First-Order/Pseudo-First-Order Reaction Gary L. Bertrand Professor Emeritus of Chemistry Missouri University of Science and Technology (formerly University of Missouri-Rolla) background                                    close A First-Order Reaction is described mathematically as: [A]t = [A]t=0e-νAkt ln ([A]t) = ln ([A]t=0) - νAkt For a Pseudo-First-Order Reaction, the reaction rate constant k is replaced by the apparent reaction rate constant k'. If the reaction is not written out specifically to show a value of νA, the value is assumed to be 1 and is not shown in these equations. The simplest way to confirm that these are the proper equations to describe the reaction and to get an approximate value for k or k', is with the method of half-lives. The half-life t1/2 is defined as the time required for the initial concentration to be halved: [A]t1/2 = [A]t=0/2 . At this point in time, ln(2) = kt1/2 = 0.693 . The time required for the concentration to be reduced to 1/4 of the initial concentration (t3/4) is ln(4) = kt3/4 = 2(0.693) . In a First-Order Reaction, the concentration of the reactant remaining after x half-lives is: [A]x/[A]t=0 = (1/2)x . This relationship is unique to First-Order and Pseudo-First-Order Reactions. This may be confirmed either by following concentration in time for a single series of measurements over three or more half-lives, or by comparing the half-lives of different series of measurements in which the initial concentration is varied by a factor of 4 or more. The reaction rate constant may then be calculated from the "best" value of the half-life: k = 0.693/t1/2 NOTE:The "First-Order Kinetics" exercise is designed so that you can get an accurate value of the half-life. Scan the concentration column for a value slightly larger than half of the initial concentration. Adjust the value of "Start Time" and the value of "Interval" to get a better estimate of the half-life. The same procedure may be used to find the time for the second and third half-lives. The best values of the reaction rate constant (k) can be obtained with data taken in the middle third of the reaction (from [A]t = (2/3)[A]t=0 to [A]t = (1/3)[A]t=0). Linear Least Squares regression with Y = ln([A]t) and X = t gives - k or - k' as the slope.