Chemical Kinetics Chapter 13 13.1-13.6
Chemical Kinetics • In learning chemical kinetics, you will learn how to: • Predict whether or not a reaction will take place. • Once started, determine how fast a reaction will proceed. • Learn how far a reaction will go before it stops.
Rate of a Reaction • Thermodynamics-Does a reaction take place? • Kinetics-How fast does a reaction proceed? • Chemical Kinetics-the area of chemistry concerned with the speeds or rates at which a chemical reaction occurs. • Reaction Rate-the change in the concentration of a reactant or product with time. (M/s)
Rate of a Reaction • Why do we need to know the rate of a reaction? • Practical knowledge is always useful • Preparation of drugs • Food processing • Home repair
Rate of a Reaction • General equation for a reaction: • A → B • Reactant → Product • In order to monitor a reaction’s speed or rate, we can look at one of two things: • Decrease in [ reactant ] • Increase in [ product ] • Can be represented as: rate = - Δ [A] / Δ t or rate = Δ [B] / Δ t
Rate of a Reaction • How do we measure this experimentally? • For reactions in solution: • Changes in concentration can be measured spectroscopically • For reactions involving gases: • Changes in pressure can be measured • For reactions in solution with ions present: • Change in concentrations can be measured through electrical conductance
time Rate of a Reaction • So if we have an aqueous solution of molecular bromine and formic acid, how do we determine the reaction rate? Br2(aq)+HCOOH(aq)→ 2Br–(aq)+2H+(aq)+CO2(g)
Rate of a Reaction • Look for color changes • Molecular bromine is usually reddish-brown in color. Formic acid is colorless. • As the reaction progresses, the color of the solution changes. • It fades until it becomes colorless. • What does this mean?
Rate Calculations • How do we calculate the rate of a reaction? • We first need this information: • Time (s) • [reactant]
Rate Calculations Br2 (aq) + HCOOH (aq) → 2Br–(aq) + 2H+(aq) + CO2(g)
Rate Calculations • Instantaneous Rate–rate of a reaction for a specific point in time. • Average Rate vs. Instantaneous rate • Examples????
Rate Calculations • Average Rate = -Δ [Br2] / Δt = - [Br2]final – [Br2]initial / [t]final – [t]initial • Instantaneous Rate = rate for specific instance in time [Br2] / t
Rate Calculations • Using this information, calculate the average rate of the bromine reaction over the first 50s of the reaction.
Rate Calculations Average Rate = - [Br2]final – [Br2]initial / [t]final – [t]initial Average Rate = - (0.0101- 0.0120)M / (50s – 0s) Average Rate = -0.002M / 50s Average Rate = 3.80 x 10-5 M/s
Reaction Rates and Stoichiometry • For reactions more complex than A → B we cannot use the rate expression initially described. • Example: • 2A → B • Disappearance of A is twice as fast formation of B • Rate = - ½ Δ[A] /Δt
Reaction Rates and Stoichiometry • In general, for the reaction • aA + bB →cC + dD • Rate = - 1/a Δ[A] /Δt = - 1/b Δ[B] /Δt = 1/c Δ[C] /Δt = 1/d Δ[D] /Δt
Reaction Stoichiometry Write the rate expression for the following reaction: CH4(g) + 2O2(g) CO2(g) + 2H2O (g) D[CO2] = Dt D[CH4] rate = - Dt D[H2O] = Dt D[O2] = - 1 1 Dt 2 2
Rate Constant • Look back to molecular bromine chart. • What is k? • K- the rate constant. A constant of proportionality between the reaction rate and the concentration of the reactant. • K may change slightly over time. • K is represented as: • K = rate/ [reactant] • K is not affected by the [reactant] or rate alone, since it is a ratio of these two. At any given point on a graph, k should be similar in value to it’s value at other points in the same graph.
