CHE 141 1st Edition Lecture 3Outline I. Time and Reaction RatesII. Integrated Rate Laws: First Order Reactions III. MathbackIV. Half-LifeV. Integrated Rate Laws: Second Order ReactionsVI. Half-Life and ConcentrationTime and Reaction Rates- Reaction rate changes with concentration (kinetic molecular theory)- Reactant concentrations change over the course of the reaction- Rate of reaction changes over the course of the reactionIntegrated Rate Laws: First Order Reactions- Consider the decomposition reactiono Xproducts- This reaction is first order (depends only on the concentration of one reactant, X) so fromthe relative rate Rate=-change in [X]/change of t=k[X]- This is a differential rate equation that relates the rate of change of concentration to the concentration itself- Integration of the differential rate equation produces the corresponding integrated rate law, which relates the concentration to time: Rate=-change in [X]/change in t=k[X] then rearrange in terms of k (change in t) so change in [X]/[X]=-k (change in t), at t=0 [X]=[X]0 rearranging in terms of ln[X] which is ln[X]=-kt+ln[X]0- This is the integrated rate law for the first order reaction: ln[X]=-kt+ln[X]0- k=rate constant- [X]0=initial concentration of reactant X- This is sometimes written in terms of [X] using the exponential function [X]=[X]0e^-ktMathback- Logarithms are basically another way of writing indices- When b^y=x then the base b logarithm of x is equal to y according to: logb(x)=y- Log is short for log10 or “log to the base 10”- This means if y=log10 then x=10^yThese 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.- ln is short for loge or “log to the base e” where e is the math constant Eulers number thus if y=lnx then x=e^y- When rearranging equations with logarithms in, you can take the exponential to both sides of the equation to get rid of the logarithm, or you can take the logarithm of both sides to get rid of the exponentialHalf-Life- The half-life (t1/2) is the time in the course of a chemical reaction during which the concentration of a reactant decreases by half- Half-life is inversely related to the rate constant of a reaction: the higher the reaction rate the shorter the half-life- Half-life for a first order reaction: t1/2=-ln.5/k=.693/kIntegrated Rate Laws: Second Order Reactions- A reaction may be second order overall if it is first order in [A] and [B]rate=k[A][B] orit is second order in one reactantrate=k[A]^2- Consider the latter case for example a second order decomposition reaction X products- The reaction is second order so can write: rate=-change in [X]/change in t=k[X]^2 then –change in [X]/[X]^2=k change in t- This is the integrated rate law for a second order reaction: 1/[X]=kt+1/[X]0- Analogous with the straight line equation y=mx+b- Where y variable=1/[X], x variable=t, gradient/slope=k and c (y-intercept)=1/[X]0 which is sometimes written in terms of [X]: [X]=[X]0/1+kt+[X]0Half-Life and Concentration- For the first order reaction: t1/2=.693/k where t1/2 is independent of [X]- For the second order reaction: t1/2=1/k[X]0 where t1/2 is inversely proportional to [X]0)- The amount of reactant remaining after time t(At) is related to the amount initially present (A0) by the equation: A0/At=.5^n where n=number of half-lives in
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