# What is the Rate of Reaction in Chemistry ## What is the Rate of Reaction?

The rate of reaction is the time rate of change of concentration of a species in a reaction mixture.

### The meaning of Rate of reaction

By rate of reaction, we mean the rate at which reactants disappear or the rate at which products form.

## The reaction between I2 and H2O2

Let’s determine the rate of reaction of the following example.

Hydrogen peroxide oxidizes iodide to iodine in acid solution in a reaction which can take many minutes to go to completion:

H2O2  +  2H+  +  2I  ->  I2  +  2H2…..(01)

A variety of ways is available for measuring the concentration of iodine as reaction proceeds. If a stopwatch started when known amounts of acidified hydrogen peroxide and iodide solution mixed, and, if at different times, after mixing, the iodine concentration in the reaction mixture is constructed. The experiment points to lie on a smooth curve. Initially, the iodine concentration is zero. But it increases as reaction proceeds. If we had continued our measurements for a long enough time, we would have found that eventually, the iodine concentration would equal the initial hydrogen peroxide concentration (i.e., all the H2O2 would have reacted to form an equimolar amount of I2). Figure 01 – Concentration of Iodine as a function of time after mixing acidified hydrogen peroxide and iodide solutions.

Because “concentration of iodine” is tedious to write, chemists have introduced an extra bit shorthand:

Square brackets around a chemical formula mean “concentration of.”

[I2] means the concentration of iodine; [H2O2] means the concentration of hydrogen peroxide.

So, let’s have a look at the rate of reaction of iodine and hydrogen peroxide.

## Rate of Reaction I2 & H2O2

In the present example, the rate of reaction means the rate of change of iodine concentration. Moles of iodine produced per liter per second, molL-1s-1. This states mathematically as differential:

Rate of reaction = d[I2] / dt   …(02)

If we want the average rate of reaction over a small interval of time, Δt, we can write,

Average rate of reaction = Δ[I2] / Δt …(03)

Where Δ[I2] is the change in iodine concentration over the interval of time, Δt.

### The calculation for the rate of reaction

To calculate the average rate of reaction over the first 100 seconds from figure 01, we note from the graph that at t = 0, [I2] = 0, and at t = 100s, [I2] = 0.0026 mol/L.

Δ[I2] = 0.0026mol/L and Δt = 100s. Hence,

Average rate of reaction = 0.0026 / 100

= 2.6 × 10-5 molL-1s-1

To calculate the average rate of reaction over the time interval, 300s to 400s, we read off the graph:

Δ[I2] = 0.0070 – 0.0059

= 0.0011 mol/L

Δt      = 400 – 300

= 100s

Average rate of reaction     = 0.0011/100

= 1.1 × 10-5 molL-1s-1

Over the time interval 600s to 700s:

Average rate of reaction     = (0.0088 – 0.0083) / (700 – 600)

= 5.0 × 10-6 molL-1s-1

The average rate of reaction decreased quite significantly as the reaction proceeded from 2.6 × 10-5 molL-1s-1 overtime interval 0 to 100s, to

1.1 × 10-5 molL-1s-1 over the interval 300s to 400s, to 0.5 × 10-5 molL-1s-1 over the interval 600s to 700s. this is by far the most usual situation.

Reaction rate decreases as reaction proceeds.

## Instantaneous reaction rate

Because of reaction rate changes as reaction proceeds, we often prefer not to use the average rate as defined by equation 03. But instead, use the instantaneous rate as defined by the differential in equation 02.

Mathematically, if y is a function of x, then the differential dy/dx at any point on the curve is the gradient at that point. Hence if [I2] is a function of time t, then d[I2]/dt is the slope of the tangent at the point in question. At point, A in figure 01 (t = 300s), the rate of reaction is the slope of the tangent BC, which is 1.8 × 10-3 / 150 = 1.2 × 10-5 molL-1s-1. It is slightly higher than the average rate over the interval 300s to 400s, as we would expect (since the rate is decreasing as time increases).

### Initial rate of the reaction over Iodine

What often proves particularly useful is the initial rate of reaction: this is the slope of the tangent drawn at the point t = 0. Its value from figure 01 is 3.0 × 10-5 molL-1s-1. Because it is difficult to draw a tangent to a curve, particularly at the end of the curve, we often prefer to use average slope over the first 10% or 20% of reaction as a reasonable approximation to the initial rate. In effect, we are saying,

d[I2]/dt ÷ Δ[I2]/Δt

providing Δt is small. In the present example, the average rate over the first 100s (26% of reaction) is 2.6 × 10-5 molL-1s-1, which is a reasonable approximation t the true initial rate, 3.0 × 10-5 molL-1s-1.

### Initial rate of the reaction over Hydrogen peroxide

So far, the rate of this reaction has defined as the rate of appearance of iodine. However, there is no reason for preferring iodine over the other species involved in the reaction. And so, the rate can define equally well in terms of hydrogen peroxide or iodide. We can say,

Rate of reaction = Rate of decrease in hydrogen peroxide concentration

= -d[H2O2] / dt

The minus sign introduced to keep the reaction rate positive. Hydrogen peroxide concentration is decreasing, and so the differential, d[H2O2]/dt, is negative.

