Question

I'm trying to study for my General Chemistry II Exam, but I want to make sure that I don't miss anything important! If you could provide your input on the following concepts, that would be greatly appreciated! Thank you so much!(:

Chapter 16 - Chemical Kinetics

I. Reaction Rates

            A. Definition of reaction rate

            B. Mathematical expression for Reaction rate

            C. Instantaneous rate

            D. Initial rate

            E. Rate constant

            F. Rate law

            G. Integrated rate law

II. Determining Reaction Order

            A. Method of initial rates

III. Types of Reactions

            A. Second-order reaction

                        1. second-order integrated rate law

                        2. What must be plotted to verify that a reaction is second order?

                        3. What does the slope equal?

            B. First-order reaction

                        1. First-order integrated rate law

                        2. What must be plotted to verify that a reaction is first order?

                        3. What does the slope equal?

                        4. Half-life

            C. Zeroth-order reaction

                        1. zeroth-order integrated rate law

                        2. What must be plotted to verify that a reaction is zeroth-order?

                        3. What does the slope equal?

            D. Overall order of reaction

IV. Temperature dependence of reacton rates

            A. Realtionship between k and E_a

                        1. Arrhenius behavior

                        2. Arrhenius parameters

            B. Collision Theory

V. Catalysis

Answer 1

Definition of reaction rate:The reaction rate (rate of reaction) or speed of reaction for a reactant or product in a particular reaction is intuitively defined as how fast or slow a reaction takes place. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second.

Rate constant:In chemical kinetics a reaction rate constant or reaction rate coefficient, k, quantifies the rate of a chemical reaction.^[1]

For a reaction between reactants A and B to form product C

the reaction rate is often found to have the form:

Here k(T) is the reaction rate constant that depends on temperature. [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution. (For a reaction taking place at a boundary one would use instead moles of A or B per unit area).

The exponents m and n are called partial orders of reaction and are not generally equal to the stoichiometric coefficients a and b. Instead they depend on the reaction mechanism and can be determined experimentally.

Rate law: he rate law or rate equation for a chemical reaction is an equation that links the reaction rate with concentrations or pressures of reactants and constant parameters (normally rate coefficients and partial reaction orders)^. For many reactions the rate is given by a power law such as

Integrated rate law:

The differential rate law describes how the rate of reaction varies with the concentrations of various species, usually reactants, in the system. The rate of reaction is proportional to the rates of change in concentrations of the reactants and products; that is, the rate is proportional to a derivative of a concentration.To illustrate this point, consider the reaction

A → B

The rate of reaction, r, is given by

r = -

d [A] d t

Suppose this reaction obeys a first-order rate law:

r = k [A]

This rate law can also be written as

r = -

d [A] d t

= k [A]

This equation is a differential equation that relates the rate of change in a concentration to the concentration itself. Integration of this equation produces the corresponding integrated rate law, which relates the concentration to time. When you viewed concentration-time curves in previous pages, you viewed the integrated rate laws.

d [A] [A]

=

- k d t

At t = 0, the concentration of A is [A]₀. The integrated rate law is thus
[A] = [A]₀ e^{- k t}

initial rate:The initial rate of a reaction is the instantaneous rate at the start of the reaction (i.e., when t = 0). The initial rate is equal to the negative of the slope of the curve of reactant concentration versus time at t = 0.

2)Method of initial rates:

One of the first steps in studying the kinetics of a chemical reaction is to determine the rate law for the reaction. One method for making this determination is to experimentally measure how the concentration of a reactant or product varies with time and then make characteristic kinetics plots. Another strategy for determining the rate law is to use the method of initial rates.

The Method of Initial Rates involves measuring the rate of reaction, r, at very short times before any significant changes in concentration occur. Suppose one is studying a reaction with the following stoichiometry:

A + 2 B → 3 C

While the form of the differential rate law might be very complicated, many reactions have a rate law of the following form:

r = k [A]^a [B]^b

The initial concentrations of A and B are known; therefore, if the initial reaction rate is measured, the only unknowns in the rate law are the rate constant, k, and the exponents a and b. One typically measures the initial rate for several different sets of concentrations and then compares the initial rates.

Consider the following set of data:

Trial	Rate (mole L-1 sec-1)	Initial Concentration of A (mole L-1)	Initial Concentration of B (mole L-1)
1	2.73	0.100	0.100
2	6.14	0.150	0.100
3	2.71	0.100	0.200

If simple multiples are chosen for the concentrations and only one concentration is varied at a time, one can determine a and b by inspection. In this case the values of a and b may not be obvious. One can employ the following algebraic technique for determining the exponents.

First, write the ratio of the rate laws for two trials.

r1 r2

=

k [A]1a [B]1b k [A]2a [B]2b

Next, substitute the numerical values into the equation.

2.73 mole L-1 sec-1 6.14 mole L-1 sec-1

=

k (0.100 mole L-1)a (0.100 mole L-1)b k (0.150 mole L-1)a (0.100 mole L-1)b

Notice that the units for each quantity and the rate constant can be removed, and in this case the exponent b is removed when the concentrations of B divide. The equation simplifies to

2.73 6.14

=

0.100a 0.150a

0.4446 = 0.6667^a

To convert a from an exponent into a coefficient, take the logarithm of both sides of the equation.

ln[0.4446] = ln[0.6667^a]

-0.8106 = -0.4054a

The value of a may now be readily determined.

a =

-0.8106 -0.4054

=

1.9995

In most cases, the exponents are integers (or less commonly fractions such as 1/2). In this case the reaction is second order in A (a = 2). A similar strategy can be employed to determine the value of b. (Actually, it should be obvious from inspection of trials 1 and 3 that the reaction is zero-order in B.) Once the exponents are known, the rate constant can be calculated. Because the data generally suffers from experimental error, it is best to calculate the rate constant for each trial and use the average value.