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# The Rate of a Chemical Reaction

Introduction

The rate of a chemical reaction is the change in concentration over the change in time.

rate = change in concentration/change in time

rate refers to the speed at which a chemical reactions occurs. It can be measured in two ways.

The Rate of Disappearance= -∆[Reactants]/∆t  (Note this is negative because it measures the rate of disappearance of the reactants).

The Rate of Formation= ∆[Products]/∆t (This is the rate at which the products are formed).

They both are equivalent and can both be used to measure the reaction rate.

-∆[Reactants]/∆t = ∆[Products]/∆t

There are many factors that can either slow or speed up the rate of a chemical reaction such as temperature, pressure, concentration, and catalysts. The Rate of a Chemical Reaction is positive. It can be confusing since the Rate of Disappearance is negative, however when you think about it, a rate should never be negative since the rate is describing how fast the concentration changes with time. The Standard units for The Rate of a Chemical Reaction is Molarity per Seconds (M/s)

### How to determine Reaction Rates from Balanced Equations

Using the equation

aA+bB -> cC +dD

where the lower case letters (i.e. a) represent the coefficient of the balanced equation and the upper case letters (i.e. A) represent the molecule.

It is seen that the Rate of Disappearance are: -∆[A]/∆t*1/a=-∆[B]/∆t*1/b

and the Rate of Formation are: ∆[C]/∆t*1/c=∆[D]/∆t*1/d

Since Rate of Disappearance and Rate of Formation are equal to one another

-∆[A]/∆t*1/a=-∆[B]/∆t*1/b=∆[C]/∆t*1/c=∆[D]/∆t*1/d

### Measuring Reagents Versus Product

It does not matter whether an experimenter monitors the reagents or products because there is no effect on the overall reaction. However, since reagents decrease during reaction, and products increase, there is a sign difference between the two rates. Reagent concentration decreases as the reaction proceeds, giving a negative number for the change in concentration. The products, on the other hand, increase concentration with time, giving a positive number.  Since the convention is to express the rate of reaction as a positive number, to solve a problem, set the overall rate of the reaction equal to the negative of a reagent's disappearing rate.  The overall rate also depends on stoichiometric coefficients.

It is worth noting that the process of measuring the concentration can be greatly simplified by taking advantage of the different physical or chemical properties (i.e.: phase difference, reduction potential, etc.) of the reagents or products involved in the reaction by using the above methods. We have emphasized the importance of taking the sign of the reaction into account in order to get a positive reaction rate. Now, we will turn our attention to the importance of stoichiometric coefficients.

### Unique Average Rate of Reaction

A reaction rate can be reported quite differently depending on which product or reagent selected to be monitored.

Given a reaction:

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,

rate  of  reaction =

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This formula can also be written as:

rate  of  reaction =

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(rate of disappearance of A)

=

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(rate of disappearance of B)

=

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(rate of formation of C)

=

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(rate of formation of D)

Even though the concentrations of A, B, C and D may all change at different rates, there is only one average rate of reaction.  To get this unique rate, choose any one rate and divide it by the stoichiometric coefficient. When the reaction has the formula:

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The general case of the unique average rate of reaction has the form:

rate of reaction =

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 Example

For the reaction,

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, a)find the reaction rate and b) find the reaction rate given
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=0.002 M and
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= 77 sec.

Solutions:

a)rate  of  reaction =

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b)rate of disappearance of A =

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= -0.000026 M per sec

rate  of  reaction =

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(rate of disappearance of A)=
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(-0.000026 M per sec) = 0.000013 M per sec

### Average and Instantaneous Reaction Rate

Reaction rates have the general form of (change of concentration / change of time). There are two types of reaction rates. One is called the average rate of reaction, often denoted by (Δ[conc.] / Δt), while the other is referred to as the instantaneous rate of reaction, denoted as either:

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or
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The average rate of reaction, as the name suggests, is an average rate, obtained by taking the change in concentration over a time period, for example: -0.3 M / 15 minutes. This is an approximation of the reaction rate in the interval; it does not necessarily mean that the reaction has this specific rate throughout the time interval or even at any instant during that time. The instantaneous rate of reaction, on the other hand, depicts a more accurate value. The instantaneous rate of reaction is defined as the change in concentration of an infinitely small time interval, expressed as the limit or derivative expression above. Instantaneous rate can be obtained from the experimental data by first graphing the concentration of a system as function of time, and then finding the slope of the tangent line at a specific point which corresponds to a time of interest. Alternatively, experimenters can measure the change in concentration over a very small time period two or more times to get an average rate close to that of the instantaneous rate. The reaction rate for that time is determined from the slope of the tangent lines.

 Example

From the graph, the blue line is the graphical representation of [A] over t. The red and green lines are tangent lines to the graph. Find the reaction rate at a) t=195 sec and b) t=395 sec.

Solutions:

To find the slopes, divide the y-intercept by the x-intercept.

1. The red line has a slope of
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= -0.0125 M per sec which is an arbitrary estimate of the reaction rate at t=195 sec.
2. The green line has a slope of
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= -0.0051 M per sec which is an arbitrary estimate of the reaction rate at t=395 sec.

Topics that Relate to the Rate of a Chemical Reaction

### References

1. Petrucci et al. General Chemistry: Principles & Modern Applications, 9th Edition. New Jersey: Prentice-Hall Inc., 2007.
2. Connors, Kenneth. Chemical Kinetics: The Study of Reaction Rates in Solution. New York City: VCH Publishers, Inc., 1990.

### Problems

Q: Consider the reaction 2A + B

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C. The concentration of [A] is 0.54321M and the rate of reaction is 3.45*10-6 M/s. What Concentration will [A] be 3 minutes later?

A:

Q: Consider the reaction A + B

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C. The rate of reaction is 1.23*10-4. [A] will go from a 0.4321M to a 0.4444M concentration in what length of time?

A: Use

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=
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/ r

Q: Write the rate of the chemical reaction with respect to the variables for the given equation.

2A+3B--->C+2D

A: False, C8H18, better known as octane in automobile petroleum, will not combust at room temperature unless there is an ignition source.

Q: True or False: The Average Rate and Instantaneous Rate are equal to each other.

A:

Q: How is the rate of formation of a product related to the rates of the disappearance of reactants?

A:

### Contributors

• Albert Law, Victoria Blanchard, Donald Le

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Some of the ground display from the Miramar Airshow. Photo courtesy PDPhoto.org. Taken by Jon Sullivan, 2004.
133.3 kB19:51, 5 Dec 2008Albert LawActions
chem wiki instantaneous rat graph.jpg
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43.65 kB22:53, 24 May 2010veblanchActions
chem wiki rate graphs catalysist and temp.jpg
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Diamond slowly turns into graphite. The picture showing the diamond turning into a graphite isn't completely accurate as a diamond won't morph into the tip of a pencil per se. However, the photo is only meant to represent that the chemical structure of a diamond will eventually become that of graphite due to a chemical reaction. I made this myself from scratch using Adobe Photoshop CS2.
36.47 kB15:18, 5 Dec 2008Albert LawActions