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What is rate of a chemical reaction? Explain average and instantaneous rate of reaction with help of graph and also give unit of rate of reaction.

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Rate of a chemical reaction: The change in concentration of reactant or product in unit time is called rate of a chemical reaction.

It can be expressed in terms of:

(i) The rate in decrease in concentration of any one of the reactants.

(ii) The rate in 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 t1 and [R]2 and [P]2 are their concentrations at time t2 then,

∆t = t2 – t1

∆[R] = [R]2 – [R]1

∆[P] = [P]2 – [P]1

(Square bracket expressing molar concentration.)

Rate of disappearance of

R = =

Rate of appearance of

P = = +

Above given equations represent the average rate of a reaction (rav).

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

Instantaneous rate of reaction: Average rate cannot be used to predict the rate of a reaction at a particular instant because the rate is generally not constant throughout the reaction.

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

Instantaneous rate is obtained when we consider the average rate at the smallest time interval say dt (when ∆t approaches zero).

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

rav = –

As ∆t → 0 or rinst = –

Unit of rate of a reaction: Units of rate are concentration time–1.

If concentration is in mol L–1 and time is in seconds then the units will be mol L–1sec–1.

However, in gaseous reactions, when the concentration of gases is expressed in terms of their partial pressure, then the units of the rate equation will be atm s–1.

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Explain the rate expression for a reaction in which stoichiometric coefficients of reactants and products are not same or unit.

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For reaction, n1A + n2B → n3C + n4D

Rate of reaction:

For expressing the rate of such a reaction where stoichiometric coefficients of reactants or product are not equal to one, rate of disappearance of any of the reactants or the rate of appearance of the products is divided by their respective stoichiometric coefficients.

For reaction, Hg(l) + Cl2(g) → HgCl2(s)

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

Rate of reaction =

For reaction, 2Hl(g) → H2(g) + I2(g) the rate of decomposition of HI is twice the rate of formation of H2 or I2, to make them equal, the term ∆[HI] is divided by 2. The rate of this reaction is given by:

Rate of reaction =

Similarly for the reaction:

5Br–(aq) + BrO3–(aq) + 6H+(aq) → 3Br2(aq) + 3H2O(l)

Rate =

=

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Explain rate law and rate constant with an example.

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Rate of a reaction depends upon the concentration of reactants.

Consider a general reaction

aA + bB → cC + dD

where a, b, c and d are the stoichiometric coefficients of reactants and products.

The rate expression for this reaction is

Rate α[A]x[B]y

where exponents x and y may or may not be equal to the stoichiometric coefficients (a and b) of the reactants.

Above equation can also be written as

Rate = k[A]x[B]y

= k[A]x[B]y

This form of equation is known as differential rate equation, where k is proportionality constant called rate constant.

The equation which relates the rate of reaction to concentration of reactants is called rate law or rate expression.

Thus, rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as stoichiometric coefficient of the reacting species in a balanced equation.

For example: 2NO(g) + O2(g) → 2NO2(g)

The rate equation for this reaction will be:

Rate = k[NO]2[O2]

This differential form of this rate expression is given as:

= k[NO]2[O2]

Some other examples are given below:

1. CHCl3 + Cl2 → CCl4 + HCl

2. CH3COOC2H5 + H2O → CH3COOH + C2H5OH

Experimental rate expression:

Rate = k[CHCl3] ·

Rate = k[CH3COOC2H5][H2O]0

In these reactions, the exponents of the concentration terms are not the same as their stoichiometric coefficients. Thus, we can say that:

Rate law for any reaction cannot be predicted by merely looking at the balanced chemical equation. i.e. theoretically but must be determined experimentally.

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What is order of reaction ? Discuss elementary and complex reactions, Explain units of rate constant in detail.

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The sum of power of the concentration of the reactants in the rate law expression is called the order of that chemical reaction.

For reaction: aA + bB → product

Rate = k[A]x[B]y x and y indicate how sensitive the rate is to change in concentration of A and B.

Sum of these exponents, i.e. x + y gives the overall order of a reaction whereas x and y represent the order with respect to the reactants A and B respectively.

Order of reaction can be 0, 1, 2, 3 and even a fraction.

A zero order reaction means that the rate of reaction is independent of the concentration of reactants.

The reactions taking place in one step are called elementary reactions.

When a sequence of elementary reactions (called mechanism) gives us the products, that reactions are called complex reactions.

Units of rate constant:

For a general reaction

aA + bB → cC + dD

Rate = k[A]x[B]y

where x + y = n = order of the reaction

k = =

(where [A] = [B])

Taking SI unit of concentration, mol L–1 and time, s, the unit of k for different reaction order listed in table.

