Rates, Kinetics, Equilibrium

Question 1

What is the rate constant of a chemical reaction?

Answer 1

A chemical reaction’s rate constant (k) is the rate at which the reaction proceeds when the concentration of all reactants is 1M at 1 atm.

Question 2

For the generic chemical reaction

aA + bB ⇒ cC + dD

where a, b, c, and d represent the coefficient of reactants A, B, C, and D respectively, what is the rate at which the reaction will proceed?

Answer 2

For the generic chemical reaction

aA + bB ⇒ cC + dD

the rate expression is:

rate = k [A]^x [B]^y

where k is the rate constant and x and y are the reaction orders of A and B, respectively.

Question 3

How is the overall reaction order of a chemical reaction calculated?

Answer 3

The overall order of a chemical reaction is the sum of the reaction orders of all the reactants.

For the rate expression:

rate = k [A]^x [B]^y

the overall order is the sum (x+y). k is the rate constant, and x and y are the reaction orders of A and B, respectively.

Question 4

What features characterize a zeroth order reaction?

Answer 4

A zeroth order reaction is one whose overall reaction order is zero. Its rate is independent of reactant concentration.

The rate of a zeroth order reaction is constant and can be given by:

rate = k

Question 5

A chemical reaction is zeroth order in [A], where A is one of the reactants. How does the reaction rate vary when [A] is doubled?

Answer 5

The reaction rate does not change.

There is no correlation between the value of [A] and the rate in a zeroth order reaction.

If the reaction is zeroth order in [A], that means that the rate can be described as:

rate = k [A]^{<span>0</span>} = k

Question 6

Define:

What features characterize a first order reaction?

Answer 6

A first order reaction is one whose overall reaction order is 1. Its rate depends on the concentration of only one reactant in a linear fashion.

If A is the reactant on which the reaction rate depends, the rate will be:

rate = k [A]

Question 7

If a chemical reaction is first order in [A], how does the reaction rate vary when [A] decreases by a certain amount?

Answer 7

The reaction rate decreases by the same amount that [A] did.

Since the reaction is first order in [A], the rate law is:

rate = k [A]

Let [A]_original = x.
Then rate_original = k * x.
If [A] decreases, then

rate_new = k (new, decreased x) = (decrease) * rate_original

Question 8

A chemical reaction is first order in [A], where A is one of the reactants. How does the reaction rate vary when [A] is doubled?

Answer 8

The reaction rate doubles.

Since the reaction is first order in [A], the rate law is:

rate = k [A]

Let [A]_original = x.
Then rate_original = k * x.
If [A] doubles, then

rate_new = k (2x) = 2 * rate_original

Question 9

What features characterize a second order reaction?

Answer 9

A second order reaction is one whose overall reaction order is 2. Its rate either depends on one second-order reactant or two separate first-order reactants.

If the reactants for the reaction are A and B, the rate will be either:

rate = k [A]²
or rate = k [B]²
or rate = k [A] [B]

Question 10

If a chemical reaction is second order in [A], how does the reaction rate vary when [A] increases by a certain amount?

Answer 10

The reaction rate increases proportionally by the square of that specific amount.

If the reaction is second order in [A], the rate law is:

rate = k [A]²

Let [A]_original = x.
Then rate_original = k * x².
If [A] increases, then

rate_new = k (new, increased x)² = (increase)² * rate_original

Question 11

A chemical reaction is second order in [A], where A is one of the reactants. How does the reaction rate vary when [A] is tripled?

Answer 11

The reaction rate increases by a factor of 9.

If the reaction is second order in [A], the rate law is:

rate = k [A]²

Let [A]_original = x.
Then rate_original = k_obs * x².
If [A] triples, then

rate_new = k (3x)² = 9 * rate_original

Question 12

If a chemical reaction is first order in both [A] and [B], how will the reaction rate vary if [A] triples and [B] is reduced by half?

Answer 12

The reaction rate will increase by a factor of 1.5.

If the reaction is first order in [A] and [B], the rate law is:

rate = k [A] [B]

Let [A]_original = x and [B]_original = y.
Then rate_original = k * x * y.
If [A] triples and [B] decreases by half, then

rate_new = k * (3x) * (½y) = 1.5 rate_original

Question 13

A reaction has chemical A as a reactant and the kinetic data given below. What is this reaction’s overall rate law?

Answer 13

Rate = 5 [A]²

To determine the reaction order for A, find how varying [A] affects the rate. Between Trials 1 and 2, [A] increases by a factor of 2, while the rate increases by a factor of 4.

