# College Chemistry : Rate Laws

## Example Questions

### Example Question #12 : Thermodynamics And Kinetics

Which of the following techniques will not increase the rate of a reaction?

Introducing a catalyst to lower the activation energy of the reaction

Increasing the surface area between reactants

Heating the reactants in order to reach the activation energy

None of these

Increasing the amount of reactants

Increasing the amount of reactants

Explanation:

Increasing the amount of reactant increases the rate of reaction only if the concentration of each reactant increases and if the reactants are dissolved in a solution. This is not the case for all reactions. Heating the reaction and introducing a catalyst enable the reactants to reach the activation energy needed to proceed into the reaction. Increasing the surface area between the reactants enables more of each reactant to interact with one another.

### Example Question #1 : Kinetics

The reaction

Follows the mechanism:

(slow)

(fast)

Determine the rate law for this reaction.

Explanation:

Remember, the rate law is always determined by the rate-determining step. This is ALWAYS the "slow" step in the reaction. In this case, the slow step is step (i).

The rate for this step alone is

And because both of the original reactants are in this rate law, it is also the rate law for the overall reaction.

### Example Question #1 : Rate Laws

If a reaction is zero order with respect to , which of the following quantities will produce a straight line when graphed against  (time)?

Explanation:

The correct answer is  because the differential rate law for a zero order reaction is . Therefore, the plot has a linear relationship to the concentration of hydrogen.

### Example Question #1 : Rate Laws

If a reaction is first order with respect to , which of the following quantities will produce a straight line when graphed against  (time)?

Explanation:

Because the differential rate law for a first order reaction is  the graph will have a linear relationship to .

### Example Question #2 : Rate Laws

If a reaction is second order with respect to , which of the following quantities will produce a straight line when graphed against  (time)?

Explanation:

Because the differential rate law for a second order equation is  the graph will have a linear relationship to .

### Example Question #1 : Rate Laws

Using the reaction and experimental data given, determine the rate equation for this reaction.

Explanation:

In order to solve this problem we must compare the initial concentrations of our two reactants between equations with how they effect the rate of the reaction. When comparing experiment 1 and 2, we see that the concentration of A was doubled. This resulted in a quadrupling of the rate. Therefore the reaction is second order with respect to . When comparing experiments 1 and 3, we see that the concentration of B was doubled, and this resulted in a doubling of the rate. Therefore, the reaction is first order with respect to . Then, we plug in all of this information into the rate law, and we get the correct answer of .

### Example Question #11 : College Chemistry

Given the equation and experimental data above determine the value of the rate constant  for this reaction.

Explanation:

In order to solve this problem we must compare the initial concentrations of our two reactants between equations with how they effect the rate of the reaction. When comparing experiment 1 and 2, we see that the concentration of A was doubled. This resulted in a quadrupling of the rate. Therefore the reaction is second order with respect to . When comparing experiments 1 and 3, we see that the concentration of B was doubled, and this resulted in a doubling of the rate. Therefore, the reaction is first order with respect to . Then, we plug in all of this information into the rate law, and we get the correct answer of .

Finally, we take the values from one of the rows of the experimental data. It does not matter which one, they will all result in the same answer. In this case, I chose experiment 1.

Because the values from the table all only have one significant figure, our answer can also only have one significant figure.

### Example Question #21 : Thermodynamics And Kinetics

What are the correct units for the rate constant  of a zero order reaction?

Explanation:

Because the rate of a chemical reaction is always in . The  value must always cancel with other units to produce these units. In a zero order reaction there is nothing to cancel, so the units are simply .

### Example Question #1 : Rate Laws

What are the units for the rate constant  for a first order reaction?

Explanation:

Because the rate of a chemical reaction is always in . The k value must always cancel with other units to produce these units. In a first order reaction the rate equation is

If we replace the variables above with their units, the equation will look like this:

Therefore, in order to match,  must simply be .

### Example Question #2 : Rate Laws

What are the units for the rate constant  for a second order reaction?