Reaction	Order	Units of rate constant
Zero order reaction	0	= mol L–1 s–1
First order reaction	1	= s–1
Second order reaction	2	= mol–1 L s–1

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Write a note on molecularity of a reaction and its different types.

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Explain how the molecularity of a complex reaction determined? Give the points showing difference between molecularity of a reaction and order of a reaction.

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Term molecularity is only applicable to elementary reactions, even though to determine molecularity of a complex reaction it is necessary to know the mechanism of that reaction.

Through mechanism of a reaction we can have information about slowest step of reaction.

The overall rate of the reaction is controlled by the slowest step in a reaction called the rate determining step.

Consider the decomposition of hydrogen peroxide which is catalysed by iodide ion in an alkaline medium,

The rate equation for this reaction is found to be: Rate = –

This reaction is first order with respect to both and .

Mechanism involve two steps:

(1)

(2)

The first step, being slow, is the rate determining step.

Thus, the rate of formation of intermediate will determine the rate of this reaction.

Thus, it can be said that, for complex reaction, order is given by the slowest step and molecularity of the slowest step is same as the order of the overall reaction.

Difference between molecularity and order of a reaction:

(i) Order of a reaction is an experimental quantity. It can be zero and even a fraction but molecularity cannot be zero or a non integer.

(ii) Order is applicable to elementary as well as complex reactions whereas molecularity is applicable only for elementary reactions. For complex reaction molecularity has no meaning.

(iii) For complex reaction, order is given by the slowest step and generally molecularity of the slowest step is same as the order of the overall reaction.

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Derive integrated rate equation for zero order reaction and also explain how the rate constant can be determine with help of graph.

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Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants.

Consider the reaction.

R → P

Rate of reaction for this reaction can be expressed as

Rate = = k[R]0

As any quantity raised to power zero is units.

Rate = = k × 1

Thus, the rate of zero order reaction is independent from concentration of reactants.

d[R] = –k dt

Integrating both sides

[R] = –kt + I ... ... Eq. (1)

Where, I is the constant of integration

At t = 0, the concentration of the reactant
R = [R]0, where [R]0 is initial concentration of the reactant.

Substituting in equation (1)

[R]0 = –kx 0 + I

[R]0 = I

Substituting the value of I in the equation (1)

[R] = –kt + [R]0 ... ... Eq. (2)

Further simplifying equation (2)

k = ... ... Eq. (3)

Comparing equation (2) with equation of straight line, y = mx + c, if we plot [R] against t, we get a straight line with slope = –k and intercept equal to [R]0

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Give examples of zero order reaction.

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Zero order reaction are relatively uncommon but they occur under special condition.

Some enzyme catalysed reaction and reaction which occur on metal surface are a few examples of zero order reactions.

The decomposition of gaseous ammonia on hot platinum surface is a zero order reaction at high pressure.

2NH3(g) N2(g) + 3H2(g)

Rate = k[NH3]0 = k

In this reaction, platinum metal acts as a catalyst.

At high pressure, the metal surface gets saturated with gas molecules.

So, a further change in reaction condition is unable to alter the amount of ammonia on the surface of the catalyst making rate of the reaction independent of its concentration.

The thermal decomposition of HI on gold surface is another example of zero order reaction.

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Derive integrated rate equation for first order reaction and also explain how the rate constant can be determine with help of graph.OR Derive the formula for Rate constant (k) and half life period for first order reaction.

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First order reaction means that the rate of reaction is proportional to the first power of the concentration of the reactant R.

For example, consider the following reaction

R → P

Rate of reaction for this reaction can be expressed as

Rate = = k[R]

Or = –kdt

Integrating this equation, we get

ln [R] = –kt + I ... ... Eq. (1)

where, I is the constant of integration and its value can be determined easily.

When t = 0, R = [R]0, where [R]0 is the initial concentration of the reactant.

Therefore, equation (1) can be written as

ln [R]0 = –k × 0 + I

ln [R]0 = I

Substituting the value of I in equation (1)

ln [R] = –kt + ln [R]0 ... ... Eq. (2)

Rearranging this equation

ln = –kt

or k = ln ... ... Eq. (3)

At time t1 from equation (1)

ln [R]1 = – kt1 + ln [R]0 ... ... Eq. (4)

At time t2

ln [R]2 = – kt2 + ln [R]0 ... ... Eq. (5)

where, [R]1 and [R]2 are the concentration of the reactants at time t1 and t2 respectively.