Because by equation 01 one mole of hydrogen peroxide consumed for every mole of iodine produced, it follows that,

-d[H2O2] / dt = -d[I2] / dt

Equation 01 tells us that at any time t,

[H2O2]t = [H2O2]0 – [I2]t   …(04)

#### Explanation

Where subscripts t and o denote values at time t and time zero, respectively. Equation 04 can use with the values of iodine concentration already measured to calculate hydrogen peroxide concentrations at various times of reaction to construct figure 02. In this diagram, the differential at any point A, for example, is negative, but the rate of reaction as defined above is positive and is equal to the rate obtained from point A in figure 01. Figure 02 – Hydrogen peroxide concentration as a function of time

Besides, the rate of reaction can define as the rate of decrease in iodide concentration, -d[I]/dt. However, since two iodide ions consumed for every hydrogen peroxide molecule which reacts, the rate of disappearance of iodide is twice the rate of disappearance of hydrogen peroxide:

d[I] / dt = -2d[H2O2] / dt

## Factors influencing the Rate of Reaction

To see what factors influence the rate of reaction, let us consider some further experiments with reaction 01. A series of experiments performed in which the initial concentrations of the reactants changed one at a time, and in each experiment, [I2] measured as a function of time of reaction. [H2O2] was calculated and plotted as a function of time, as shown in figure 03. The initial concentrations are in Table 01. The initial rate measured for each experiment, as explained above, and values are given in Table 01 also. Figure 03 – Kinetic curves for the hydrogen peroxide-iodide reaction with varying initial conditions.

### Factor 01

Comparison of curves 1 and 2 and their initial rate in Table 01 shows that increasing the initial concentration of hydrogen peroxide increases the initial rate. Similarly, increasing the concentration of iodide (curves 2 and 3) and increasing the concentration of hydrogen ions (curves 3 and 4) each increases the initial rate of reaction. These and many similar experiments on a wide range of other reactions allow us to conclude that generally (though not always), the rate of a reaction increases as the concentration of reactants increases. Table 01 – Initial conditions and initial rates for the experiments

### Factor 02

So, this then explains the shape of the kinetic curves we have considered so far. As a reaction proceeds, the concentrations of the reactants decrease, and so the rate of reaction continuously decreases, as shown by the experiment curves in Figures 01 and 03.

### Factor 03

Further factors that affect the rate of reaction can identify by examining the curves in figure 03(b) and the initial conditions and rates given in table 01. Comparison of experiments 5 and 6 show that increasing the temperature increases the rate of reaction. This is a very general result.

For most reactions, the rate increases as the temperature increases.

### Factor 04

Comparison of experiments 6 and 7 shows that the presence of sodium molybdate increases the rate of the reaction, although this substance does not appear in the stoichiometric equation 01.

If you like to know how to calculate the stoichiometry of a chemical reaction, have a look at an informative article about “The stoichiometric calculator.”

Substances that increase the rate of a reaction without undergoing a permanent chemical change in the reaction are called Catalysts. The molybdate is a catalyst for the hydrogen peroxide-iodide reaction.

## Factors that affect the rate of Homogeneous reaction

The reaction which we have just considered involves species which are in solution, and the reaction occurs uniformly throughout the whole solution. Such a reaction is called a homogeneous reaction. To summarise then, the factors which influence the rate of homogeneous reactions are:

1. Concentration of reactants in a solution (or pressure of reactants in the gas phase).
2. Nature and concentration of any catalyst present.
3. Temperature.

## Heterogeneous reaction

There are many reactions, some extremely important industrially, which occur at the interface between two phases. Such reactions are called heterogeneous reactions. Some common examples are:

1. The reaction of zinc metal with hydrochloric acid (to form hydrogen gas and zinc chloride solution).
2. Decomposition of hydrogen peroxide in solution (to form oxygen and water) occurring on the surface of various solids such as manganese dioxide.
3. Hrdrogeneration of liquid alkenes and vegetable oils (to form alkanes and solid fats respectively) on the surface of finely divided nickel metal.
4. Haber process for the industrial synthesis of ammonia from gaseous hydrogen and nitrogen on the surface of metallic catalysts.

## Factors that affect the rate of Heterogeneous reaction

The rate of heterogeneous reactions, as well as depending upon the three factors listed above, also depend upon

1. The state of division of the solid phase.
2. The rate of stirring is used.

For example, 1g of finely crushed limestone, CaCO3, added to 1L hydrochloric acid and causes carbon dioxide to produce at a much greater rate than does one solid lump of the same mass. Also, the reaction will be faster if the mixture continuously stirred to keep the crushed limestone dispersed throughout the solution instead of letting it settle to the bottom of the flask. Both these effects are since the reaction is occurring on the surface of the solid. The more finely divided the solid has the greater surface area and, therefore, the more CaCO3 units which are in contact with the acid solution. If the solid allowed to settle to the bottom of the flask, much of its surface will not b in contact with the solution. Agitation keeps the maximum area of the solid in contact with the solution and, in this way, increases the rate of reaction.

### For extra knowledge,

For some reactions, the rate of reaction depends upon the intensity (brightness) of visible or ultra-violet light shining upon the reactants. Mixtures of methane and chlorine react very slowly in the dark, but when irradiated with ultra-violet light, the reaction proceeds rapidly.

CH4 + Cl2 -> CH3Cl + HCl

Ozone, O3, is decomposed by ultraviolet light.

2O3 -> 3O2

This reaction occurs in the stratosphere and filters out the harmful ultraviolet radiation from sunlight. The reaction between hydrogen and chlorine,

H2 + Cl2 -> 2HCl

Will proceed in the dark but occurs far more rapidly with a higher rate of reaction with ultraviolet light.

### Conclusion

As we discussed above, the rate of reaction is an important factor in Chemistry. It is very useful, especially when determining the order of a reaction. Rare of reactions depends on many factors, as we discussed above.

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