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Chapter 14

How fast the chemical reactions occur? Study with chemical kinetics. Call these reaction rates.

Rates depend on:

1) Concentrations of reactants; more reactants, faster reaction.

2) Temperature; higher temperature, faster rates.

3) Catalyst; presence of a catalyst increases the rate.

4) Surface area; more surface area, faster rate.

14.1 Reaction rates

A B

Time	A	B
0 min	1.0 mol	0.0 mol
20 min	0.54 mol	0.46 mol
40 min	0.30 mol	0.70 mol

Average rate for interval of time = =

This depends on the starting in ending times of the interval:

For the period 0 to 20 minutes, Average Rate = +.46/ 20 = 0.023 mol/min.

For the period 20 to 40 minutes, Average Rate = +.24/20 = 0.012 mol/min.

Rates are often expressed in terms of the concentrations of the various species.

Average rate =, this has units of M/time.

We are most interested in the average rate as the time interval becomes very small and at particular points in time. The limit as t 0 is just the slope of the curve of [B] vs. time (or -[A] vs. time) and is the first derivative of the concentration with respect to time.

Reaction rates and stoichiometry:

aA + bB cC + dD

14.2

Dependence of rate on concentration:

As concentrations of reactants decrease, rates decrease.

Can we quantify this relationship?

Look at how the initial rate (instantaneous rate at time = 0) varies concentration.

NH₄⁺(aq) + NO₂^-(aq) N₂(g) + 2H₂O(l)

Experiment	[NH₄⁺]₀	[NO₂^-]₀	Initial Rate	Increase
1	0.0100	0.200	5.4 x 10^-7
2	0.0200	0.200	10.8 x 10^-7	x 2
3	0.200	0.0202	10.8 x 10^-7
4	0.200	0.0404	21.6 x 10^-7	x 2

Therefore, the initial instantaneous rate is proportional to [NH₄⁺][NO₂^-]. Introducing the proportionally constant we write:

Rate = k[NH₄⁺][NO₂^-]; where k is called the rate constant. In this example, the rate constant is:

5.4 x 10^-7 M/s = k (0.0100M)(0.200M) or k = 2.7 x 10^-4M^-1s^-1.

In general, the rate will be proportional to the reactants' concentrations raised to various powers. The sum of the various powers is called the overall reaction order; the order with respect to particular a reactant is the power of that reactant.

Rate k[reactant 1]^m[reactant 2]ⁿ....

In our example, the reaction is first order with respect to NH₄⁺, first order with respect to NO₂, and second-order overall.

Ex: 2N₂O₅(g) 4NO₂(g) + O₂(g) Rate = k [N₂O₅]

First order with respect to N₂O₅ and first order overall. Note that the order is not necessarily related to the stoichiometric coefficients.

Ex: CHCl₃(g) + Cl₂(g) CCl₄(g) + HCl(g) Rate = k[CHCl₃][Cl₂]^1/2

First order in [CHCl₃], 1/2 order in [Cl₂], and 3/2 order overall.

Units of rate constants

Rate = k (M)^{overall order} = k M^y = M s^-1, so k = M^1-y s^-1.

We use initial rates to determine rate laws.

2NO(g) + O₂(g) 2NO₂(g)

R=k[NO]^x[O₂]^y

[NO]	[O₂]	Increase	Rate
0.0126	0.0125	1	1.41 x 10^-2 = k[0.0126]^x[0.0125]^y R
0.0252	0.0250	8	1.31 x 10^-1 = k[0.0126]^x[2 x 0.0125]^y = 2^yR	2^y = 8; y=3
0.252	0.125	4	5.64 x 10^-2 k[2 x 0.0126]^x[0.0125]^y = 2^xR	2^x = 4; x =2

Therefore, R = k[NO]²[O₂]³.

14.3 Change of concentration with time

We want more than just the initial rate and dependence of the initial rate on the concentrations. We would like to know the concentrations as a function of time; we need to use calculus to do this. We will look at the results of using calculus to study the time dependence of some simple orders of reaction.

First order

A products is a typical example.

Rate =

This is the first order differential equation. The solution is:

y = mx +b

Also,

The half-life, t_1/2, of a reaction is the time for the concentration of a reactant to decrease to 1/2 of its initial value. ()

Second-order

Rate = k[A]² or Rate =k[A][B]

; y = mx +b

14.4 Dependence of rates a temperature

As temperature increases, rates increase. k increases. Why?

Molecules must collide to react. As temperature increases, velocities increase, so the number of collisions increases.
In it is not sufficient for the molecules to simply collide:H₂+ I₂ collide 10¹⁰ times per second, but only one in 10¹³ collisions react!
Molecules must overcome in energy barrier to react (must then bonds, rate bonds, etc.). The minimum energy required to react is called the activation energy, E_a. E_a varies from reaction to reaction.

More molecules have E_a Arrhenius Equation high temperature.

Orientation factor

Molecules must be correctly oriented in order to react.

Reduces rate.

Arrhenius Equation

14.5 Reaction mechanisms.

How does a reaction actually occur?

NO(g) + O₃(g) NO(g) + O₂(g)

single collision, reaction

The number of molecules involved is called the molecularity of the reaction (in this case, 2).

If the molecularity is 1, A B+C, we say this is unimolecular.

If the molecularity is 2, A+B C+D, we say this is bimolecular.....

Multistep reactions:

NO₂(g) + CO(g) NO(g) + CO₂(g)

Requires 2 steps (2 elementary processes)

1) NO₂ + NO₂ NO₃ + NO

2) NO₃ + CO NO₂ + CO₂ NO₃ is an intermediate.

Often, one elementary step is slow and controls the rate. This step is called the rate limiting step.

14.6 Catalysis

A catalyst is a substance that change the speed of a reaction without undergoing a permanent chemical change. The

2KclO₃(s) 2KCl(s) + 3O₂(g) when heated

Addition of MnO₂(s) speed up the reaction.

Catalysts are important industrial applications and biological systems (enzymes).

Catalysts lower the activation barrier for a reaction.

Example: nitrogen fixation (Brian Hales); plants use NH₃, NH₄⁺, NO₃^- to synthesize complex biological proteins.

N₂(g) NH₃ (nitrogen fixation)

An enzyme called nitrogenase catalyzes this process. The research in Dr. Hales' group is attempting to determine the structure of this catalyst.