 -NH2 -0.66 -0.15 0.03 0.10 -0.74 0.08 -OH -0.35 0.08 0.04 0.25 -0.70 0.33 -OCH3 -0.26 0.08 0.00 -0.76 0.05 0.25 -0.56 0.29 -C(CH3)3 -0.20 -0.10 -0.52 -0.26 -0.18 -0.02 -CH3 -0.16 -0.07 -0.13 -0.31 -0.06 -0.05 -0.18 0.01 -CH(CH3)2 -0.15 -0.04 -0.23 -0.28 -0.19 0.04 -CH2C6H5 -0.09 -0.08 -0.28 -0.05 -0.04 -CH=CHC6H5 -0.07 0.03 -1.00 -0.17 0.10 -CH=CH2 -0.04 0.06 -0.16 -0.17 0.13 -OC6H5 -0.03 0.25 -0.50 -0.40 0.37 -C6H5 -0.01 0.06 0.00 -0.18 0.11 0.10 -0.13 0.12 -H 0 0 0 0 0 0 0 0 -NHCOCH3 0.00 0.21 -0.60 -0.31 0.31 -CH2OH 0.01 0.01 0.04 -F 0.08 0.35 0.54 -0.07 0.35 0.52 -0.39 0.45 -Cl 0.23 0.37 0.68 0.11 0.40 0.47 -0.19 0.42 -Br 0.23 0.39 0.70 0.15 0.41 0.45 -0.22 0.45 -I 0.28 0.35 0.63 0.14 0.36 0.39 -0.24 0.42 -CONH2 0.36 0.28 0.72 0.10 0.26 -CHO 0.42 0.35 0.75 0.73 0.09 0.33 -COC6H5 0.43 0.34 0.51 0.12 0.31 -COOCH3 0.45 0.36 0.49 0.11 0.34 -COCH3 0.50 0.38 0.17 0.33 -CN 0.68 0.62 1.32 0.66 0.56 0.58 0.15 0.51 -CH3SO2 0.71 0.65 0.59 -NO2 0.79 0.71 1.40 0.79 0.67 0.63 0.13 0.65

Note that σo values are estimated for phenols; source: Appendix A5 in Perrin, Dempsey & Serjeant, 1981, pKa Prediction for Organic Acids and Bases, Chapman & Hall.