Chemical Kinetics

Isolation Method

A common challenge in chemical kinetics is to determine the rate law for a reaction with multiple reactants. With the concentrations of several species changing simultaneously, real rate laws might not follow simple zero-, first-, and second-order rate laws. The Method of Initial Rates can, in principle, be used to determine the rate law, but in practice the Method of Initial Rates poses serious experimental challenges. The primary challenge is to accurately determine the initial rate.

A better and more commonly used strategy is the Isolation Method. In this method the concentration of one reactant is made much smaller than the concentrations of the other reactants. Under this condition, all reactant concentrations except one are essentially constant, and the simple zero-, first-, and second-order kinetic plots often be used to interpret the concentration-time data.

To see how this method works, consider the following substitution reaction:

CH₃Br (aq)   +   OH^- (aq)   →   CH₃OH (aq)   +   Br^- (aq)

The rate law for this substitution reaction is first-order in bromomethane and first-order in hydroxide ion; second-order overall.

r = k [CH₃Br] [OH^-]

Suppose the reaction were performed starting with 0.100 mole/L OH^- and 0.00100 mole/L CH₃Br. When the reaction is finished, the solution will contain 0.099 mole/L OH^- and essentially no CH₃Br. Notice that the concentration of hydroxide ion is approximately unchanged. The total change in [OH^-] is 1%, which is often comparable to or smaller than the experimental error. The value of [OH^-] can therefore be treated as a constant, and the rate law becomes

r = k_obs [CH₃Br]

The above rate law is first-order. The observed rate constant, k_obs, is a pseudo-first-order rate constant. The term pseudo rate constant means k_obs is not the real rate constant. The reaction only appears to be first order with a rate constant k_obs. In reality, the reaction is second order overall and the rate constant is k. The pseudo-first-order rate constant is related to the true rate constant by

k_obs = k [OH^-]

Performing the reaction with 0.100 mole/L OH^- and 0.00100 mole/L CH₃Br allows one to determine the order of the reaction with respect to CH₃Br by creating the characteristic graphs for various rate laws and looking for the graph that is linear. To determine the order of the reaction with respect to OH^-, one would perform a series of experiments in which [OH^-] varies but is always much larger than [CH₃Br]. For each experiment, k_obs would be determined, and one would then prepare a plot of ln k_obs vs ln [OH^-]. Such a plot should be linear with a slope of b.

k_obs = k [OH^-]^b

ln k_obs = ln k + b ln [OH^-]

Once the value of b is known, one calculate a value for k for each experiment. These values for k would be averaged to obtain the best estimate for the rate constant.

How large a concentration excess is required to effectively "isolate" the effects of a single reactant? As a general rule, a minimum of a 20-fold stoichiometric excess is necessary. A 50-fold or 100-fold stoichiometric excess is preferrable.

Experiment

Objectives

• Determine the rate law for a chemical reaction using the isolation method.
• Determine the rate constant for a chemical reaction.

An important reaction that occurs in the atmosphere is

2 NO (g)   +   O₂ (g)   →   2 NO₂ (g)

Nitrogen oxides (NO_x) are produced by automobile engines, and the fate of these oxides in the environment is of considerable concern. Modeling reactions involving nitric oxide (NO) and nitrogen dioxide (NO₂) are important in understanding the behavior of air pollution and in developing effective regulations. Nitric oxide is a reactive, colorless gas; nitrogen dioxide is an orange-brown gas that is responsible for the characteristic color of Los Angeles smog.

In this experiment, the stopped-flow apparatus has been adapted to handle gases. Both syringes are charged with gas mixtures at 1 atm pressure. The syringe on the left contains 99% N₂ and 1% NO, which at 25^o C and 1 atm corresponds with 4.09 x 10^-4 mole/L NO. The syringe on the right contains pure oxygen, which corresponds to 0.0409 mole/L O₂. Both syringes are loaded with 10 mL of gas.

The reactants are colorless and the NO₂ product has an orange-brown color. Thus the NO₂ concentration is readily measured experimentally using visible spectrophotometry. The graph at the right of the stopped-flow apparatus shows how the concentration of NO₂ varies with time during the experiment. (This is the characteristic zero-order kinetic plot.) By clicking the appropriate button, characteristic first-order and second-order kinetic plots can also be prepared. In the first- and second-order plots, it is necessary to plot [NO₂]_f - [NO₂] rather than [NO₂], because NO₂ is a product rather than a limiting reactant. [NO₂]_f is the final nitrogen dioxide concentration, which is known from the initial concentrations and the reaction stoichiometry.

Perform this reaction several times, using various proportions of NO and O₂. Note that for each volume proportion available for the experiment, the concentration of O₂ is always present in large excess. The concentration of O₂ never changes by more than 1% during any of the reaction conditions. For each experiment, use the appropriate kinetic plot to determine the order of the reaction with respect to NO and the pseudo-rate constant k_obs for the chosen oxygen concentration.

For each experiment, enter the oxygen concentration and k_obs in the table at the bottom of the page. The points in the table are used to construct plot of ln k_obs vs ln [O₂]. Use the slope of this plot to determine the order of the reaction with respect to oxygen. Then go back to the set of values for [O₂] and k_obs and calculate a value for k for each trial. Finally obtain an average value for k.

Here is a list of things to remember when analyzing the experimental data.

• The concentration of O₂ gas in the right syringe is 0.0409 mole/L. Recall that this gas is diluted when mixed with the gas from the left syringe to produce the reacting gas mixture.
• For ease of viewing, the zero-order and second-order kinetics plots use concentrations of mmole/L rather than mole/L. Take these units into account in calculating rate constants, which should use mole rather than mmole.
• The slope of the ln k_obs vs ln [O₂] provides a value for b (the order of the reaction with respect to oxygen). Although there are exceptions, one expects b to be an integer. In practice, however, experimental error and the fact that [O₂] is not perfectly constant result in a slope that is not an exact integer. The slope should, however, be close to an integer (zero is a possibility). Round the slope to the nearest integer to obtain a value for b.
• k_obs is based upon the simple rate law     - d[NO]/dt   =   d[NO₂]/dt   =   k_obs [NO] ^a
  When calculating k take the stoichiometry of the reaction into account.
  The rate is formally defined to be     r   =   - ½ d[NO]/dt   =   ½ d[NO₂]/dt   =   k [NO] ^a [O₂] ^b