Chemistry Rate of a Reaction and It's Unit

### Topics Covered :

● Introduction
● Average Rate of a Reaction
● Instantaneous Rate of a Reaction
● Units of Rate of a Reaction

### Introduction :

=> Chemistry, by its very nature, is concerned with change.

=> Substances with well defined properties are converted by chemical reactions into other substances with different properties.

=> For any chemical reaction, chemists try to find out :

(a) the feasibility of a chemical reaction which can be predicted by thermodynamics ( as you know that a reaction with ΔG < 0, at constant temperature and pressure is feasible);

(b) extent to which a reaction will proceed can be determined from chemical equilibrium;

(c) speed of a reaction i.e. time taken by a reaction to reach equilibrium.

=> Along with feasibility and extent, it is equally important to know the rate and the factors controlling the rate of a chemical reaction for its complete understanding.

=> Example :

(i) Which parameters determine as to how rapidly food gets spoiled?

(ii) How to design a rapidly setting material for dental filling?

(iii) What controls the rate at which fuel burns in an auto engine?

All these questions can be answered by the study of reaction rates and their mechanisms, called chemical kinetics.

=> The word kinetics is derived from the Greek word ‘kinesis’ meaning movement.

=> Thermodynamics tells only about the feasibility of a reaction whereas chemical kinetics tells about the rate of a reaction.

=> Example : Thermodynamic data indicate that diamond shall convert to graphite but in reality the conversion rate is so slow that the change is not perceptible at all.

● Therefore, most people think that diamond is forever.

=> Kinetic studies not only help us to determine the speed or rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.

=> The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.

=> At the macroscopic level, we are interested in amounts reacted or formed and the rates of their consumption or formation.

=> At the molecular level, the reaction mechanisms involving orientation and energy of molecules undergoing collisions, are discussed.

color{purple}(✓✓)color{purple} " DEFINITION ALERT"
The branch of chemistry which deals with the study of the speeds or the rates of chemical reactions, the factors affecting the rates of the reactions and the mechanism by which the reactions proceed is known as chemical kinetics.

### Rate of a Chemical Reaction :

=> Some reactions such as ionic reactions occur very fast, for example, precipitation of silver chloride occurs instantaneously by mixing of aqueous solutions of silver nitrate and sodium chloride.

=> While some reactions are very slow, for example, rusting of iron in the presence of air and moisture.

=> Also there are reactions like inversion of cane sugar and hydrolysis of starch, which proceed with a moderate speed.

color{green} ✍️ color{green} mathbf("KEY CONCEPT")
Reaction involves the breaking and making of bonds. As different bonds require different amounts of energy for breaking and different amounts of energies are evolved when different kinds of new bonds are forrmed, the rates of different reactions are different.
The instantaneous nature of the ionic reactions is due to the fact that these do not involve any breaking of bonds.

=> You must be knowing that speed of an automobile is expressed in terms of change in the position or distance covered by it in a certain period of time.

=> The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.

=> To be more specific, it can be expressed in terms of :

(i) the rate of decrease in concentration of any one of the reactants, or

(ii) the rate of increase in concentration of any one of the products

=> Consider a hypothetical reaction, assuming that the volume of the system remains constant.

R → P

One mole of the reactant R produces one mole of the product P. If [R]_1 and [P]_1 are the concentrations of R and P respectively at time t_1 and [R]_2 and [P]_2 are their concentrations at time t_2 then

Δt = t_2 – t_1

Δ[R] = [R]_2 – [R]_1

Δ [P] = [P]_2 – [P]_1

The square brackets in the above expressions are used to express molar concentration.

Rate of disappearance of R = text(Decrease in concentration of R)/text(Time taken) = ( - Delta [R])/(Deltat) .......(1)

Rate of appearance of P = text(Increase in concentration of P)/text(Time taken) = (+ Delta [P])/(Deltat) .......(2).

Since, Δ[R] is a negative quantity (as concentration of reactants is decreasing), it is multiplied with –1 to make the rate of the reaction a positive quantity.

color{green} ✍️ color{green} mathbf("KEY CONCEPT")
It may be emphasised that the rate of reaction is always positive. The minus sign along with first term is used simply to show that the concentration of reactant is decreasing. The plus sign along with second term is used to show that the concentration of the product is increasing.

Equations (1) and (2) given above represent the average rate of a reaction, r_(av).

