Prove that the time required for 99 % completion of a first order reaction is twice the required time for the completion of 90 % reaction.

The time for completion for a first order reaction, is given as: t = 2 . 303 k log Initial concentration Final concentration Suppose initial concentration = 100 On, 99 % completion the final concentration is 1 . ∴ t 1 = 2 . 303 k log 100 1 = 2 . 303 k × 2 . . . . . ( 1 ) On, 90 % completion the final concentration is 10 . ∴ t 2 = 2 . 303 k log 100 10 = 2 . 303 k × 1 . . . . . ( 2 ) Dividing equation ( 1 ) by ( 2 ) , we get, t 1 t 2 = 2 1 Hence, the given statement is proven.

The following data were obtained during the first order thermal decomposition of N 2 O 5 ( g ) at constant volume- 2 N 2 O 5 → 2 N 2 O 4 ( g ) + O 2 ( g ) S . No . Time / s Total Pressure / atm . 1 0 0 . 5 2 100 0 . 512 Calculate the rate constant.

Let the pressure of N 2 O 5 ( g ) decrease by 2 x atm . As two moles of N 2 O 5 decompose to give two moles of N 2 O 4 ( g ) and one mole of O 2 ( g ) , the pressure of N 2 O 4 ( g ) increases by 2 x atm and that of O 2 ( g ) increases by x atm . 2 N 2 O 5 → 2 N 2 O 4 ( g ) + O 2 ( g ) At t = 0 0 . 5 atm 0 atm 0 atm At time t 0 . 5 - 2 x atm 2 x atm x atm p t = p N 2 O 5 + p N 2 O 4 + p O 2 = 0 . 5 - 2 x + 2 x + x = 0 . 5 + x ⇒ x = p t - 0 . 5 p N 2 O 5 = 0 . 5 - 2 x = 0 . 5 - 2 p t - 0 . 5 = 1 . 5 - 2 p t At t = 100 s , p t = 0 . 512 atm p N 2 O 5 = 1 . 5 – 2 × 0 . 512 = 0 . 476 atm k = 2 . 303 t log p i p f = 2 . 303 t log 0 . 5 0 . 476 = 2 . 303 100 s × 0 . 0216 = 4 . 98 × 10 - 4 s - 1

Write collision theory of chemical reaction.

According to collision theory of chemical reaction, the reactant molecules are assumed to be hard spheres and reaction is postulated to occur when molecules collide with each other. The number of collisions per second per unit volume of the reaction mixture is known as collision frequency ( Z ). Another factor which affects the rate of chemical reactions is activation energy. For a bimolecular elementary reaction, A + B → Products The rate of reaction can be expressed as: Rate = Z AB e - E a / RT Where Z AB represents the collision frequency of reactants, A and B and e - E a / RT represents the fraction of molecules with energies equal to or greater than E a .

Derive the integrated rate equation of Zero Order Reaction.

The reaction in which the rate of the reaction is independent of the concentration of the reactant is called a zero-order reaction. Consider a general zero-order reaction A → Product Rate of the reaction = - d A dt = k A 0 = d A = k + dt On integrating the equation on both sides, we get, A = kt + C Here, C is a constant. At initial time t = 0 , A = A 0 , A 0 = C On putting the value of constant ⇒ A = kt + A 0 ⇒ kt = A - A 0 ⇒ k = A - A 0 t This is the expression of the rate constant for a zero-order reaction.

A first order reaction has a specific reaction rate of 2 . 31 × 10 - 3 sec - 1 . Calculate Half life period of the reaction.

We are given the reaction rate which is equal to: k = 2 . 31 × 10 - 3 sec - 1 For a first-order reaction, the half-life can be written as: t 1 2 = 0 . 693 k = 0 . 693 2 . 31 × 10 - 3 sec - 1 t 1 2 = 300 s Therefore, the hal-life time of the given first-order reaction is 300 s .

What is activation energy? How is the rate constant of a reaction related to its activation energy?

Activation energy is the minimum energy which must be available to a chemical system with potential reactants to result in a chemical reaction. The activation energy of a reaction is usually denoted by Ea and given in units of kJ / mol or k cal / mol . The rate constant k = Ae - E a RT .

What do you understand by order of reaction? Give an example of a reaction of first order. How order of a reaction differs from molecularity?

Order of a reaction can be defined as the power to which the concentration or pressure (in case of gaseous reactions) terms are raised in the rate expression of a reaction. Rate = k A x , where x is the order of reaction. An example of a first-order reaction is the hydrolysis of aspirin and the reaction of t-butyl bromide with water to give t-butanol. The difference between order and molecularity of a reaction is given below, Molecularity Order The number of ions or molecules that take part in the rate-determining step is known as molecularity. The sum of powers to which the reactant concentrations are raised in the rate law equation is known as the order of the reaction. It is always a whole number. It can either be a whole number or a fraction. The molecularity of the reaction is determined by looking at the reaction mechanism. The order of the reaction is determined by the experimental methods.

What is activation energy? How is the rate constant of a reaction related to activation energy?

The minimum amount of extra energy required by reactant molecules to be converted to products is known as activation energy ( E a ). The rate constant k = Ae - E a RT .

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What is difference between molecularity of reaction and order of reaction?

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