1. What is the effect of catalyst on the Rate of Reaction?

  Catalyst is a substance that changes the reaction rate without undergoing any permanent change in its chemical behaviour. Broadly, there are two types of catalysts; positive catalyst, and negative catalyst. The positive catalysts increase the rate of reaction, while negative catalysts retard the reaction. The positive catalyst is simply called as catalyst. A catalyst provides an alternative path involving lower activation energy for the reaction that is  a catalyst accelerates a chemical reaction by lowering its activation energy. A catalyst lowers the activation energy for both, the forward and the backward reactions.

The lowering of activation energy by a catalyst permits more and more molecules to take part in the chemical reaction, leading to an increase in the rate of reaction because more molecules will have energy equal or greater than the lowered threshold energy.
A catalyst does not affect the positive of equilibrium in a reversible reaction. In other words, a catalyst does not change the extent of completion of a reaction. It simply speeds up the attainment of the equilibrium.

2. Explain the effect of catalyst on the enthalpy of reaction.

  The presence of a catalyst in any reaction does not affect its energetics. The energy change (ΔE) in a reaction is given by.
Energy change in a reaction = Energy of products - Energy of reactants

                               or                         

                         ΔE = E_products - E_Reactants

That is the energy change in any reaction depends on the relative energies of the reactants and products.
The relative energies of reactants and products in any reaction remain unchanged even in the presence of a catalyst. Therefore, catalyst has no effect on the energy change in any reaction. The energy change in any reaction at constant pressure is called enthalpy of reaction (ΔH_r). So, catalyst has no effect on the enthalpy of reaction.

3. Write the effect of radiation on the rate of a reaction.Give some examples for photo chemical reactions .

All reaction need activation energy for its reactants to take part in the reaction. Activation energy may be provided by molecular collisions, heat or light. The reactions which are caused by the absorption of light (the visible or near ultraviolet radiation) are called photochemical reactions.

The energy associated with the absorbed light may be sufficient to break chemical bonds and form highly reactive intermediates called free radicals. Some of the examples where light is used for initiating chemical reactions are:

1. Photosynthesis
2. Vision
3. Fading away of the colour of bright coloured fabrics on long exposures to the sunlight.
4. Certain polymerisation reactions are initiated by light.
5. Photography is based on the action of light on silver halides in the presence of photosensitisers.
6. Photoetching used in electronic industry.
7. In the manufacture of integrated circuits, photo-processes are very important.
8. Sterilization of water by exposing it to UV (ultraviolet) light.
9. Blue printing.

4. Derive rate equation for a zero order reaction

The reaction whose rate does not depend upon the concentration of the reactant is called zero order reaction. Thus, for a reaction of zero order.

If the initial concentration of A be 'a' moles per litre, and at any instant 'x' of it gets converted into products, then the rate of reaction is given by,

Separation of variables gives, dx = k dt

Integration gives,                       x = kt + I

Where, I is the integration constant.

Under the condition.         when t = 0    x = 0

So.                                             I =  0

is the general rate equation for a zero order reaction .
 
5. Write some examples of zero order reactions.

Some typical zero order reactions are.

• Photochemical combination of H₂ and Cl₂ over the surface of water (saturated with HCl).
• Thermal decomposition of HI(g) on gold surface.
• Enzyme reactions.

6. Derive rate equation for a first order reaction.

Consider the first order reaction.
              A → B
Then, the reaction rate is given by the differential rate equation.

7. The rate for the decomposition of NH₃ on platinum surface is of zero order. What are the rates of production of N₂ and H₂ if k = 2.5 × 10^-4 M s^-1?

It is the reaction and not the rate of reaction which has the order associated with it. For the reaction,  2NH₃ → N₂ + 3H₂

8. What is the effect of temperature on the rate constant of a reaction? How can this temperature effect on rate constant be represented quantitatively?

The rate constant of most reactions increases exponentially with a rise in temperature.

The effect of temperature on the rate constant of a reaction can be described by Arrhenius equation.

                                   k = A exp (-E_a / RT)

                                log k = log A -  E_a/ (2.303 RT)

9. Calculate the half-life of a first order reaction from their rate constants given below:
      1.  200 s^-1
      2. 2 min^-1
      3. 4 year^-1
    

For a first order reaction,

10. Show that time required for 99% completion is twice the time required for the completion of 90% reaction.

It is assumed that the reaction is of first order (the order of reaction is not given here). Then,

11. The rate constant for the decomposition of hydrocarbons is 2.418 × 10^-5 s^-1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.

The Arrhenius equation is,              k = A exp (-E_a/RT)

Where A is the pre-exponential factor.

12. Consider a certain reaction, A → Products with k = 2.0 × 10^-2 s^-1. Calculate the concentration of A remaining after 100s if the initial concentration of A is 1.0 mol L^-1.

Initial concentration of A, = 1.0 mol L^-1

          Final duration of A = ?

Time duration                  = 100 s

Rate constant               k = 2.0 × 10-2 s^-1

From the units of rate constant, it is clear that the reaction is of first order.

Then,

13. The decomposition of hydrocarbon follows the equation

k = (4.5 × 10¹¹ s^-1) e ^{-28000 K/T} .  Calculate E_a.

Comparing the given equation, with the Arrhenius equation, k = A exp (-E_a/RT), one can write,
                                         A= 4.5 × 10¹¹s^-1

14. The time required for 10% completion of a first order reaction at 298 K is equal to that required for its 25% completion at 308 K. If the value of A is 4 × 10¹⁰ s^-1. Calculate k at 318 k and E_a.

From the given data,

15. Define 'energy of activation' of a reaction. How does it vary with a rise in temperature?

 The minimum energy or average energy which must be gained by the molecules before they could react to from products is called the energy of activation. It is denoted by E_a.
According to the Arrhenius theory, activation energy is independent of temperature. However, precise measurements indicate that the activation energy tends to decrease slightly with a rise in temperature.

16. What is meant by an elementary reaction?

A single step reaction is called elementary reaction.
The reaction between H₂ (g)and l₂(g) to form Hl(g) is an elementary reaction, (except at high temperature and in the presence of light).
The various steps involved in a complex reaction are also elementary reactions.

17. What do you mean by average rate of reaction?

The average rate of a reaction is defined as the rate of change of concentration of reaction (or of a product) over a specified measurable period of time. The average rate is denoted by , or by R_av.

The reaction,                    A   →   B

18. What is instantaneous rate of reaction?

The rate of reaction at any particular instant during the course of reaction is called the instantaneous rate of reaction.
                                    Instantaneous rate = (Average rate) _{Δt → 0}

The instantaneous rate of a reaction  may also be defined as, the time derivative of the concentration of a reactant (or a product) converted to a positive number is called the instantaneous rate of reaction. Thus,

19. Explain

1. Order of reaction
2. First order reaction
3. Half life period of the first order reaction

1. Order of reaction: The sum of the powers of all the concentration terms in the differential rate law equation is called the order of reaction.
The order of reaction may also be defined as follows:
The total number of concentration variables which determine the rate of any reaction is called the overall order of the reaction.

2. First order reaction: The reaction whose rate is directly proportional to the concentration of the reactant is called first order reaction. The differential rate equation for a first order reaction is given by,

3. Half-life period of a first order reaction: The half - life of a first order reaction is independent of the initial concentration of the reaction.