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# Rate of Reaction

For the reaction to be useful, either in the laboratory or in nature, it must occur at a reasonable rate. Chemical kinetics deals with the study of reaction rate. Every chemical reaction occurs at a definite rate under a given set of conditions. Some reactions are very fast and some other reactions are comparatively slow.

For example, the reaction between aqueous silver nitrate solution and sodium chloride solution is almost instantaneous.
Therefore, the reaction occurs between ions in the solution,

Ag+ + NO3- + Na+ + Cl- AgCl + Na+ + NO3-

Hence ionic reactions are very fast. However molecular reactions are slow.

CH3COOH + C2H5OH CH3COOC2H5 + H2O

When reactions proceed slowly, one can compare the velocities of such reactions under identical conditions. The rate of reactions is measured in terms of change in concentrations of reactants or products.

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## Reaction Rate Definition

To define the rate of a reaction, let us take a look at the following reaction

H2 + I2 $\rightarrow$ 2HI

When hydrogen and Iodine are placed in the flask, those molecules with sufficient kinetic energy will collide and undergo a chemical reaction, with the formation of HI.

As time passes, the concentration of substrates H2 and I2 in the flask will decrease, and the concentration of HI increases. Thus, reaction rate can be defined as,
"The change in the concentration of a reactant or product per unit time"The rate of the above reaction can be expressed using rate expression:

Rate = $\Delta$ [H2] / $\Delta$ t.

Since the concentration of H2 in the flask is decreasing, the above expression for rate will have a negative sign. Since reaction rate cannot be expressed as a negative number, we provide the expression itself with a negative sign.

Also, rate of disappearance of products should be equal to the rate of appearance of products. So, the rate of a reaction equation is expressed as:

Rate = - $\Delta$ [H2] / $\Delta$t = - $\Delta$ [I2] / $\Delta$ t = 1/2 $\Delta$ [HI] / $\Delta$ t

So, rate is expressed as change in concentration /time taken for the change.

## Reaction Rate Units

Reaction rate has the units of concentration divided by time. We express concentration n in moles per liter (mol / liter or mol / L or mol L-1 ) but time may be given in any convenient unit seconds (s) , minutes (min), hours (h), days (d), or possible years.

Therefore, the units of reaction rates may be Mole/liter sec or mol. L-1 S-1   or   Mole /Liter. Min (or) Mole/liter. Hour

## Reaction Rate Constant

At a fixed temperature, the rate of a given reaction depends on the concentrations of reactants. The exact relation between concentration and rate is determined by measuring the reaction rate with different initial reactant concentrations. By a study of numerous reactions, it is shown that
"The rate of a reaction is directly proportional to the reactant concentrations, each concentration being raised to some power."
Thus, for a substance A undergoing reaction,

Rate $\propto$ [A]n

In this rate law equation, the ‘k’ is called as the rate constant for a particular reaction. The unit of a rate constant for a particular reaction depends upon the reactants and products. Sometimes, the concentration terms cancel out and the unit of rate constant would be nil.

## Order of a Reaction

The order of a reaction is defined as the sum of the powers of concentration terms in the rate law.
For example, in the reaction
mA + nB Products

Rate = k [A]m [B]n

The order of such reaction is (m+n). The order of a reaction can also be defined with respect to a single reactant. Thus the reactant order with respect to A is m and with respect to B, it is n. The overall order of the reaction (m + n) may range from 1 to 3 and can be fractional.

## First Order Rate Reaction

Let us consider the reaction:

A Products

Suppose that at the beginning of the reaction ( t = 0), the concentration of A is a moles / liter. If after time‘t’, x moles of A have changed, the concentration of A would be (a-x). We know that for a first order reaction, the rate of reaction, dx/dt , is directly proportional to the concentration of the reactant.

Thus, the first order rate reaction is given by,

K = 2.303/t log a / a-x

The value of k can be found by substituting the values of (a) and (a-x) determined experimentally at time intervals t during the course of the reaction.

### Unit of first order rate reaction

The rate constant of a first order reaction is given by,

K = 2.303 / t log [A]0/[A]t

Time may be in seconds, hours or minutes or year, thus, the unit would be mol/L time.

## Factors that Affect Rate of Reaction

### Concentration or pressure of the reactants

As the concentration (or pressure) of the reactants increases, the rate of the reaction increases. This is because, in a gaseous reaction, with the increase in pressure, the reactant molecules come closer to each other and so, the reaction proceeds faster than at a lower pressure. In a reaction with liquid reactants, with the increase in concentration, two reactants come closer to each other and react faster.

### Temperature

With the increase in temperature the rate of the reaction also increases. So, an increase of 10K in temperature increases the reaction rate by two or three fold. With the increase in temperature, the collision of the molecules increase, thereby increasing the rate of the reaction.

### Presence of catalyst

Presence of a suitable catalyst alters the speed of the reaction considerably. A positive catalyst increases the rate of the reaction and a negative catalyst decreases the rate of the reaction. Catalysts lower the activation energy of a reaction, and thus increase the rate of a reaction.

### General nature of the reacting substances

Generally, inorganic reactions are fast and the reactions occur instantaneously. But organic reactions are comparatively slow. Inorganic reactions involve reaction between the oppositely charged ions which readily attract each other to form products.

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