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section 3: Reaction Rate Laws Writing Reaction Rate Laws A rate law: is the relationship between the rate of a chemical reaction and the concentration of reactants. For example, the reaction A → B is a one-step reaction. The rate law for this reaction is expressed as follows. rate = k[A] A rate law must be determined experimentally. The rate law shows that the reaction rate is directly proportional to the molar concentration of A. The specific rate constant(K): a numerical value that relates the reaction rate and the concentrations of reactants at a given temperature. Properties the specific rate constant: The specific rate constant is unique for every reaction and can have a variety of units including L/(mol.s), L2 /(mol² .s), and s-¹. The specific rate constant, k, does not change with concentration. However, k does change with temperature. A large value of k means that A reacts rapidly to form B. First-order reaction rate laws In the expression Rate = k[A], it is understood that the notation [A] means the same as [A]¹. For reactant A, the understood exponent 1 is called the reaction order. The reaction order: for a reactant defines how the rate is affected by the concentration of that reactant.
Finally, because the rate constant, k, describes the reaction rate, it must also be determined experimentally. The graph shows how the initial reaction rate for the decomposition of H2O2 changes with the concentration of H2O2. If the reaction order for a reactant is first order, how will the rate of the reaction change if the concentration of the reactant is tripled?.
Other-order reaction rate laws The overall reaction order of a chemical reaction: is the sum of the orders for the individual reactants in the rate law. Many chemical reactions, particularly those that have more than one reactant, are not first-order. Consider the general form for a chemical reaction with two reactants. In this chemical equation, a and b are coefficients. aA + bB → products The General Rate Law rate = k[A] [B]" The rate of a reaction: is equal to the product of k and the concentrations of the reactants each raised to a power (order) that is determined experimentally. Only if the reaction between A and B occurs in a single step (and with a single activated complex) does m = a and n = b. That is unlikely, however, because single-step reactions are not common. For example, consider the reaction between nitrogen monoxide (NO) and hydrogen (H2), which is described by the following equation. 2NO(g) + 2H2 (g) → N2 (g) + 2H2O(g) This reaction occurs in more than one step, and has the following rate law. rate = k[NO]² [H2] The rate law was determined from experimental data that indicate that the rate depends on the concentration of the reactants as follows: If [NO] doubles, the rate quadruples; If [H2] doubles, the rate doubles. The reaction is described as second order in NO, first order in H2, and third order overall.
The overall order is the sum of the orders for the individual reactants (the sum of the exponents), which is (2 + 1), or 3. Determining Reaction Order The method of initial rates: is one common experimental method of evaluating reaction order The method of initial rates determines reaction order by comparing the initial rates of a reaction carried out with varying reactant concentrations. The initial rate measures how fast the reaction proceeds at the moment at which the reactants are mixed and the concentrations of the reactants are known. To understand how this method works, consider the general reaction aA + bB → products. Suppose that the reaction is carried out three times with varying concentrations of A and B and yields the initial reaction rates shown in Table. Recall that the general rate law for this type of reaction is as follows. rate = k[A] [B]" To determine m, the exponent of [A], compare the concentrations and reaction rates in Trials 1 and 2. As you can see from the data, while the concentration of B remains constant, the concentration of A in Trial 2 is twice that of Trial 1. Note that the initial rate in Trial 2 is twice that of Trial 1. Because doubling [A] doubles the rate, the reaction must be first order in A. That is, because 2m = 2, m must equal 1. The same method is used to determine n, the exponent of [B], except this time Trials 2 and 3 are compared. Doubling the concentration of B causes the rate to increase by four times. Because 2n = 4, n must equal 2.
