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## Chemical Kinetics

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**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