12: Chapter Chemical Kinetics Part 1
Chemical kinetics is the study of how fast chemical reactions occur and how they occur. Four important factors affect rates of reactions: Concentration of reactants. Temperature of reactions. Presence or absence of a catalyst. Surface area of solid or liquid reactants or catalysts. Goal: to understand chemical reactions at the molecular level. The speed of a reaction is defined as the change that occurs per unit time. It is often determined by measuring the change in concentration of a reactant or product with time. The speed of the chemical reaction is its reaction rate. For a reaction A B
Average rate = change in the number of moles of B change in time
Reaction Rates
Here the change in the number of moles of B is defined as: (moles of B) = (moles of B at final time) (moles of B at initial time) Illustrate this with an example: Suppose A reacts to form B. Let us begin with 1.00 mol A. At t = 0 (time zero) there is 1.00 mol A and no B present. At t = 10 min, there is 0.74 mol A and 0.26 mol B. At t = 20 min, there is 0.54 mol A and 0.46 mol B. Eventually, there will be no more A left, and only B will be present.
We can use this data (and others determined at other times) to find the average rate:
Average rate =
(moles B) (moles of B at t = 10 min) (moles of B at t = 0 min) = t 10 min 0 min
For the reaction A B there are two ways of measuring rate: The rate of appearance of product B (i.e., change in moles of B per unit time) as in the preceding example.
Average rate = 0.26 mol 0 mol mol = 0.026 10 min 0 min min
The rate of disappearance of reactant A (i.e., the change in moles of A per unit time).
Average rate = (moles of A) t
Note the minus sign! This reminds us that rate is being expressed in terms of the disappearance of a reactant. Thus, rates are always positive numbers.
Rates in Terms of Concentrations In most chemical reactions we will determine the reaction rate by monitoring a change in concentration (of a reactant or product). The most useful unit to use for rates is molarity. (Pressure is used for gases.) Since volume is usually constant, molarity and moles are directly proportional. Consider the following reaction: C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
We can calculate the average rate in terms of the disappearance of C4H9Cl. The units for average rate are mol/Ls or M/s. The average rate decreases with time. We can plot [C4H9Cl] versus time. The rate at any instant in time is called the instantaneous rate. It is the slope of the straight line tangent to the curve at that instant. Instantaneous rate is different from average rate. It is the rate at that particular instant in time. For our discussion we will call the "instantaneous rate" the rate, unless otherwise indicated.
Reaction Rates and Stoichiometry of Balanced Equation For the reaction (rxn): C4H9OH(aq) + HCl(aq) C4H9Cl(aq) + H2O(l) The rate of appearance of C4H9OH must equal the rate of disappearance of C4H9Cl.
Rate =
[C4H9Cl] = [C4H9OH]
t t
What if the stoichiometric relationships are not 1:1? For the rxn: 2HI(g) H2(g) + I2(g) For this rxn, it should be clear that as HI is consumed or disappears, half as much H2 (or I2) appears. So the rate of disappearance of HI is twice the rate of appearance of H2 (or I2). rateHI = 2rateH2 or 0.5rateHI = rateH2
As we now have 2 different rates for the same reaction (related by the stoichiometry), it is common to talk in terms of the rxn rate, or the rate of the rxn, not just in terms of the rate of appearance of a product or the rate of disappearance of a product. The rate of the rxn, or called just the rate, may be expressed as:
Rate = 1 2
[HI] = [H2] = [I2]
t t t
Or we can write it more generally: raterxn = 0.5rateHI = rateH2 = rateI2
We can generalize this equation a bit. For the rxn: aA + bB cC + dD
So, the overall rate of a rxn may be expressed as:
Rate = 1 a
[A] =
t
1 b
[B] = 1 [C ] = 1 [D]
t c t d t
or in nonmathematical terms: 1 1 1 Rate 1 = rateA = rateB = rateC = rateD a b c d Be careful! Experiments are always conducted in terms of the rates of appearance or disappearance of a product or reactant. These rates may then be converted to rxn rates using the overall balanced equation. Read the problems carefully so you know whether you are dealing with a rxn rate or a rate of reactant or product. Although it makes NO difference if the stoichiometry is 1:1, it will make a difference if the coefficient of that reactant or product is not 1. If it is not specified, it is by default a rxn rate.
The Dependence of Rate on Concentration In general, rates: Increase when reactant concentration is increased. Decrease as the concentration of reactants is reduced. We often examine the effect of concentration on reaction rate by measuring the way in which the reaction rate at the beginning of a reaction depends on the starting conditions. Consider the reaction: NH4+(aq) + NO2 (aq) N2(g) + 2H2O(l)
We measure initial reaction rates. The initial rate is the instantaneous rate at time t= 0. We find this at various initial concentrations of each reactant. As [NH4+] doubles, with [NO2] constant, the rate doubles. We conclude that the rate is proportional to [NH4+]. As [NO2] doubles, with [NH4+] constant, the rate doubles. We conclude that the rate is proportional to [NO2]. The overall concentration dependence of reaction rate is given in a rate law or rate expression. For our example, the rate law is: Rate = k[NH4+][ NO2]
So a rate law is a mathematical description of how the concentration of the reactant(s) affect(s) the rxn rate. The proportionality constant k is called the rate constant. Once we have determined the rate law and the rate constant, we can use them to calculate initial reaction rates under any set of initial concentrations.
Reaction Order For a general reaction with rate law: Rate = k[reactant 1]m[reactant 2]n The exponents m and n are called reaction orders. The overall reaction order is the sum of the reaction orders. The overall order of reaction is m + n + .... For the reaction: NH4+(aq) + NO2 (aq) N2(g) + 2H2O(l) The reaction is said to be first order in [NH4+], first order in [NO2], and second order overall. So rate law is:
Note that reaction orders must be determined experimentally. They do not necessarily correspond to the stoichiometric coefficients in the balanced chemical equation! We commonly encounter reaction orders of 0, 1 or 2. Even fractional or negative values are possible.
Units of Rate Constants Units of the rate constant depend on the overall reaction order. For example, for a reaction that is second order overall: Units of rate are:
Units of rate = (Units of rate constant )(Units of concentrat ion )
2
Thus the units of the rate constant are: Units of rate constant = (Unitsof rate) M s = = M 1s 2 2 (Unitsof concration) M
1
Using Initial Rates to Determine Rate Laws To determine the rate law, we observe the effect of changing initial concentrations. For the general rxn: aA + bB The rate law is: Rate = k[A]m[B]n cC + dD
Mathematically, we compare the rates of 2 or more experiments, conducted at different concentrations of reactants.
k [A ]m [ B]n [ A]m [ B] n Rate2 2 2 2 2 = m n = m n Rate1 k [A ]1 [ B]1 [ A]1 [ B]1
Solving this gives us the 2 exponents, which gives us the rxn order. Once the exponents are known, k may be calculated. We then know the complete rate law. If a reaction is zero order in a reactant, changing the initial concentration of that reactant will have no effect on rate (as long as some reactant is present). If a reaction is first order, doubling the concentration will cause the rate to double. If a reaction is second order, doubling the concentration will result in a 22 increase in rate. Similarly, tripling the concentration will result in a 32 increase in rate. A reaction is nth order if doubling the concentration causes a 2n increase in rate. Note that the rate, not the rate constant, depends on concentration.