Concept of rate of chemical reaction

Concept of rate of chemical reaction

The concept of rate of chemical reaction is not a completely new one but it is those which is used or done every day but we are not thinking about it. E.g. the rate of flow of water through trap, the rate where automobile travels, the rate in which man can run in morning walk etc. Each rate is supposed to be the interval of chosen. A chemical reaction may be defined as change in concentration of reactant or products with per unit time.

Let’s consider a general reaction where reactant A gives product i.e.A $$\longrightarrow$$B. At time interval the rate of reaction in terms of reactant = A → B.

At time interval the rate of reaction in terms of reactant = $$-\frac{dA}{dt}$$

With increasing time, reactions proceeds increases and concentration of reactant decreases. Due to which negative sign comes on rate of reaction in terms of reactants.

Rate of reaction in terms of product= $$\frac{dB}{dt}$$

Here positive sign comes on the rate of reaction in terms of products which indicates the increase in concentration of product with time in which reaction proceeds.

At a given time, rate of reaction or reactant is equal to the rate of reactant in terms of products. Which can be shown mathematically.

Rate of reaction of reactant =rate of reaction of products

$$-\frac{dA}{dt}$$=$$\frac{dB}{dt}$$

Or,

Above equation is for general reaction in which our expectation fallows or in case of former reaction. In case of backward reaction we can express as opposite of forward reaction i.e.

$$\frac{dA}{dt}$$ = $$-\frac{dB}{dt}$$

Fig: plot showing the relation of concentration of reaction and product with time.

Square bracket around the substance like [A],[B],[$$NO_2$$] [$$NH_3$$] etc. are representation of concentration in mole per liter. In above example stoichiometric coefficient of reactant A and product B is same due to which it can be equal and crosses each other and not included in rate of reaction. The rate of decrease in concentration of reactant is exactly same as increase In concentration of product in any time.

When we consider another type of reaction,A + B→ 2C

In this case two mole of product is formed by the collision of one molecules of reactant A and one molecule of reactant B. It also shows that rate of decreasing concentration or disappearance of A and B are same and rate of formation of product C is exactly twice of each reactant.

Which can be express as:

2×rate of disappearance of A= 2×rate of disappearance of B= rate of appearance of C

In above reaction,

Rate of reaction in terms of A = $$-\frac{dA}{dt}$$

Rate of reaction in terms of B= $$-\frac{dB}{dt}$$

Rate of raction in terms of C=$$\frac{dC}{dt}$$

At a given time

$$-\frac{dA}{dt}$$ =$$-\frac{dB}{dt}$$ =$$\frac{dC}{dt}$$

For example of similar to above reaction may be

$$2N_2O_5(g)\longrightarrow4NO-2(g) + O_2$$

Average rate of reaction or rate of reaction at given time is:

$$-\frac{1}{2}$$× $$\frac{dN_2O_5}{dt}$$ = $$\frac{1}{4}$$× $$\frac{NO_2}{dt}$$ + $$\frac{dO_2}{dt}$$

The rate of reaction is dependent upon the concentration of reactant at that time exactly. Therefore if concentration of reactant decreases at a given time, rate of reaction is also decreases at particular time simultaneously. It seems that concept of average rate of reaction can’t be applied in rate of reaction. It also tell us that it is most better to express rate of reaction in particular moment of time as far as possible. Thus rate of reaction can be explained as rate of change in concentration of reactant or product at a given time. This type of reaction is termed as instantaneous rate. The time interval dt is made small value as far as possible so that rate of reaction becomes constant values during time interval.

For general type of reaction :- aA +bB→ cC +dD

Rate of reaction in term of A,

A = $$-\frac{1}{a}$$×$$\frac{dA}{dt}$$

Rate of reaction in term of B,

B = $$-\frac{1}{b}$$×$$\frac{dB}{dt}$$

Rate of reaction in term of C,

C = $$\frac{1}{c}$$× $$\frac{dC}{dt}$$

Rate of reaction in term of D,

D =$$\frac{1}{d}$$× $$\frac{dD}{dt}$$

Rate of reaction at given time,

$$\frac{dx}{dt}$$ =$$-\frac{1}{a}$$×$$\frac{dA}{dt}$$ =$$-\frac{1}{b}$$×$$\frac{dB}{dt}$$ =$$\frac{1}{c}$$× $$\frac{dC}{dt}$$ =$$\frac{1}{d}$$× $$\frac{dD}{dt}$$

At beginning in which reaction is not started (t=0) is termed as initial rate which helps to study the kinetic of reaction. After the reaction proceeds at time ‘t∞’, it is termed as rate at that particular time. is termed as reaction rate in infinite. These helps to calculate and finding out the kinetics of the reaction with reference whether reaction is first order, second order or pseudo order.

Unit of rate of reaction

Unit of rate of reaction is rate of unit change in concentration of any one reactant or product at a given time which is,

Unit of rate of reaction = unit of concentration ÷a given time

The concentration is usually in mole per litter i.e. mol⁄L and time can be expressed in second, minute, hours etc. By using it, thus unit of rate of reaction can be expressed as If concentration is expressed in then unit of rate of reaction can be expressed asmol⁄L⁄s,mol⁄L⁄minn,mol⁄L⁄hour

There are three types of rate of reaction i.e. initial rate, average rate and final rate.

Initial rate → the rate of reaction which is determined in initial time is called initial rate. Which is observed by using different kinetic parameter before the reaction begins.

Avarage rate→ the rate of reaction which is measured in large time interval is called average rate. Average rate is used to determine structure of intermediate in chemical reaction.

Instantaneous rate→ the rate which is measured at very small time interval is called instantaneous rate. In instantaneous rate time gap between them should be equal or same. The instantaneous rate is used to determine structure of transition state in very fast type of reaction.

Summary

Rate of reaction is generalize form which relates concentration of reactant or product with respect to time. Rate of reaction is better to express or measured in short time interval but explosive reaction can’t be measured by using kinetic parameter. Unit of rate of reaction is usually mol/L time and sometimes mol/dm3 time in which time may be second, minute or hour. Type of rate of reaction is classified as initial rate, average rate and instantaneous rate based upon at which time is measured. Concept of rate of chemical reaction can be expressed practically as well as theoretically. Positive and negative sign in rate of reaction comes due to the basis of decrease or increase of concentration either reactant or product.