Average rate depends upon the change in concentration of reactants or products and the time taken for that change to occur.
Q 2917280180

From the concentrations of C_4H_9Cl (butyl chloride) at different times given below, calculate the average rate of the reaction :
C_4H_9Cl + H_2O → C_4H_9OH + HCl during different intervals of time.

t/s 0 50 100 150 200 300 400 700 800
[C_4H_9Cl]//mol L^(-1) 0.100 0.0905 0.0820 0.0741 0.0671 0.0549 0.0439 0.0210 0.017

Solution:

We can determine the difference in concentration over different intervals of time and thus determine the average rate by dividing Δ[R] by Δt

### Units of Rate of a Reaction :

=> From equations (1) and (2), we can see that units of rate are concentration timetext()^(–1). For example, if concentration is in mol L^-1 and time is in seconds then the units will be mol L^(-1)s^(–1).

=> However, in gaseous reactions, when the concentration of gases is expressed in terms of their partial pressures, then the units of the rate equation will be atm s^(–1).

### Instantaneous Rate of a Reaction :

=> Average rate cannot be used to predict the rate of a reaction at a particular instant as it would be constant for the time interval for which it is calculated.

=> So, to express the rate at a particular moment of time we determine the instantaneous rate.

=> It is obtained when we consider the average rate at the smallest time interval say dt (i.e. when Δt approaches zero).

=> Hence, mathematically for an infinitesimally small dt instantaneous rate is given by

r_(av) = (- Delta [R])/(Delta t) = (Delta [P])/(Delta t) ........(3).

As Deltat → 0 or r_text(inst) = (- d [R])/(dt) = ( d [P])/(dt)

=> Now consider a reaction

Hg (l) + Cl_2 (g) → Hg Cl_2 (s) .

● Where stoichiometric coefficients of the reactants and products are same, then rate of the reaction is given as

● Rate of reaction = (- Delta [Hg])/(Delta t) = ( - Delta [Cl_2])/(Delta t) = (Delta [HgCl_2])/(Delta t)

i.e., rate of disappearance of any of the reactants is same as the rate of appearance of the products.

=> But in the following reaction, two moles of HI decompose to produce one mole each of H_2 and I_2,

2HI (g) → H_2 (g) +I_2(g)

● For expressing the rate of such a reaction where stoichiometric coefficients of reactants or products are not equal to one, rate of disappearance of any of the reactants or the rate of appearance of products is divided by their respective stoichiometric coefficients. Since rate of consumption of HI is twice the rate of formation of H_2 or I_2, to make them equal, the term Δ[HI] is divided by 2.

● The rate of this reaction is given by

Rate of reaction  = -1/2 (Delta [HI])/(Deltat) = ( Delta [H_2])/(Delta t) = (Delta [I_2])/(Deltat)

=> Similarly, for the reaction

5 Br^(-) (aq) +BrO_3^(-) (aq) + 6 H^+ (aq) → 3 Br_2 (aq) +3H_2O (l)

● Rate  = -1/5 ( Delta [Br^-])/(Delta t) = - (Delta [BrO_3^-])/(Deltat t) = - 1/6 (Delta [H^+])/(Deltat) = 1/3 (Delta [Br_2])/(Deltat) = 1/3 (Delta [H_2O])/(Deltat)

color { maroon} ® color{maroon} ul (" REMEMBER")
Symbol △ is used for larger change,i.e., for average rate whereas symbol "d" is used for small change,i.e., for instantaneous rate.

=> 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 rate of change in partial pressure of the reactant or the product.

color{purple}(✓✓)color{purple} " DEFINITION ALERT"
The instantaneous rate of reaction,i.e., the rate of reaction at any instant of time is the rate of change of concentration of any one of the reactants or products at that particular instant of time.
Q 2917380280

The decomposition of N_2O_5 in C Cl_4 at 318K has been studied by monitoring the concentration of N_2O_5 in the solution. Initially the concentration of N_2O_5 is 2.33 mol L^(–1) and after 184 minutes, it is reduced to 2.08 mol L^(–1). The reaction takes place according to the equation

2N_2O_5 (g) → 4NO_2 (g) +O_2 (g)

Calculate the average rate of this reaction in terms of hours, minutes and seconds. What is the rate of production of NO_2 during this period?

Solution:

Average Rate  = 1/2 { -(Delta [N_2O_5])/(Deltat)} = -1/2 [ ((2.08-2.33) mol L^(-1))/(184 mi n)]

 = 6.79xx10^(-4) mol L^(-1) // mi n = (6.79 xx 10^(-4) mol L^(-1) mi n^(-1)) xx ( 60 mi n // 1h)

 = 4.07 xx 10^(-2) mol L^(-1) // h

= 6.79 xx 10^(-4) mol L^(-1) xx 1 mi n //60s

 = 1.13 xx 10^(-5) mol L^(-1) s^(-1)

It may be remembered that text(Rate) = 1/4 { ( Delta [NO_2])/(Delta t)}

(Delta [NO_2])/(Deltat) = 6.79 xx 10^(-4) xx 4 mol L^(-1) mi n^(-1) = 2.72xx 10^(-3) mol L^(-1) mi n^(-1)