Chemistry 101: Kinetics

For the generic chemical reaction

aA + bB ⇒ cC + dD

the rate expression is:

rate = kobs [A]x [B]y

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

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

For the rate expression: rate = kobs [A]x [B]y
the overall order is the sum x+y. kobs is the rate constant, and x and y are the reaction orders of A and B respectively.

A chemical reaction’s rate constant, kobs, is the rate at which the reaction proceeds when the concentration of all reactants is 1M or 1 atm.

A zeroth order reaction is one whose overall reaction order is zero, and is independent of reactant concentration.

A zeroth order reaction’s rate is constant, and can be given by: Rate = kobs

The reaction rate is unchanged, since there is no correlation between the value of [A] and rate in a zeroth order reaction.

If the reaction is zeroth order in [A], that means that the rate can be described as: rate = kobs [A]0 = kobs

A first order reaction is one whose overall reaction order is 1, and whose 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 = kobs [A]1

The reaction rate decreases by the same amount that the concentration did.

First order in [A] means the rate law is: rate = kobs [A]1
Let [A]orig = x.
Then rateorig = kobs x.
If [A] decreases, then ratenew = kobs (decreased x) = (decreased) rateorig

The reaction rate doubles.

First order in [A] means the rate law is: rate = kobs [A]1
Let [A]orig = x.
Then rateorig = kobs x.
If [A] doubles, then ratenew = kobs (2x) = 2 rateorig

A second order reaction is one whose overall reaction order is 2, and whose rate either depends on one reactant to the second order, or two separate reactants to the first order.

If the reactants for the reaction are A and B, the rate will be one of:
rate = kobs [A]2
or rate = kobs [B]2
or rate = kobs [A]1[B]1

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

Second order in [A] means the rate law is: rate = kobs [A]2
Let [A]orig = x
Then rateorig = kobs x2.
If [A] increases, then ratenew = kobs (increased x)2 = (increase)2 rateorig

The reaction rate increases by a factor of 9.

Second order in [A] means the rate law is: rate = kobs [A]2
Let [A]orig = x
Then rateorig = kobs x2.
If [A] triples, then ratenew = kobs (3x)2 = 9 rateorig

The reaction rate increases by a factor of 1.5.

If the reaction is first order in [A] and [B] means the rate law is: rate = kobs [A]1 [B]1

Let [A]orig = x and [B]orig = y
Then rateorig = kobs x y.
If [A] triples and [B] decreases by half, then ratenew = kobs (3x) (½y) = 1.5 rateorig

Rate = 5 [A]2

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

Since the rate increases by a factor of the concentration increase to the second power, 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 kobs.

Rate = 2 [A]1 [B]0

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

Between Trials 2 and 3, [B] doubles, while [A] stays constant, and the reaction rate is unchanged, so 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 kobs.

Rate = 2 [A]1 [B]2

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

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

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

Ex: the reaction
NO2 + CO ⇒ NO + CO2
is actually two sub-reactions,
NO2 + NO2 ⇒ NO3 + NO (slow)
NO3 + CO ⇒ NO2 + CO2 (fast)
The slow first step is the rate-determining step, and limits the overall reaction rate.

The rate-determining step can be identified because the substances which appear in the rate law must be reactants in the rate-determining step.

Ex: If the overall reaction rate depends only on [NO2] for the following steps:
NO2 + NO2 ⇒ NO3 + NO
NO3 + CO ⇒ NO2 + CO2
Then the first step, in which NO2 appears as a reactant, must be the rate-determining step.

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 by the fact that it is a product of an early reaction step, and a reactant in a later one.

O is the intermediate.

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

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 reactions.

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

NO + NO3→ 2NO2

The reaction has two individual molecules as reactants. Therefore, it is bimolecular.

In 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.

A is the activation energy Ea.
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.

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, and the reaction rapidly proceeds to the products once the transition state is reached.

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.

It is exothermic.

The products' enthalpy is lower than the reactants', so ΔH \< 0, meaning the reaction is exothermic.

It is endothermic.

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

The Arrhenius equation relates a reaction's activation energy Ea, rate constant kobs, the temperature of the chemical system T, and the ideal gas constant R.

As the temperature increases, the reaction's rate increases as well.

As T increases, the term e-Ea/RT, which starts out as a small fraction, moves closer and closer to 1, raising the calculated value of kobs and speeding up the reaction.

In general, the Arrhenius equation predicts that a reaction's rate will double for every 10ºK increase in temperature.

Reaction B is kinetically preferred.

A reaction's activation energy determines whether it is kinetically preferred or not. In this case, Ea is smaller for reaction B than it is for reaction A. So reaction B runs faster, and is kinetically preferred.

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.

Reaction A is thermodynamically preferred.

A reaction's enthalpy change determines whether it is thermodynamically preferred or not. In this case, ΔHA is larger in magnitude than ΔHB, so the products of A are more thermodynamically stable, and reaction A is thermodynamically preferred.

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.

A catalyst is a chemical which participates in a reaction and serves to increase the reaction's rate, usually by lowering the activation energy for the reaction. Catalysts are not themselves depleted by the reaction.

Chemical catalysts decrease a reaction's activation energy.

Ex: The below energy profile demonstrates positive catalysis. Note that Ea decreases, but ΔH is unaffected by the catalyst.

Enzymes serve as catalysts in chemical reactions.

Therefore, they speed up or slow down reactions, but they are not affected by the reaction, and they cannot change the thermodynamic favorability of a reaction.

• A homogeneous catalyst is in the same phase as the remaining reactants.

• A heterogeneous catalyst is in a different phase from the remaining reactants.

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