Integrated Rate Law Goal: To determine the order and rate law from concentration and time data

Using the calculator to determine order The test with the best linear fit is the order of the reaction: Ø order  Time vs. Concentration 1 st order  Time vs. ln(concentration) 2 nd order  Time vs. (1/concentration)

Enter the data into your calculator Time (s)[NO 2 ] (mol/L) x x x x x For equation: NO 2 + CO  NO + CO 2 Below 225°C only depends on [NO 2 ] Enter 4 columns of data: 1 st column = time 2 nd column = concentration 3 rd column = ln (concentration) 4 th column = 1/concentration

Perform 3 linear regressions The linear regressions: Ø order test  Time vs. Concentration  (1 st column, 2 nd column) 1 st order  Time vs. ln(concentration)  (1 st column, 3 rd column) 2 nd order  Time vs. (1/concentration)  (1 st column, 4 th column) Each time: 1. Perform linear regression 2. Write down the slope 3. Write down the correlation coefficient Winner= Best correlation coefficient (closest to ±1)

Writing the rate law and ½ life equation: zero orderRate = k[A] o plot concentration [A] vs. time (t) k = +slope integrated rate law  [A] t = -kt + [A] 0 half life  t 1/2 = [A] 0 /2k [A] Time (t) 1 st order Rate = k[A] 1 plot of ln conc. vs. time is linear k = + slope integrated rate law  ln[A] t = -kt + ln[A] 0 half life  t 1/2 =.693/k Ln[A] Time (t) 2 nd order Rate = k[A] 2 plot inverse of conc. vs. time is linear k = + slope integrated rate law  1/[A] t = kt + 1/[A] 0 half life  t 1/2 = 1/k[A] 0 1/[A] Time (t)

Let’s clarify some things zero orderRate = k[A] o plot concentration [A] vs. time (t) k = +slope integrated rate law  [A] t = -kt + [A] 0 half life  t 1/2 = [A] 0 /2k [A] Time (t) 1 st order Rate = k[A] 1 plot of ln conc. vs. time is linear k = + slope integrated rate law  ln[A] t = -kt + ln[A] 0 half life  t 1/2 =.693/k Ln[A] Time (t) 2 nd order Rate = k[A] 2 plot inverse of conc. vs. time is linear k = + slope integrated rate law  1/[A] t = kt + 1/[A] 0 half life  t 1/2 = 1/k[A] 0 1/[A] Time (t) Order are exponents

Let’s clarify some things zero orderRate = k[A] o plot concentration [A] vs. time (t) k = +slope integrated rate law  [A] t = -kt + [A] 0 half life  t 1/2 = [A] 0 /2k [A] Time (t) 1 st order Rate = k[A] 1 plot of ln conc. vs. time is linear k = + slope integrated rate law  ln[A] t = -kt + ln[A] 0 half life  t 1/2 =.693/k Ln[A] Time (t) 2 nd order Rate = k[A] 2 plot inverse of conc. vs. time is linear k = + slope integrated rate law  1/[A] t = kt + 1/[A] 0 half life  t 1/2 = 1/k[A] 0 1/[A] Time (t) k from linear regression Units = M (1-order) s Y = mx + b

Let’s clarify some things zero orderRate = k[A] o plot concentration [A] vs. time (t) k = +slope integrated rate law  [A] t = -kt + [A] 0 half life  t 1/2 = [A] 0 /2k [A] Time (t) 1 st order Rate = k[A] 1 plot of ln conc. vs. time is linear k = + slope integrated rate law  ln[A] t = -kt + ln[A] 0 half life  t 1/2 =.693/k Ln[A] Time (t) 2 nd order Rate = k[A] 2 plot inverse of conc. vs. time is linear k = + slope integrated rate law  1/[A] t = kt + 1/[A] 0 half life  t 1/2 = 1/k[A] 0 1/[A] Time (t) [A] 0 = start concentration (From data table)