Subtracting Eq. (5) from (4)

ln [R]1 – ln [R]2 = –kt1 – (–kt2)

ln = k(t2 – t1)

k = ln ... ... Eq. (6)

So, equation (2) can also be written as

ln = –kt

Taking antilog of both the sides

[R] = [R]0 e–kt ... ... Eq. (7)

Comparing equation (2) with y = mx + c, if we plot ln [R] against t, we get a straight line with slope = – k and intercept equal to ln [R]0

The first order rate equation (3) can also be written in the form

k = log ... ... Eq. (8)

or log

If we plot a graph between log vs t,

the slope =

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Give examples of first order reaction.

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Hydrogenation of ethene is an example of first order reaction.

C2H4(g) + H2(g) → C2H6(g)

Rate = k[C2H4]

All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.

→ +

Rate = k[Ra]

Decomposition of N2O5 and N2O are some more examples of first order reactions.

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Derive integrated rate equation for first order reaction containing gaseous components.

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Let us consider a typical first order gas phase reaction.

A(g) → B(g) + C(g)

Let pi be the initial pressure of A and pt the total pressure at time ‘t’. Integrated rate equation for such a reaction can be derived as

Total pressure pt = pA + pB + pC (pressure units)

pA, pB and pC are partial pressures of A, B and C respectively. If x atm can be the decrease in pressure of A at time t and one mole each of B and C is being formed. The increase in pressure of B and C will also be X atm each

A(g) → B(g) + C(g)

At t = 0 pi atm 0 atm 0 atm

At time t (pi– x) atm x atm x atm

where, pi is the initial pressure at time t = 0.

pt = (pi – x) + x + x = pi + x

x = (pt – pi)

where, pA = pi – x = pi – (pt – pi) = 2pi – pt

k =

= log

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What is half-life of a reaction? Derive formula for half-life of zero and first order reaction. OR Derive equation of rate constant and half life of reaction for the zeroth order reaction.

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Half-life of a reaction: The time in which the concentration of a reactant is reduced to one half of its initial concentration is called half-life of a reaction.

Half-life for zero order reaction:

For a zero order reaction, rate constant is given by following equation

k =

At t = , [R] = [R]0

The rate constant at becomes

k =

=

It is clear that for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.

Half-life for first order reaction:

For the first order reaction,

k = log

at t = [R] =

So, the above equation becomes

k = log

or = log2

= × 0.301

=

It can be seen that for a first order reaction, half-life period is constant, i.e. it is independent of initial concentration of the reacting species.

The half-life of a first order equation is readily calculated from the rate constant and vice versa.

For zero order reaction × [R]0 for first order reaction is independent of [R]0

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Explain pseudo first order reaction with example.

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The order of a reaction is sometimes altered by conditions.

There are many reactions which obey first order rate law although they are higher order reactions.

Consider the hydrolysis of ethyl acetate which is a chemical reaction between ethyl acetate and water. In reality, it is second order reaction and concentration of both ethyl acetate and water affect the rate of the reaction.

But water is taken in large excess for hydrolysis, therefore, concentration of water is not altered much during the reaction.

Thus, the rate of reaction is affected by concentration of ethyl acetate.

For e.g. 0.01 mol ethyl acetate react with 10 mol of water amounts of the reactants and products at the beginning (t = 0) and completion (t) of the reaction are give as under.

CH3COOC2H5 + H2O CH3COOH + C2H5OH

t = 0 0.01 mol 10 mol 0 mol 0 mol

t = t 0 mol 9.99 mol 0.01 mol 0.01 mol

The concentration of water does not get altered much during the course of the reaction. So, the reaction behaves as first order reaction. Such reactions are called pseudo first order reactions.

Inversion of cane sugar is another pseudo first order reaction.

C12H22O11 + H2O C6H12O6 + C6H12O6

Cane sugar Glucose Fructose

Rate = k [C12H22O11]

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What is activation energy? Explain with the help of graph by suitable example.

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Activation energy can be understood clearly using the formation reaction of hydrogen iodide.

H2(g) + I2(g) → 2HI(g)

According to Arrhenius, this reaction can take place only when a molecule hydrogen and molecule of iodine collide to form an unstable intermediate. It exists for a very short time and then breaks up to form two molecules of hydrogen iodide.

Intermediate

The energy required to form this intermediate, called activated complex (C), is known as activation energy (Ea).

Below figure is obtained by plotting potential energy vs reaction coordinate. Reaction coordinate represents the profile of energy change when reactant change into products.

Some energy is released when the complex decomposes to form products. So, the final enthalpy of the reaction depends upon the nature of reactants and products.

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Derive the formula for determining activation energy from Arrhenius equation using rate constant at different temperatures and also explain how activation energy can be determined using graph.