Since the rate increases by a factor of the concentration increase squared, the reaction must be second order in [A].

Once the reaction orders are solved, plug in the value of [A] for either trial to solve for k.

Question 14

A reaction has chemicals A and B as reactants and the kinetic data given below. What is this reaction’s overall rate law?

Answer 14

Rate = 2 [A]

Between Trials 1 and 2, [A] doubles while [B] stays constant. Since the reaction rate doubles, the reaction order for A is 1.

Between Trials 2 and 3, [B] doubles while [A] stays constant. Since the reaction rate is unchanged, the reaction order for B is 0.

Plugging in the values [A] = 1 and [B] = 1 from Trial 1 delivers a final value of 2 for k.

Question 15

A reaction has chemicals A and B as reactants and the kinetic data given below. What is the reaction’s overall rate law?

Answer 15

Rate = 2 [A] [B]²

Between Trials 1 and 2, [A] doubles while [B] stays constant. Since the reaction rate doubles, the reaction order for A is 1.

Between Trials 2 and 3, [B] doubles while [A] stays constant. Since the reaction rate increases by a factor of 4, the reaction order for B is 2.

Plugging in the values [A] = 2 and [B] = 1 from Trial 1 delivers a final value of 2 for k.

Question 16

Define:

rate-determining step

Answer 16

A chemical reaction’s rate-determining step is the slowest step of the multi-step reaction. As such, it limits how fast the overall reaction can proceed.

For example, the reaction

NO₂ + CO ⇒ NO + CO₂

is actually a two-step reaction:

1) NO₂ + NO₂ ⇒ NO₃ + NO (slow)
2) NO₃ + CO ⇒ NO₂ + CO₂ (fast)

The slow first step is the rate-determining step, so it limits the overall reaction rate.

Question 17

Define:

intermediate

Answer 17

A reaction intermediate is a species that plays a role in a reaction, but does not appear in the overall chemical equation.

An intermediate can be identified because it will be both a product of an early reaction step and a reactant in a later one.

Question 18

Identify the intermediate in the reaction below:

Overall Reaction: 2 O₃ ⇒ 3 O₂
Step 1: O₃ ⇒ O₂ + O
Step 2: O + O₃ ⇒ 2 O₂

Answer 18

O is the intermediate.

O is a product of Step 1 and a reactant of Step 2; it does not appear in the overall reaction. Therefore, it is an intermediate.

Question 19

What is the molecularity of an elemental chemical reaction?

Answer 19

Molecularity is the number of reactant molecules taking part in a single reaction step. Therefore, it is a concept that can only be applied to elementary (one-step) reactions.

A reaction involving one molecule of reactant is unimolecular, two is bimolecular, and three is termolecular.

Question 20

What is the molecularity of the elementary reaction below?

NO + NO₃ → 2NO₂

Answer 20

The reaction is bimolecular, as it has two individual molecules as reactants in its only, and thus rate-determining, step.

NO + NO₃ → 2NO₂

Question 21

In the chemical reaction energy profile shown below, where are the reactants and the products located?

Answer 21

In reaction energy profiles, the reactants are on the left, at the beginning of the reaction. The products are on the right, at the end of the reaction.

Question 22

In the chemical reaction energy profile below, what does the quantity labeled as A represent?

Answer 22

A is the activation energy (E_a).

The activation energy determines how much energy the reactants require to convert to the activated complex, or transition state. The higher the activation energy, the slower the reaction proceeds.

Question 23

In the chemical reaction energy profile below, what component of the reaction is located at point C?

Answer 23

The reaction’s transition state is located at the peak of the reaction profile.

The transition state, also known as the activated complex, is the chemical intermediate between the reactants and the products. Since it is the highest-energy point in the reaction profile, it is the least stable part of the reaction. The reaction rapidly proceeds to the products once the transition state is reached.

Question 24

In the chemical reaction energy profile below, what does the quantity labeled as B represent?

Answer 24

B is the reaction enthalpy, ΔH.

The reaction enthalpy is a measure of the difference in energy level between the reactants and the products. If ΔH < 0, the reaction is exothermic; if ΔH > 0, the reaction is endothermic.

Question 25

Is the chemical reaction depicted below endothermic or exothermic?

Answer 25

This reaction is exothermic.

The products’ enthalpy is lower than that of the reactants, so ΔH < 0, meaning the reaction is exothermic.

Question 26

Is the chemical reaction depicted below endothermic or exothermic?

