Kaplan MCAT General Chemistry Review

Consider the nitration reaction of benzene, an example of electrophilic aromatic substitution:

The rate data below were collected with the nitration of benzene carried out at 298 K. From this information, determine the rate law for this reaction.

Takeaways

Remember that the rate constant k depends only on temperature.

A shortcut to determine order is to use the following relation when you find two trials where one reagent’s concentration changes but all other concentrations are constant:

Change in rate = (Proportional change in concentration)^x, where x = the order with respect to that reagent.

1) Write down the general form of the rate law.

Rate = k[C₆H₆]^x [HNO₂]^y

Remember: The general form of the rate law must include a constant, k, that is multiplied by the concentrations of each of the reactants raised to a certain power.

2) Determine the order of the reaction with respect to each reactant. Choose two trials in which the concentration of one reagent is changing but the other is not. Take the ratio of these two trials and set up an equation.

Cancel the rate constants because they are equal to each other. Collect terms raised to the same exponent together.

Plug and chug. Substitute numbers from the rate data table into the equation.

The term raised to the y power disappears because 1 raised to any power equals 1. The only way that 4^x can equal 1 is if x = 0.

To determine the order with respect to HNO₂, note that there are no two trials in which the concentration of benzene stays the same. However, this does not matter, because the reaction is zero order with respect to benzene.

Plug in numbers from the table as before.

Simplify the numbers to make them easy to handle. Note that 5.40 × 10^–5 is the same thing as 54.0 × 10^–6.

The only way this equation can be true is if y = 2.

3) Write down the rate law with the correct orders.

Rate = k[C₆H₆]⁰[HNO₂]² = k[HNO₂]²

Things to Watch Out For

Make sure that initially you select two trials where one reagent’s concentration changes but all other concentrations are constant. Otherwise, you won’t come out with the correct rate law!

Similar Questions

1) What is the value of the rate constant k for the original reaction above? What are its units?

2) Given the data below, determine the rate law for the reaction of pyridine with methyl iodide. Find the rate constant k for this reaction and its units. Use the rate law to determine what type of reaction this is.

3) Cerium(IV) is a common inorganic oxidant. Determine the rate law for the following reaction and compute the value of the rate constant k along with its units.

Rate Law from Reaction Mechanisms

Key Concepts

Chapter 5

Equilibrium

Rate laws

Reaction mechanisms

Often, changing the medium of a reaction can have a dramatic effect on its mechanism. In the gas phase, HCl reacts with propene according to the following reaction mechanism:

Step 1: HCl + HCl H₂Cl₂ (fast, equilibrium)

Step 2: HCl + CH₃CHCH₂CH₃CHClCH₃* (fast, equilibrium)

Step 3: CH₃CHClCH₃* + H₂Cl₂ CH₃CHClCH₃ + 2 HCl (slow)

where CH₃CHCH₂ is propene and CH₃CHClCH₃* represents an excited state of 2–chloropropane.

Based on these reaction steps, derive the rate law for this reaction.

1) Identify the slow step in the reaction and write down the rate law expression for that step.

Rate = k₃[CH₃CHClCH₃*][H₂Cl₂]

Takeaways

With reaction mechanisms, the goal is to eliminate the concentrations of intermediates, because they are usually high-energy species that exist only briefly.

2) If intermediates exist in the rate law from step 1, use prior steps to solve for their concentration and eliminate them from the rate law.

k₁[HCl]² = k_–1[H₂Cl₂]

Here, we are taking advantage of the fact that step 1 of the mechanism is in equilibrium; therefore, the rates of the forward and reverse reactions are equal.

Solve for the concentration of H₂Cl₂, one of the intermediates from above.

Step 2 from the mechanism is also in equilibrium, so the rates of the forward and reverse reactions are equal.

Solve for the intermediate, as above.

Plug the concentrations into the rate law for the slow step.

Similar Questions

1) What are the units of the rate in the original question? Based on this, what must the units of k_obs be for this reaction?