Using the method of initial rates

The following data were obtained on the initial rate of binding of glucose to the enzyme hexokinase  

The enzyme concentrations are (a) 1.34 mmol dm (b) 3.00 mmol dm and (c) 10.0 mmol dm l Find the orders of reaction with respect to glucose and hexokinase and the rate constant. 

Strategy We assume that the initial rate law has the form I d = /Cj[glucose]g[hexokinase]o 

We need to make a plot of log Vo against log (glucoseJo for a given [hexokinaseJo and find the reaction order a from the slope and the value of from the intercept at log [glucose]o=0. Then, because 

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Since X + In X is a transcendental function, Eq. (2-67) cannot be solved for [A], Two methods are usually used. The method of initial rates is the more common one, since it converts the differential equation into an algebraic one. Values of v(, determined as a function of [A]o, are fit to the equation given for v. This application to enzyme-catalyzed reactions will be taken up in Chapter 4. The other method regularly used relies on numerical integration these techniques are given in Chapter 5. 

The following reaction was studied using the method of initial rates. 

Given the following experimental data, use the method of initial rates to determine the rate law for the reaction aA + t>B —> products. Hint Any number to the zero power equals one. For example,... 

Formulating Models Create a table of concentrations, starting with O.IOOM concentrations of all reactants, that you would propose in order to establish the rate law for the reaction aA + fcB + cD products using the method of initial rates. 

We can use the method of initial rates to deduce the rate law from experimentally measured rate data. Usually we know the concentrations of all reactants at the start of the reaction. We can then measure the initial rate of the reaction, corresponding to these initial concentrations. The following tabulated data refer to the hypothetical reaction... 

The rate law for any reaction must always be determined by experiment, often by the method of initial rates described previously. There is no way to simply look at a chemical equation and determine the rate law for the reaction. When the reaction has two or more reactants, the concentration of each reactant is usually varied independently of the others to determine the dependence of the rate on the concentration of that reactant. Example 13.2 shows how to use the method of initial rates to determine the order of a reaction with multiple reactants. 

Student Annotation This graphical determination is an alternative to using the method of initial rates to determine the value of k. 

The kinetics of the redox reaction between iron(m) and iodide ion have been reinvestigated over a very wide range of reactant conditions using the method of initial rates. Both stopped-flow and conventional spectrophotometry were used, the first-order dependence on the oxidant and second-order on iodide being confirmed. No evidence was found for any intermediate complex and the reaction scheme proposed may be described as... 

The oxidation of iodide by vanadium(v) has been studied in the absence of oxygen, kinetic data being derived using the method of initial rates. In the... 

Use the method of initial rates if the experimental data are given in the form of reaction rates at different initial concentrations. 

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