Let’s clarify some things zero orderRate = k[A] o plot concentration [A] vs. time (t) k = +slope integrated rate law  [A] t = -kt + [A] 0 half life  t 1/2 = [A] 0 /2k [A] Time (t) 1 st order Rate = k[A] 1 plot of ln conc. vs. time is linear k = + slope integrated rate law  ln[A] t = -kt + ln[A] 0 half life  t 1/2 =.693/k Ln[A] Time (t) 2 nd order Rate = k[A] 2 plot inverse of conc. vs. time is linear k = + slope integrated rate law  1/[A] t = kt + 1/[A] 0 half life  t 1/2 = 1/k[A] 0 1/[A] Time (t) t = time in seconds

Let’s clarify some things zero orderRate = k[A] o plot concentration [A] vs. time (t) k = +slope integrated rate law  [A] t = -kt + [A] 0 half life  t 1/2 = [A] 0 /2k [A] Time (t) 1 st order Rate = k[A] 1 plot of ln conc. vs. time is linear k = + slope integrated rate law  ln[A] t = -kt + ln[A] 0 half life  t 1/2 =.693/k Ln[A] Time (t) 2 nd order Rate = k[A] 2 plot inverse of conc. vs. time is linear k = + slope integrated rate law  1/[A] t = kt + 1/[A] 0 half life  t 1/2 = 1/k[A] 0 1/[A] Time (t) [A] t = concentration at time (t)

Let’s clarify some things zero orderRate = k[A] o plot concentration [A] vs. time (t) k = +slope integrated rate law  [A] t = -kt + [A] 0 half life  t 1/2 = [A] 0 /2k [A] Time (t) 1 st order Rate = k[A] 1 plot of ln conc. vs. time is linear k = +slope integrated rate law  ln[A] t = -kt + ln[A] 0 half life  t 1/2 =.693/k Ln[A] Time (t) 2 nd order Rate = k[A] 2 plot inverse of conc. vs. time is linear k = +slope integrated rate law  1/[A] t = kt + 1/[A] 0 half life  t 1/2 = 1/k[A] 0 1/[A] Time (t) t 1/2 = time when concentration halves

Let’s try it: Time (s)[NO 2 ] (mol/L) x x x x x Enter 4 columns of data: 1 st column = time 2 nd column = concentration 3 rd column = ln (concentration) 4 th column = 1/concentration

Let’s try it: Do the linear regressions: Ø order test Time vs. Concentration  (1 st, 2 nd ) 1 st order  Time vs. ln(concentration)  (1 st, 3 rd ) 2 nd order  Time vs. (1/concentration)  (1 st, 4 th ) Each time: 1. Perform linear regression 2. Write down the slope 3. Write down the correlation coefficient

What you should get: Do the linear regressions: Ø order test Time vs. Concentration  (1 st, 2 nd ) slope= -1.7 x 10 5 corr coef. = st order  Time vs. ln(concentration)  (1 st, 3 rd ) slope= -5.8 x 10 5 corr coef. = nd order  Time vs. (1/concentration)  (1 st, 4 th ) slope= 2.1 x 10 4 corr coef. = M = slope r= correlation coefficient Winner= 2 ND ORDER!!!

Use formulas to solve for lots of stuff!!! 2 nd order Rate = k[NO 2 ] 2 k = +slope = 2.1 x /Ms k from linear regression Units = M (1-order) = M (1-2) s s = M (-1) = 1 s Ms

Use formulas to solve for lots of stuff!!! 2 nd order Rate = k[NO 2 ] 2 k = +slope = 2.1 x /Ms integrated rate law  1/[NO 2 ] t = kt + 1/[NO 2 ] 0 1/[NO 2 ] t = (2.1 x /Ms)·t + 1/(0.500 M) half life  t 1/2 = 1/k[NO 2 ] 0 t 1/2 = 1/((2.1 x /Ms)·(0.500M)

NOW YOU KNOW!!! How to determine the order from concentration and time data How to write the rate law, integrated rate law and half-life equation Can use this to solve for time at any given concentration or concentration at any given time!