Answer 26

This reaction is endothermic.

The products’ enthalpy is higher than that of the reactants, so ΔH > 0, meaning the reaction is endothermic.

Question 27

What is the Arrhenius equation?

Answer 27

The Arrhenius equation relates a reaction’s activation energy E_a, rate constant k_obs, the temperature of the chemical system T, and the ideal gas constant R.

Question 28

Of the two reactions shown below, which is kinetically favored?

Answer 28

Reaction B is kinetically favored.

The reaction with the lower activation energy will be kinetically favored. In this case, E_a is smaller for reaction B than it is for reaction A. Reaction B, then, runs faster, and is kinetically preferred.

Question 29

If reactions A and B are run simultaneously at low temperature, which set of products will result?

Answer 29

At low temperature, reaction B’s products will dominate.

At low temperatures, the kinetically preferred reaction will be favored. Since B is kinetically preferred, it will dominate under these conditions.

Question 30

Of the two reactions shown below, which is thermodynamically favored?

Answer 30

Reaction A is thermodynamically preferred.

The reaction with the more stable products will be thermodynamically favored; this can be discerned from the enthalpy change. In this case, ΔH_A is larger in magnitude than ΔH_B, so the products of A are more thermodynamically stable and reaction A is thermodynamically preferred.

Question 31

If reactions A and B are run simultaneously at high temperature, which set of products will result?

Answer 31

At high temperature, reaction A’s products will dominate.

At high temperatures, the thermodynamically preferred reaction will be favored. Since A is thermodynamically preferred, it will dominate under these conditions.

Question 32

Define:

chemical catalyst

Answer 32

A catalyst is a chemical which participates in a reaction and serves to increase the reaction’s rate, usually by lowering the activation energy of the reaction.

Catalysts themselves are not depleted by the reaction.

Question 33

How does a chemical catalyst change the energy profile of a chemical reaction?

Answer 33

Chemical catalysts decrease a reaction’s activation energy.

The energy profile below demonstrates catalysis. Note that E_a decreases, but ΔH is unaffected by the catalyst.

Question 34

What role do enzymes play in chemical reactions?

Answer 34

Enzymes serve as catalysts in chemical reactions.

Like all catalysts, enzymes can speed up reactions but cannot change the thermodynamic favorability of the actual products.

Question 35

What is the difference between a homogeneous catalyst and a heterogeneous catalyst?

Answer 35

A homogeneous catalyst is in the same phase as the reactants, while a heterogeneous catalyst is in a different phase.

Question 36

Define:

autocatalysis

Answer 36

A reaction undergoes autocatalysis if the product of the reaction further catalyzes the reaction.

Question 37

Define:

law of mass action

Answer 37

The law of mass action states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an ideal equilibrium constant, K_eq.

For the chemical reaction

aA (g) + bB (g) ⇔ cC (g)

if [C]_eq is the concentration of C at equilibrium,

Question 38

For the chemical reaction

aA (g) + bB (g) ⇔ cC (g)

what is the value of the reaction quotient (Q)?

Answer 38

The expression for the reaction quotient (Q) is very similar to the expression for K_eq. However, Q can apply to a chemical system at any set of concentrations, while K_eq specifically refers to the system at equilibrium.

Question 39

For the chemical reaction

A (g) ⇔ B (g)

what does it mean about the equilibrium concentrations of A and B if:

1. K_eq > 1
2. K_eq = 1
3. K_eq < 1

Answer 39

For this system,

K_eq = [B]_eq/[A]_eq

1. If K_eq > 1, [B]_eq > [A]_eq. At equilibrium, B will be in excess.
2. If K_eq = 1, [B]_eq = [A]_eq. At equilibrium, A and B will have equal concentrations.
3. If K_eq < 1 , [A]_eq > [B]_eq. At equilibrium, A will be in excess.

Question 40

What is the equilibrium constant for the reaction:

NO + NO₃ ⇔ 2NO₂

Answer 40

The value of the equilibrium constant is calculated from the actual concentrations of the products and reactants at equilibrium. The general formula for this reaction is:

Question 41

What is the equilibrium constant (K_eq) for the following reaction:

CaCO₃(s)→CaO(s)+CO₂(g)

Answer 41

K_eq = [CO₂]

The value of the equilibrium constant (and reaction quotient) depends only on the concentration of reactants and products present in the aqueous or gaseous phases. Chemicals in the solid or liquid phase do not affect the equilibrium levels.

