# MCAT Physical : Reaction Rate and Rate Laws

## Example Questions

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### Example Question #1 : Reaction Rate And Rate Laws

If the reactants and/or products in a chemical reaction are gases, the reaction rate can be determined by measuring the change of pressure as the reaction proceeds. Consider the following reaction and pressure vs. reaction rate data below.

 Trial PXY(torr) PZ(torr) Rate (torr/s) 1 100 200 0.16 2 200 200 0.32 3 200 100 0.04 4 200 150 0.14

What is the value of the rate constant, k, for this reaction?

k = 2 * 10-13

k = 2 * 10-10

k = 1.6 * 10-13

k = 1.6 * 10-10

k = 2 * 10-10

Explanation:

The rate law can be determined by comparing changes in reactant concentration to changes in rate. In this reaction, doubling XY doubles the reaction rate; the reaction is first-order for XY. Doubling Z increases the rate by a factor of eight, so the reaction is third-order for Z (23 = 8).

Knowing that Rate = k[XY] [Z]3, we can solve for k by using data from one of the trials. Plugging in data from trial 1, we can calculate the value of k.

0.16 = k[100][200]3

k = 2 * 10-10

### Example Question #2 : Reaction Rate And Rate Laws

 Initial Reaction Rate M M M 2000 1.0 1.0 1.0 2000 1.0 1.0 2.0 4000 2.0 1.0 1.0 16000 2.0 2.0 1.0

Using data in the table above to determine the rate law for the reaction.

Explanation:

Let's look at each of the three reactants individually.

Compare trials 1 and 3. Doubling  without changing the other reactants doubles the rate from to ; therefore  has a superscript of 1.

Compare trials 3 and 4. Doubling  without changing the other reactants results in a rate that is four times faster, increasing from to . The rate increases with the square of concentration of

Compare trials 1 and 2. Doubling without changing the other reactants has no effect on the rate, which remains at , so  is not part of the final rate equation.

The final rate law will be .

### Example Question #1 : Reaction Kinetics

If the reactants and/or products in a chemical reaction are gases, the reaction rate can be determined by measuring the change of pressure as the reaction proceeds. Consider the following reaction and pressure vs. reaction rate data below.

 Trial PXY(torr) PZ(torr) Rate (torr/s) 1 100 200 0.16 2 200 200 0.32 3 200 100 0.04 4 200 150 0.14

What is the rate law for this reaction?

Explanation:

Comparing trials 2 and 3, we see that when PXY is constant and PZ doubles, the rate increases by a factor of 8, or 23. Rate is therefore proportional to [Z]3.

Comparing trials 1 and 2, we see that when PZ is held constant and PXY doubles, the rate doubles. Rate is therefore proportional to [XY].

Remember that in these problems, you are looking for the value of n in the function . When doubling the concentration does not affect the reaction rate, n = 0. When doubling the concentration doubles the reaction rate, n = 1. When doubling the concentration quadruples the reaction rate, n = 2.

### Example Question #2 : Reaction Kinetics

Which of the following is a second-order rate law?

Rate = k[A]0[B]0

Rate = k[A]0[B]1

Rate = k[A]1[B]2

Rate = k[A]1[B]1

Rate = k[A]1[B]1

Explanation:

The order of a reaction or rate law is given by the sum of the exponents in the rate expression. Rate = k[A]1[B]is the only second-order rate law. This is the case since the reaction order is determined by the number of reactants involved. Rate = k[A]1[B]2 is not second-order; since it has one A reactant and two B reactants, this is a third-order reaction.

### Example Question #3 : Reaction Kinetics

Consider the reaction .

A set of trials is set up in order to see how manipulating the starting concentrations of reactants can affect the initial rate of the reaction. The experiments are outlined in the table below.

 Trial Initial [A] Initial [B] Initial [C] Initial reaction rate (M/s) 1 0.3 0.4 0.2 0.04 2 0.3 0.4 0.6 0.12 3 0.3 0.8 0.6 0.48 4 0.6 0.4 0.2 0.04

Based on the above information, determine the rate law for the reaction.

Explanation:

The coefficients in front of the reactants simply show the balanced equation, and do NOT give any information on the order of the reactants. The order of the reactants must be determined experimentally by comparing how reaction rates change when the reactant's concentration is altered.

