Third-order overall rate

The first piece of evidence that must be accounted for is the rate law. For the reaction of benzalde-hyde with hydroxide, the reaction is first-order with respect to hydroxide ions and second-order with respect to benzaldehyde (third-order overall), rate = k3[PhCHO]2[H0 ]... 

First order with respect to A, second order with respect to B, zero order with respect to C, and third order overall. Rate = [N02"] NH4+]. The value of the rate constant is... 

The reaction between benzoyl chloride and phenol, catalyzed by amines, follows a third-order overall rate, being first order on each of the reactants. 

Furthermore kinetic studies reveal that electrophilic addition of hydrogen halides to alkynes follows a rate law that is third order overall and second order in hydrogen halide... 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

Nc = 0.0 gmol, Nq = 0.0 gmol, respectively. A mixture of A and B is charged into a 1-liter reactor. Determine the holding time required to achieve 90% fractional conversion of A (X = 0.9). The rate constant is k = 1.0 X 10 [(liter) /(gmoP min)] and the reaction is first order in A, second order in B and third order overall. 

Brown and Grayson reported that the rate of alkylation reactions with benzyl chloride was third order overall first order in aromatic component, first order in AICI3, and first order in benzyl chloride. This indicates that a rate determining nucleophilic attack by the aromatic component on a polar alkyl chloride-aluminum... 

The reaction is first order in H2, second order in NO and, therefore, third order overall. Inserting values into Equation (8.23), we say, rate = [NO]2[H2],... 

The reaction is first-order with respect to X, second-order with respect to Y and third-order overall k is the rate constant. Note that the order of a reaction does not necessarily have to have integral values. 

The constant k in the rate equation is known as the rate constant and the units of the rate constant vary depending on the overall order of the reaction. Suppose that a reaction is third order overall. Its rate equation could take the form rate = k[A] [B] ... 

In accord with this rate law, which is second order in NO, first order in 02, and third order overall, the initial rate increases by a factor of 8 when the concentrations of both NO and 02 are doubled (experiments 1 and 4). 

Suppose in a reaction whose rate depends only on [A] and [B] that a= 1 and b = 2 the overall order then is 3. We say that the reaction rate is first-order in A, second-order in B, and third-order overall. 

This rate law was determined experimentally. The data tell that the rate depends on the concentrahon 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 because the sum of the orders for the individual reactants (the sum of the exponents) is (2 + 1), or 3. 

This reaction is first-order w t respect to A and C, second-order in B, and third-order overall. Benson (1960), Gardiner (1972), and Lasaga (1981 a) discuss the rate expressions for third- and higher-order reactions. Such reactions are uncommon in natural systems and will not be considered here. 

Plan We inspect the exponents in the rate law, not the coefficients of the balanced equation, to find the individual orders, and then take their sum to find the overall reaction order. Solution (a) The exponent of [NO] is 2, so the reaction is second order with respect to NO, first order with respect to O2, and third order overall. 

Thus, the reaction rate is first-order in sucrose, first-order in the catalyst, and first-order in H2O. The reaction is said to be third-order overall, third because of the sum of the powers on the three concentration factors. 

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