The Rate Law • Rate Law-expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some power. • Using the general reaction: aA + bB →cC + dD Rate Law is: rate = k [A]x[B]y
The Rate Law aA + bB cC + dD Rate = k [A]x[B]y reaction is xth order in A reaction is yth order in B reaction is (x + y)th order overall
Reaction Order • Reaction Order-the sum of the powers to which all reactant concentrations appearing in the rate law are raised. • Reaction order is always defined in terms of reactant concentration. • Overall reaction order- x + y • Example: • Rate = k [F2] [ClO2] • Reaction order = first • Overall reaction order = second
Reaction Order • What is the rate expression for aA + bB →cC + dD where x=1 and y=2? • Rate = k[A][B]2 • What is the reaction order? • First in A, second in B • Overall reaction order? • 2 +1 = 3
Reaction Order F2(g) + 2ClO2(g) 2FClO2(g) rate = k [F2]x[ClO2]y
Reaction Order If initially [F2] = 1.0M and [ClO2]=1.0M, what will happen to the reaction rate if F2 is doubled? Rate1 = k(1.0M)(1.0M)2 Rate1 = k(1.0M3)[F2 ] = 1.0M Rate2 = k(2.0M)(1.0M)2 Rate2 = k(2.0M3)[F2 ] = 2.0M Rate2 = 2 x Rate1
Reaction Order What will happen in the same reaction if the [ClO2] is doubled? Rate1 = k(1.0M)(1.0M)2 Rate1 = k(1.0M3)[ClO2 ] = 1.0M Rate2 = k(1.0M)(2.0M)2 Rate2 = k(4.0M3)[ClO2 ] = 2.0M Rate2 = 4 x Rate1
Determination of Rate Law F2(g) + 2ClO2(g) 2FClO2(g)
Determination of Rate Law • Experiments 1 & 4 As [F2] doubles, so does the rate • Experiments 2 & 3 As [ClO2] doubles, so does the rate • 2:2 ratio…..1:1 ratio x = 1 and y = 1 • Rate = k [F2] [ClO2]
Rate law/Expression Calculations Determine the rate law and calculate the rate constant for the following reaction from the following data: S2O82- (aq) + 3I- (aq) 2SO42- (aq) + I3- (aq) rate k = 2.2 x 10-4 M/s = [S2O82-][I-] (0.08 M)(0.034 M) Double [I-], rate doubles (experiment 1 & 2) Double [S2O82-], rate doubles (experiment 2 & 3) rate = k [S2O82-]x[I-]y y = 1 x = 1 rate = k [S2O82-][I-] = 0.08/M•s
Rate Law/Reaction Order Rate laws are always determined experimentally Reaction order is always defined in terms of reactant Reactant order is not related to the stoichiomteric coefficient in the overall reaction. F2(g) + 2ClO2(g) 2FClO2(g) rate = k [F2][ClO2]
Relation between Reactant Concentration and Time • First Order Reaction-a reaction whose rate depends on the reactant concentration raised to the first power. Reaction Type: A→B Rate of: -Δ [A]/Δt or k[A] Combining and simplifying these equations brings us to the following rate equation: ln[A]t = -kt + ln[A0]
Reaction Time The reaction 2A B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ? 0.88 M ln 0.14 M = 2.8 x 10-2 s-1 ln ln[A]0 – ln[A] = k k [A]0 [A] [A]0 = 0.88 M ln[A] = ln[A]0 - kt [A] = 0.14 M kt = ln[A]0 – ln[A] = 66 s t =
Decomposition of Nitrogen Pentoxide • Data on page 560 • Plot of ln[N2O5] (M) vs. t (s) will allow us to see and calculate more information about the reaction taking place
Gas Phase Reactions • First order gas phase reactions have a linear relationship between partial pressure of gas and time. lnPt = -kt + lnP0
Reaction Half-life • As a reaction proceeds, the concentrations of the reactants decreases. • Another way to measure [reactant] over time is to use the half-life. • Half-life, t1/2 –the time required for the concentration of a reactant to decrease to half of its initial concentration.
Reaction Half-life • Expression for half-life of a first order reaction is: t1/2 = ln2/k or t1/2 = 0.693/k