# Chemical Kinetics

MCQs

**Rate of Reaction**The rate of a reaction tells us to what speed the reaction occurs. Let us consider a simple reaction-

R → P

The concentration of R decreases and that of P increases with time. The rate of a reaction is defined as the change in concentration of any of reactant or product with time. As we know that during the progress of a reaction the concentration of R keeps on falling with time. The rate of reaction at any given instant is given by the expression

Rate of reaction = − d[R]/dT

Since the rate of reaction is not uniform throughout the reaction, hence, the rate of disappearance of reactants or rate of appearance of product in small interval of time is given as-

Rate of reaction = − d[R]/dT = + d[P]/dT

Example: 3H

_{2}+ N

_{2}= 2NH

_{3}

for this reaction, the rate of reaction may be written as:

− 1/3 d[H

_{2}]/dT = − d[N

_{2}]/dT = + 1/2 d[NH

_{3}]/dT

**Factors Affecting the Rate of a Chemical Reactions:**

There are a number of factors which affect the rate of a reaction, the most important of them are:

**Effect of concentration:**The rate of a chemical reaction is influenced by the no. of collisions per second between the reacting molecules. On increasing the concentration of the reactant, the number of collisions will increase and the rate of reaction will increase and on decreasing the concentration the rate will decrease.

**Effect of nature of reactants:**Reactions between polar or ionic molecules occur almost instantaneously. Those reactions in which the bonds are arranged or electrons are transferred takes a comparatively longer time than the reaction between ionic molecules.

**Effect of catalyst:**A catalyst can increase or decrease the rate of a chemical reaction. For example the combination of hydrogen and oxygen to form water is slow at ordinary temperature, while it proceeds rapidly in presence of platinum.

**Effect of surface area of reactant:**Surface area of reactants is of importance only for heterogeneous reactions. As particle size decreases, surface area for the same mass increases. The smaller particle thus reacts more rapidly than the larger particles. For example, burning of coal dust in air takes place more rapidly than large lump of coal.

**Effect of temperature:**With the exception of few reactions, the rate of reaction is increased considerably with an increase of temperature. Generally the rate of a reaction is almost doubled or tripled by an increase of 10

^{o}C in temperature.

**Rate Constant(k):**

The proportionality constant of rate equation is called rate constant. It is also called specific rate constant as it has specific value for specific reaction.

Let us consider a chemical reaction-

R → P

Rate = − d[R]/dT = + d[P]/dT

rate of reaction ∝ [R]

so, the rate law equation: − d[R]/dT = k[R]

where K is rate constant

When [R] = 1, then-

− d[R]/dT = k

So, the rate constant k is the rate of the reaction at unit molar concentration of the reactant.

**Order of Reaction:**

The sum of powers of the concentration term in the rate equation of a chemical reaction is called Order of reaction.

Order of reaction obtained from the rate law equation which is obtained experimently.

Let us consider a general chemical reaction-

nA + mB = Product

then, the rate of reaction = k[A]

^{x }[B]

^{y}

The value of x and y may or may not be equal to n and m respectively because the value of x and y are determined experimently.

If the reaction takes place in more than one steps, then, the slowest step is rate determining step.

The value of order of reaction may be positive, negative, zero, fraction or integer. The order of reaction can never be more than or equal to the molecularity of the reaction.

Try to Answer:

If the rate of reaction is given by r = k[A]

a. 5/2 b. 1/2 c. 2 d. 1

If the rate of reaction is given by r = k[A]

^{2}[B]^{1/2}The overall order of reaction isa. 5/2 b. 1/2 c. 2 d. 1

**Molecularity:**

The number of reactant molecules which take part in the formation of activated complex in the slowest step of a chemical reaction is caleed Molecularity of that reaction. Molecularity is a whole number but can never be zero or fraction. Molecularity more than three is generally rare.

Reaction may be uni, bi or ter-molecular depending upon whether one, two or three reactant molecules are involved in the slowest step of a chemical reaction.

Molecularity of a reaction is a theoretical value. So, it is not the real quantity like order of reaction. For a complex reaction, the molecularity of reaction is expressed for each step and hence overall value is meaningless.

2 O

_{3}= 3 O

_{2}

O

_{3}→ O

_{2}+ O (Fast) (Unimolecular)

O

_{3}+ O = 2 O

_{2}(Slow) (Bimolecular)

**Rate Constant for First Order Reaction:**

The reaction in which rate is determined by the variation of only one concentration term is called first order reaction.

Let us consider the following first order reaction-

This is the First order kinetics or rate constant for first order reaction.

Try to Answer:

1. A first order reaction is 20% complete in 10 minutes. Calculate the rate constant of the reaction.

2. Shows that for a first order reaction the time required for 99.9% completion is three times required for the completion of 90% reaction.

1. A first order reaction is 20% complete in 10 minutes. Calculate the rate constant of the reaction.

2. Shows that for a first order reaction the time required for 99.9% completion is three times required for the completion of 90% reaction.

**Half life period (t**

_{1/2}) for First Order Reaction:The time during which initial concentration of reactant is reduced to half is called half life period. It is denoted as t

_{1/2}

We know that, for first order reaction, the rate constant (k) is-

k = (2.303/t) log(a/a-x) -------1

where a is initial concentration of reactant and (a-x) is concentration after time t.

From equation 1-

t = (2.303/k) log(a/a-x) -------2

Now, when, t = t

_{1/2}then, x = a/2

Now putting the value of t and x in equation 2 we get-

t

_{1/2}= (2.303/k) log2

or, t

_{1/2}= 0.693/k --------3

From the equation 3 we see that half life period is inversely proportional to k and independent of initial concentration of the reactant.

### Explain why the rate of a reaction increases with increase in temperature.

As the temperature increases, the rate of average kinetic energy of colliding molecules increases as a result effective collisions increases consequently rate of reaction increases.### What is Activation Energy ?

The excess energy needed for reactant molecules to collide effectively to form the product is called activation energy. It is denoted by Ea.Activation Energy = Threshold Energy – Energy possessed by reactant molecules.

### What is Threshold energy ?

The minimum energy that all colliding molecules must possess in order to make the effective collisions is called threshold energy.Threshold Energy = Energy possessed by the reacting molecules + Activation Energy (Ea).

If the reacting molecules have sufficient energy for the collisions, then the threshold energy is equal to Activation Energy (Ea).

Molecules that have a Kinetic Energy equal to or higher than the Threshold Energy will react.

**Arrhenius Equation**Arrhenius proposed an equation to calculate the activation energy of a chemical equation having rate constant 'K' and temperature 'T' in 1889.

By knowing the value of K

_{1}, K

_{2}, T

_{1}and T

_{2}, we can easily calculte the value of Activation Energy.

Straigh line equation for Arrhenius equation-