Concentration and the Rate Law

1. aA + bB cC + dD Concentration and the Rate Law Consider the following hypothetical reaction We would like to know a relation that tells us how the rate of the reaction changes with change in concentration of each reactant. Such a relation is called the “rate equation” or the “rate law”, which is expressed as [A] and [B] are the molar concentration of reactants A and B, respectively m is the orders of the reaction with respect to the attractant A n is the orders of the reaction with respect to the attractant B The overall order of the reaction = m + n k is called the rate constant of the reaction. The constant k is independent of time. However k depends on the temperature and the catalyst (as will be discussed later)

2. The Method of Initial Rates The method of initial rates is a simple method for determining the “rate equation” or the “rate law” In this method we determine the way in which the initial rate depends on the initial concentration

3. Const. NH4+(aq) + NO2−(aq) N2(g) + 2 H2O(l) Const. The Method of Initial Rates Consider the following reaction To determine the rate law we need to know the exponents m and n

4. Consider a reaction for which rate = k[A][B]2. Each of the following boxes represents a reaction mixture in which A is shown as red spheres and B as purple ones. Rank these mixtures in order of increasing rate of reaction. Answer Box 1 contains 5 red spheres and 5 purple spheres, giving the following rate: Box 2 contains 7 red spheres and 3 purple spheres: The order 2 < 1 < 3 Box 3 contains 3 red spheres and 7 purple spheres: EXERCISE:Relating a Rate Law to the Effect of Concentration on Rate A Key Point: Because all three boxes have the same volume, we can put the number of spheres of each kind into the rate law and calculate the rate for each box.

5. Check Rate = k[A][B]2 Rate depends [B]2 A is shown as red spheres and B as purple ones Five of B Three of B Seven of B This analysis confirms that the order is 2 < 1 < 3

6. PRACTICE EXERCISE Consider the previous exercise and assume that the rate = k[A][B], rank the mixtures represented in this Sample Exercise in order of increasing rate. Answer: 2 = 3 < 1

7. = −kt ln [A]t [A]0 Integrated Rate Laws First-Order Reactions For example Integrating the above equation within a time period (time = 0 to time = t) provide the integrated rate law for a first-order process us Differential Rate Law Integrated Rate Equation [A]0 is the initial concentration of A. [A]t is the concentration of A at some time, t, during the course of the reaction. k is the rate constant, unit of k depends on the overall order of the reaction For a first-order reaction: Unit of k = unit of rate/ unit of concentration = M.s-1/M = s-1

8. Integrated Rate Laws Integrated First-Order Rate Equation Manipulating this equation produces… ln [A]t− ln [A]0 = − kt ln [A]t = − kt + ln [A]0 …which is in the form y = mx + b

9. Slope = k t ln [A]t = -kt + ln [A]0 y = mx + b Slope = -k t First-Order Processes y = mx Or