Fundamentals Of Chemical Kinetics

Chemical Kinetics Feasibility of a reaction under given conditions can be predicted on the basis of Gibbs energy. Based on this fact, the extent to which reaction proceeds can be explained with the help of equilibrium constant. The speed with which chemical reaction proceeds can only be explained by branch of chemistry called chemical kinetics. Kinetics means movement. The study of kinetics not only explains the speed of the reaction but also describes the condition, which affects the rate of reaction. Mechanism of reaction: The study of rates of reactions helps us to understand the pathways from reactants to products, which is called mechanism of reaction. Rate of a chemical reaction: In our daily life we experience various chemical reactions with varying rates. Some reactions are rapid and some are slow. The reactions involving ionic species are fast e.g. neutralization of acid by base and mixing of silver nitrate and sodium chloride to form silver chloride (ppt.). In these reactions, only ions are involved and no bonds are broken. Therefore these are fast. There are some reactions, which are extremely slow e.g. rusting of iron. However there are some reactions, which occur, in a measurable time and their rates can be measured easily in the lab e.g. 1) Hydrolysis of an ester in the presence of sodium hydroxide

2) Decomposition of hydrogen peroxide

3) Inversion of cane sugar to give glucose and fructose

4) Decomposition of nitrogen (V) oxide

The rate of chemical reaction is a measure of the speed with which the reactants are converted into products. It may also be defined as the change in any one of the reactants or products per unit time. Consider an equation, R → P where one mole of reactant R produces one mole of product P. Then the rate of reaction may be expressed in either of the following two ways:

1. The rate of disappearance or decrease in concentration of R (reactant) Rate of reaction = decrease in concentration of R / time taken

2. The rate of increase in concentration of P (product) Rate of reaction = increase in concentration of P / time taken If [R] 1 and [P] 1 are the concentrations of R and P respectively at time t1 and [R] 2 and [P] 2 at t2 then,

Where square brackets express the molar concentration and ∆[R] and ∆[P] are the change on concentration of R and P during the time interval ∆t. Then the rate of reaction may be expressed as:

It may be noted that in case of concentration of reactants minus (-) sign is used which shows the decrease in concentration of reactant with time. The above rate is also called the average rate of reaction. It has the dimensions of concentration / time.

In the above example stoichiometric coefficients of the reactants and products are same. Therefore the rate at which the concentration of R decreases will be the same as the concentration of P increases. Taking the example of PCl5

Reactions involving different stoichiometric coefficients Consider the reaction A + B → 2C In this case one mole of A combines with one mole of B and forms 2 moles of C. It means that the rate of disappearance of A and B are the same but rate of appearance of C must be twice the rate of disappearance of A and B. Thus,

To get unique value of the reaction rate, we divide the rate of reaction defined with any of the reactants or products by the stoichiometric coefficients of that reactant or product involved in that reaction.

For example, for the decomposition of gaseous nitrogen pentaoxide (N2O5) as: 1)

Similarly, for the reaction:

For a gaseous reaction at constant temperature, concentration is directly proportional to the partial pressure of a species and hence rate can also be expressed as the rate of change in partial pressure of reactants or products.

Average rate and instantaneous rate The rate expression given so far gives the average rate of reaction over the time interval (∆t), which can be expressed as Rate = change in concentration / time interval = ∆x /∆t This concept is similar to the mechanical speed. But in case of reactions, the rate depends on the concentration of the reactants. As the reaction proceeds, the concentration of the reactant decreases. Thus the rate of reaction may not be constant in the time interval in which we measure. Thus, rate of a reaction cannot be determined by simply dividing the total change in concentration by time taken as in case of mechanical speed. On the other hand, the rate of a reaction may be expressed at a particular moment of time. Thus rate of a reaction may be defined as

the rate of change of concentration of any one of the reactants or products at a given time. Such type of reactions are called instantaneous rate. For this purpose, the time interval (t) is made as small as possible so that rate of reaction remains almost constant during that time interval. Mathematically, instantaneous rates may be expressed as –d[R]/dt or d [P]/dt instead of - ∆[R] / ∆t or - ∆[P] / ∆t .Here d[R] or d[P] represents very small changes in the concentration of Ror Pin very small interval of time,dt. Thus, average rate approaches the instantaneous rate as ∆t becomes smaller and smaller i.e.,

In general, if dx represents very small change in concentration of any species during the very small change of time, dt, the rate of the reaction may be expressed as Rate = dx/dt For general reaction,

Instantaneous rate of some reactions;

1)

2)

3)

Experimental measurement of reaction rate The rate of any reaction is measured by plotting a graph between the concentrations of any of the reactants or products as a function of time. To explain this, let us consider a reaction i.e. decomposition of

dinitrogen pentaoxide. It decomposes in the presence of carbon tetrachloride. This reaction can be easily studied by measuring the concentration of N2O5 at various time intervals. To measure concentration at different time intervals we must know the increase in the pressure of the reaction mixture at different time intervals.

From the measured values of the pressure, the partial pressure of N2O5 is calculated and then the molar concentration of N2O5 can be calculated. The values of molar concentration of N2O5 at 318K art different time are given below.

Then graph is plotted between the concentration of N2O5 and time and rate of reaction is measured by measuring the change in the concentration with time.

Measurement of average rate of reaction

Calculation of average rate of a reaction The average rate of reaction is measured by noting the concentration of reactants at two different time intervals t1 & t2.Then average rate is:

From the above equation, it is clear that concentration of reactant decreases that is represented by negative sign.

Calculation of instantaneous rate of reaction As we know that rate of a reaction is changing constantly so, it is more appropriate to measure the instantaneous rate. It gives the rate at a specific instant of time. It is determined by drawing a tangent to the curve at a point corresponding to the given time. Then the slope of the tangent will give the instantaneous rate of a reaction. The slope can be determined by extending the tangent to intersect both the axes.

Measurement of instantaneous rate of a reaction In the above graph distance OA along the ordinates gives the change in concentration. (dx) while the distance along the abscissa OB gives the corresponding change in time (dt). The ratio OA/OB ordx/dt gives the slope of the tangent Thus, Instantaneous rate of reaction = OA/OB =dx/dt