14.4 Change of rate with time

So Far…. We have looked at the rate of a reaction based on rate law equations showing how concentration changes can affect the rate. We have seen that reaction concentrations have various affects on rates depending on if they are 0, 1st or 2nd order reactions.

Now… We will look at how the concentration of a reaction changes over time. We will also look at how to determine the rate constant from data using the integrated rate law equations.

The rate laws so far have allowed us to calculate the rate of a reaction from the rate constant and reactant concentration. Rate laws can also be written to show the relationship between the concentrations of reactants or products and time.

Zero Order reaction rate is independent of the concentration of the chemicals. So, the rate law simplifies to rate = k

First order reactions First-Order reaction rates depend on the concentration of a single reactant raised to the first power. A + B  AB rate = k [A] or rate = k[B]

First Order ln[A]t - ln[A]0 = - k t The following is the integrated rate law and can be used to solve for variables k , t , or [A]0. So they can be used to determine: ln[A]t - ln[A]0 = - k t Concentration of reactant remaining at any time after started. Time interval required for a given fraction of a sample to react Rate constant of a reaction [A]t  concentration at particular time t. k  rate constant t time for the particular concentration [A]0 initial concentration of the chemical

The equation and be used with any concentration units. Including pressure as a concentration for gases

Example The decomposition of chemical A is a first order reaction. The [A] is monitored and the following data was recorded. (a) Calculate the rate constant. (b) Calculate the [A] at 5 min. Time (min) 0.00 1.00 2.00 4.00 [A] (Molarity) 0.100 0.0905 0.0819 0.0670

Second Order Second order reaction rates depend on the reactant concentration raised to the second power or on the concentrations of two reactants, each raised to the first power. A + B  AB rate = k [A]2 or rate = k[B]2 or rate = k [A][B]

Second Order 𝟏 [𝑨 ] 𝒕 − 𝟏 𝑨 𝟎 =𝒌𝒕 The following equation is the integrated rate law for 2nd order reactions 𝟏 [𝑨 ] 𝒕 − 𝟏 𝑨 𝟎 =𝒌𝒕

Example The synthesis reaction of butadiene is second order: 2 C4H6(g)  C8H12(g). The rate constant at some temperature is 0.100 M /min. The initial concentration of butadiene [C8H12 ] is 1.00 M. Calculate the concentration of butadiene when t is 1.0 and 5.0 min.

Half-Life Half life is the time required for the concentration of a reactant to reach half its original value. For a first order reaction the half life only depends on the rate constant. The following equation is used to find the half life of a first order reaction t1/2 = 0.693 𝑘

Example A certain first order reaction is 45.0% reacted in 65 s. Determine the rate constant and half-life for this process.