CHE 141 1st Edition Lecture 4 OutlineI. Pseudo-First Order Reactions II. Zero Order Reactions III. Half Life of Zero Order ReactionsIV. Temperature and Reaction RatesV. The Arrhenius EquationVI. Energy ProfilePseudo-First Order Reactions- Second order reactionso Second order in one reactant: Rate=k[A]^2o Integrated rate law: 1/[X]=kt+1/[X]0o First order in two reactants: rate=k[A][B]- We use pseudo-first order rate law for an overall second order reaction rate=k[A][B] when one reactant is at a much higher concentration than the other (in excess)- If we take a generic rate law for a second order reaction which is first order in two reagents: rate=k[A][B]- Assume that [A]>>[B]- [A] remains virtually constant throughout the reaction at [A]=[A]0 o Rate=k[A]0[B]- Thus we can simplify to o Rate=k’[B]- k’=the pseudo first order rate constant- k=the second order rate constant- A pseudo-first order rate law looks like the rate law for a first order reaction because the reaction appears to follow first order kinetics- A pseudo-first order reaction has the same integrated rate law as a first order reaction, butthe rate of the pseudo-first order reaction depends on the concentration of more than one reactant- This is the integrated rate law for a pseudo first order reaction where reactant A is in excess:o ln[B]=-k’t+ln[B]0o where k’=the pseudo-first order rate constantThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- To calculate the second order rate constant from k’ we need to use the substitution we made and solve for ko k’=k[A]0o k=k’/[A]0o where k is the second order rate constant- NO2(g)+CO(g)NO(g)+CO2(g)o This reaction is second order in a single reactant, NO2, and zero order in CO, so the rate law iso Rate=k[NO2]^2[CO]^0o Rate=k[NO2]^2o Integrated rate law for a second order reaction: 1/X=kt+1/[X]0o This situation is a second order reaction in one reactant, not pseudo-first order reactiono [CO] is comparable to [NO2]-no reactant in excessZero Order Reactions- Consider a generic reaction Xproduce which is zero order in reactant X and zero order overall:- Rate law:Rate=k[X]0- Rate of consumption of X: rate=-change in X/change in t=k[X]0- The integrated rate law for a zero order reaction is [X]=-kt+[X]0- Comparing to y=mx+b, the gradient of a plot of [X] versus t equals the negative of the zero order rate constant, k, with y intercept=[X]0Half Life of Zero Order Reactions- Half-life for a zero order reaction: t1/2=[X]0/2k- Reaction rate of a zero order reaction is independent of concentration, but half-life is notTemperature and Reaction Rates- In general, increasing concentration increases rateo Defined mathematically through rate laws- For a collision to be successful, molecules needo Correct orientationso Sufficient kinetic energy to reactThe Arrhenius Equation- k=Ae^-Ea/RT- k is the rate constant- A is the frequency factor- Ea is the activation energy- R is the gas constant- T is the reaction temperature- Log (linear) form of Arrhenius equation: lnk=-Ea/R(1/T)+lnA- The frequency factor (A) is the product of collision frequency and a term expressing the probability that a collision has the correct orientation to result in a chemical reaction- The frequency of collisions is affected by factors such as physical state, concentration of reactants and temperature- The proportion of successful collisions depends on correct orientation and sufficient energy- Activation energy (Ea) is the minimum energy that molecules need to react when they collide- Rise in temperature, rise in kinetic energy, rise in frequency of collisions, rise in fraction of molecules with enough KE to react and thus rate rises- Once know the value of Ea we can use the data from the rate constant (k1) of the reactionat one temperature (T1) to calculate the value of the rate constant (k2) at another temperature (T2)o Take the natural log of both sideso Substitute k1 and T1o Substitute k2 and T2o Subtracting these two expressions (lnk1-lnk2)o The frequency factor cancels outo As lnx-lny=ln x/yEnergy Profile- Energy profile shows the changes in energy over the course of a chemical reaction
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