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Activation energy using graph:

Taking natural logarithm on both the side of Arrhenius equation k = Ae

ln k = + ln A ... ... Eq. (1)

The plot of ln k vs 1/T gives a straight line as shown in figure.

In figure, slope = and intercept = lnA. So, we can calculate activation energy (Ea) and Arrhenius constant A using these values.

Formula of activation energy: It has been found from Arrhenius equation that increasing the temperature or decreasing the activation energy will result in an increase in the rate of the reaction and an exponential increase in rate constant.

Thus, at temperature T1, equation (1) is

ln k1 = + lnA ... ... Eq. (2)

at temperature T2, equation (1) is

ln k2 = + lnA ... ... Eq. (3)

(since A is constant for given reaction)

k1 and k2 are rate constant at temperatures T1 and T2 respectively.

Subtracting equation (2) from (3), we obtain

lnk2 – lnk1 =

ln

log

log

From above formula activation energy can be calculate using measured values of rate constants at different temperatures.

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Explain the effect of catalyst on rate of reaction and also give its characteristics.Or

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Answer the following questions on catalyst:

(i) How it increases the rate of reaction.

(ii) Write any 4 characteristics of catalyst.

Ans. A catalyst is a substance which increase the rate of a reaction without itself undergoing any permanent chemical change.

For example, MnO2 catalyses the following reaction so as to increase its rate considerably.

2KClO3 2KCl + 3O2

The word catalyst should not be used when the added substance reduces the rate of reaction. The substance is then called inhibitor.

The action of catalyst can be explained by intermediate complex theory.

According to this theory, a catalyst participates in a chemical reaction by forming temporary bond with the reactants resulting in an intermediate complex.

It is believed that the catalyst provides an alternate path or reaction mechanism by reducing the activation energy between reactants and products hence lowering the potential energy barrier as shown in figure.

It is clear from Arrhenius equation that lower the value of activation energy faster will be the rate of reaction.

This has transitory existence and decomposes to yield products and the catalyst.

Characteristics of catalyst:

A small amount of catalyst can catalyses a large amount of reactants.

A catalyst does not alter Gibbs energy of a reaction.

It catalysis the spontaneous reaction but does not catalyze the non-spontaneous reactions.

It is also found that a catalyst does not change the equilibrium constant of a reaction rather, it helps in attaining the equilibrium faster, that is, it catalyses the forward as well as backward reaction to the same extent so that the equilibrium state remains same but is reached earlier.

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Write Arrhenius equation. Explain the terms involved in it.

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The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation.

k = A

Where, A is the Arrhenius factor or frequency factor. It is also called per-exponential factor. It is a constant specific to a particular reaction. R is gas constant and Ea is activation energy measured in joules/mole (J mol–1).

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Write a note on collision theory of chemical reaction.Or What is meant by collision theory? Explain.

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Collision theory, which was developed by Max Trautz and William Lewis in 1916-18, provides greater insight into the energetic and mechanistic aspects of reaction.

It is based on kinetic theory of gases.

According to this theory, the reactant molecules are assumed to be hard spheres and reaction is postulated to occur when molecules collide with each other.

The number of collision per second per unit volume of the reaction mixture is known as collision frequency (Z).

Another factor which affects the rate of chemical reaction is activation energy.

For a bimolecular elementary reaction;

A + B → Products

Rate of reaction can be expressed as:

Rate = ZAB ... ... Eq. (1)

where ZAB represents the collision frequency of reactants A and B, and represents the fraction of molecules with energies equal to or greater than Ea.

Comparing equation (1) with Arrhenius equation, we can say that A is related to collision frequency.

Equation (1) predicts the value of rate constant fairly accurately for the reaction that involve atomic species or simple molecule but for complex molecules significant deviations are observed.

The reason could be that all collision do not lead to the formation of products.

The collision in which molecules collide with sufficient kinetic energy (called threshold energy) and proper orientation, so as to facilitate breaking of bonds between reacting species and formation of new bonds to form products are called as effective collision.

For example, formation of methanol from bromomethane CH3Br + OH – → CH3OH + Br– depends upon the orientation of reactant molecule as shown in figure.

The proper orientation of reactant molecules lead to bond formation whereas improper orientation makes them simply bounce back and no product are formed.

To account for effective collision, another factor P, called the probability factor or steric factor is introduced.

It takes into account the fact that in a collision, molecules be properly oriented i.e.

Rate = PZAB

Thus, in collision theory activation energy and proper orientation of the molecules together determine the criteria for an effective collision and hence the rate of chemical reaction.

Class 12 Chemistry (Part 1) 012