Question 42

What is true of the relationship between K_eq and Q for any chemical system at equilibrium?

Answer 42

Q = K_eq at equilibrium.

Equilibrium occurs when the forward and reverse reactions are proceeding at the same rate. At this time, the reactants and products are at concentrations such that the reaction quotient, Q, is equal to the equilibrium constant K_eq. If, at any given time, Q does not equal K_eq, the concentrations will change in such a way as to make the two values equal.

Question 43

What can be said about the rates of the forward and reverse reactions for any chemical system which is at equilibrium?

Answer 43

When the system is at equilibrium, by definition, the rates of the forward and reverse reactions are equal.

Question 44

If the chemical system

NO + NO₃ ⇔ 2NO₂

is in a state of dynamic equilibrium, what can be said about the rates of the forward and reverse reactions?

Answer 44

The rates of the forward and reverse reactions are equal.

For every molecule of NO that joins with a molecule of NO₃ to make 2 molecules of NO₂, 2 molecules of NO₂ will also form a molecule of NO and NO₃.

Question 45

Define:

Le Chatelier’s principle

Answer 45

Le Chatelier’s principle states that when a system in equilibrium is placed under stress, the system adjusts to restore equilibrium.

There are three kinds of stress commonly tested in relation to this principle:

1. concentration
2. temperature
3. pressure

Question 46

If the chemical system

aA (g) + bB (g) ⇔ cC (g)

is in equilibrium, and additional A is added, what does Le Chatelier’s principle predict will occur?

Answer 46

The reaction will shift to the right, creating more C.

According to Le Chatelier’s principle, the system will respond to relieve any stress placed on one side of the system.

In this case, the reactant side is stressed by the addition; the amount of reactants is too large. The system will respond by shifting to the right, favoring the forward reaction, and more products will be created.

Question 47

If the chemical system

aA (g) + bB (g) ⇔ cC (g)

is in equilibrium, and additional A is added, what happens to the reaction quotient Q?

Answer 47

Q decreases.

This circumstance favors the forward reaction, or the creation of more products.

As a general rule, when Q < K_eq, the forward reaction is favored and more products are created.

Question 48

If the chemical system

aA (g) + bB (g) ⇔ cC (g)

is in equilibrium, and additional C is added, what does Le Chatelier’s Principle predict will occur?

Answer 48

The reaction will shift to the left, creating more A and B.

In this case, the product side is stressed by this addition; the amount of products is too large. The system will respond by shifting to the left, favoring the reverse reaction and creating more reactants.

Question 49

If the chemical system

aA (g) + bB (g) ⇔ cC (g)

is in equilibrium, and if the reaction is endothermic, what will happen if the temperature is increased?

Answer 49

The reaction will shift to the right, creating more C.

For an endothermic reaction, heat must be added; for this reason, it can be thought of as a reactant. Increasing the temperature is akin to adding more of a reactant, and therefore shifts the reaction to the right.

Question 50

If the chemical system

aA (g) + bB (g) ⇔ cC (g)

is in equilibrium, and if the reaction is exothermic, what will happen if the temperature is increased?

Answer 50

The reaction will shift to the left, creating more A and B.

For an exothermic reaction, heat is released; for this reason, it can be thought of as a product. Increasing the temperature is akin to adding more product, and therefore shifts the reaction to the left.

Question 51

If the chemical system

A (g) + 2 B (g) ⇔ C (g)

is in equilibrium, what happens if the pressure is increased?

Answer 51

The reaction will shift to the right, creating more C.

Increasing the pressure will add stress to the side with more moles of gas. In this case, the reactant side has 3 moles of gas compared to 1 mole on the product side.

So, when the pressure is increased, the system will shift to the right and form more products.

Question 52

If the chemical system

A (g) + B (g) ⇔ 3 C (g)

is in equilibrium, what happens if the pressure is decreased?

Answer 52

The reaction will shift to the right, creating more C.

Decreasing the pressure promotes the creation of more moles of gas. In this case, the product side has 3 moles of gas compared to 2 moles on the reactant side.

So, when the pressure is decreased, the system will shift to the right and form more products.

Question 53

What is the relationship between a substance’s Gibbs free energy and the equilibrium constant of the reaction that forms the substance?

Answer 53

ΔGº = -RT ln(K_eq)

where

• R = the ideal gas constant (L-atm/K-mol)
• T = absolute temperature (K)

A K_eq with a value greater than one correlates to a negative ΔGº value, while a K_eq less than one correlates to a positive ΔGº.