Instantaneous rate of a reaction

From now on, whenever we speak of a reaction rate, we shall always mean an instantaneous rate. The definitions in Eqs.l and 2 can easily be adapted to refer to the instantaneous rate of a reaction. 

To set up expressions for the instantaneous rate of a reaction, we consider At to be very small so that t and t + At are close together we determine the concentration of a reactant or product at those times and find the average rate from Eq. 1. Then we decrease the interval and repeat the calculation. We can imagine continuing the process until the interval At has become infinitely small (denoted d/) and the change in molar concentration of a reactant R has become infinitesimal (denoted d R]). Then we define the instantaneous rate as... 

The instantaneous rate of a reaction is the rate of the reaction at a particular time. To find the instantaneous rate of a reaction using a concentration-time graph, draw a tangent line to the curve and find the slope of the tangent. A tangent line is like a secant line, but it touches the curve at only one point. It does not intersect the curve. 

In this section, you learned how to express reaction rates and how to analyze reaction rate graphs. You also learned how to determine the average rate and instantaneous rate of a reaction, given appropriate data. Then you examined different techniques for monitoring the rate of a reaction. Finally, you carried out an investigation to review some of the factors that affect reaction rate. In the next section, you will learn how to use a rate law equation to show the quantitative relationships between reaction rate and concentration. 

Distinguish between an average rate and an instantaneous rate of a reaction. 

The differential coefficients d[R]/df and d P]/df are the mathematical expressions for the slope of the tangent drawn to a curve at the time of interest. Similarly, the unique instantaneous rate of a reaction is defined as in Eq. 2, but with differential coefficients ... 

When the stoichiometric coefficients, va, vy, etc., are included in the rate law, as in Equation 3.5, the reaction has a unique rate constant (k) under specified conditions regardless of whether the rate is measured by monitoring the changing concentration of A, B or C. It also follows from Equation 3.5 that (except for zero-order reactions) the instantaneous rate of a reaction changes as the reaction proceeds, as will be illustrated later in Fig. 3.1. Thus, k is the parameter which measures whether the reaction (imprecisely expressed) is fast or slow . In any case, it follows that any property of a reacting system which relates (preferably directly) to the concentration of any component in the chemical reaction maybe monitored to measure the rate and, hence, to investigate the rate law and quantify the rate constant. 

Instantaneous Rate of a Reaction It is the rate of a reaction when the average rate is taken over a very small interval of time. 

Reaction rate — The (instantaneous) rate of a reaction can be expressed by the derivative of any quantity X, which changes during a chemical reaction, with respect to time [i]. 

The instantaneous rate of a reaction is obtained by considering smaller and smaller time increments At (with correspondingly smaller values of A[NO]). As At approaches 0, the rate becomes the slope of the line tangent to the curve at time t (see Fig. 18.3). This slope is written as the derivative of [NO] with respect to time ... 

Throughout the rest of this book, we refer to the instantaneous rate simply as the rate. The instantaneous rate of a reaction at the moment that it begins (at t = 0) is the initial rate of that reaction. 

The theory of the method is as follows. The instantaneous rate of a reaction of the nth order involving only one reacting substance is proportional to the nth power of its concentration,... 

Table 12.2 illustrates how the average rate of a reaction decreases with time. Why does the average rate decrease with time How does the instantaneous rate of a reaction depend on time Why are initial rates used by convention ... 

The instantaneous rate of a reaction is the slope of the tangent to the graph of concentration against time (expressed as a positive quantity). 

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