Only the reactant in question must have an altered concentration between two trials; all others must be kept constant. When a reaction rate is doubled and the initial reaction rate is quadrupled, we determine that the reaction is second order with respect to the reactant. If the concentration of a reactant is altered but the reaction rate is unaffected, the order of the reactant is zero. Finally, if the reaction rate and reactant are multiplied by the same factor between two trials, the reactant is first order.

In the table, we can compare trial 1 and 4 to see the effect of doubling A, with constant B and C. This does not affect the rate, to A must be zeroth order. Comparing trials 2 and 3 shows that doubling B, with A and C held constant, will quadruple the rate. The reaction must be second order for B. Finally, comparing trials 1 and 2 shows us that tripling C, with A and B held constant, will triple the reaction rate. The reaction must be first order for C. This yields the rate law .

If the concentration of a reactant is doubled, . The relationship between this change and the change in rate is, therefore, , where n is the order of the reaction with respect to X. This can be reduced to , allowing us to find the reaction order from the experimental rate.

### Example Question #6 : Reaction Rate And Rate Laws

What is the order for a reaction with the rate law given below?

Third order

First order

Second order

Fourth order

Third order

Explanation:

The reaction order is equal to the sum of the exponents of the concentration variables in the rate law.

Because reactant B has an exponent of two and reactant C has an exponent of one, the total sum is three, and the reaction is therefore third order.

### Example Question #4 : Reaction Kinetics

A student is studying the kinetics of the following reaction.

In trying to determine the rate law, he collects the following set of data.

What is the value of if the rate law is ?

Explanation:

To determine , the data from any of the three trials could be used. Using trial 1 and the rate law, we can solve for .

Note that the units have to be adjusted, based on the order of  and .

### Example Question #5 : Reaction Kinetics

A scientist is studying a reaction, and places the reactants in a beaker at room temperature. The reaction progresses, and she analyzes the products via NMR. Based on the NMR readout, she determines the reaction proceeds as follows:

In an attempt to better understand the reaction process, she varies the concentrations of the reactants and studies how the rate of the reaction changes. The table below shows the reaction concentrations as she makes modifications in three experimental trials.

What is the overall order for this reaction as written?

Zero order overall

First order overall

Third order overall

Second order overall

Fourth order overall

Second order overall

Explanation:

The rate law is written as .

Compare trials 1 and 2 to see that doubling the ammonium concentration doubles the rate. The reaction is first order for ammonium: .

Compare tirals 2 and 3 to see that tripling nitrate concentration triples the rate. The reaction is first order for nitrate: .

The final rate law is .

The sum of the orders for each reactant gives you the overall order of the reaction. In this case, the reaction is first order with regard to each reactant, and is thus second order overall.

### Example Question #6 : Reaction Kinetics

Which of the following parameters can affect the rate of the given reaction?

Each of these can affect the rate law

Changing the ratio of products to reactants

Altering the temperature

Introducing an enzyme

Running the reaction in reverse

Each of these can affect the rate law

Explanation:

The rate law for the given reaction will be given by the formula:

The variables and need to be determined experimentally, and the value will be given by another formula.

The coefficient is a constant, and the variables in the exponent are the activation energy and temperature.

Adding an enzyme will lower the activation energy, affecting the rate constant. Changing the temperature will also affect the rate constant. Adjusting the ratio of reactants to products will alter the concentrations of the reactants. As the reaction runs, the rate declines as the reactants are consumed until it reaches equilibrium. Changing the reactant concentrations will change the reaction rate with respect to this equilibrium. Running the reaction in reverse will result in a completely different rate law since the reactants will be altered.

### Example Question #7 : Reaction Kinetics

A student is studying the kinetics of the following reaction.

In trying to determine the rate law, he collects the following set of data.

Based on these data, what is the rate law for this reaction?

Explanation:

The rate law will have the general formula . The exponents,  and , DO NOT necessarily correlate with the reaction stoichiometry. They must be determined from the experimental data.

To determine , compare trials 1 and 3, where  is held constant.

Since  is constant and  is the same for both experiments, by plugging in the values for rate and  for trials 1 and 3, we get this equation.

.

This reduces to , which means .

To find , compare trials 1 and 2, where  is held constant. Following the same type of calculation as shown above would give .

The rate law is .

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