Which of the following relation is correct for elementary bimolecular reaction?

Order of reaction = molecularity

Order of reaction ⩽ molecularity

Order of reaction > molecularity

Order of reaction < molecularity

The decomposition of N 2 O 5 dissolved in carbon tetrachloride occurs as follows. N 2 O 5 ( Solution ) ⇌ 2 NO 2 ( Solution ) + 1 2 O 2 This reaction is of first order and its rate constant is 5 . 0 × 10 - 4 sec - 1 . If initial concentration of N 2 O 5 for this reaction is 0 . 50 mole litre - 1 , then (a) What will be the initial reaction rate? (b) What will be half life period of this reaction? (c) What will be the concentrations of N 2 O 5 and NO 2 at the end of 50 minutes after the starting of reaction?

First-order reaction means a) rate = − d [ N 2 O 5 ] dt = k [ N 2 O 5 ] 1 Given: k = 5 × 10 − 4 s − 1 and N 2 O 5 = 0 . 5 M On substitution, we get: Initial reaction rate = 5 × 10 − 4 × 0 . 5 = 2 . 5 × 10 − 4 M / s b) The half-life for a first order reaction: t 1 / 2 = 0 . 693 k = 1380 s = 23 min c) The rate law of first order reaction is: ln [ N 2 O 5 ] 0 [ N 2 O 5 ] t = kt Given: [ N 2 O 5 ] 0 = 0 . 5 M , t = 50 min = 3000 s Substituting the values we get: ln 0 . 5 x = 5 . 0 × 10 - 4 3000 ⇒ x = 0 . 11 M N 2 O 5 ( Solution ) ⇌ 2 NO 2 ( Solution ) + 1 2 O 2 Initial 0 . 5 M 0 At t = 50 min 0 . 5 - y M 2 y = 0 . 11 M Therefore, concentration of N 2 O 5 and NO 2 after 50 min are 0 . 11 M and 0 . 78 M respectively.

The rate constant of a reaction at 300 K is 5 . 0 × 10 - 4 minute - 1 . The temperature was increased by 20 K and the value of rate constant ' K ' increased three times. Calculate the energy of activation of the reaction? What will be the value of rate constant at 37 ° C ? [ R = 1 . 987 calori . Kelvin - 1 . mol - 1 ]

Given: Rate constant K 1 = 5 . 0 × 10 - 4 min - 1 K 2 = 3 × 5 . 0 × 10 - 4 min - 1 Temperature, T 1 = 300 K T 2 = 300 + 20 = 320 K T 3 = 37 ° C = 37 + 273 = 310 K Using Arrhenius equation we get, ln K 1 K 2 = E a R 1 T 2 − 1 T 1 On substitution we get: ln 5 . 0 × 10 - 4 3 × 5 . 0 × 10 - 4 = E a 1 . 987 1 320 − 1 300 ⇒ E a = 10478 . 12 cal mol - 1 Calculation of Arrhenius constant A : ln K = ln A - E a RT ⇒ log A = 7 . 63 + log 5 . 0 × 10 - 4 Or, log A = 4 . 32 Hence, the rate constant at T 3 is: log K = log A - E a 2 . 303 RT = 4 . 32 - 7 . 38 = - 3 . 06 ⇒ K = 8 . 71 × 10 - 4 min - 1

Derive the formula of first order reaction for the half-life period t 1 / 2 (graph is not required).

For a first order reaction, the rate constant, k = 2 . 303 t log R 0 R . Let t 1 / 2 represents the half-life period of the reaction. When t = t 1 / 2 , R = R 0 2 , therefore, the above equation becomes, k = 2 . 303 t 1 / 2 log R 0 R 0 2 Or k = 2 . 303 t 1 / 2 log 2 = 2 . 303 × 0 . 3010 t 1 / 2 = 0 . 693 t 1 / 2 Therefore, t 1 / 2 = 0 . 693 k .

Derive the formula of first order reaction for the rate constant k .

The reaction in which, the overall rate of the reaction is proportional to the first power of concentration of one of the reactants only is called first order reaction. R → P Rate of reaction = - d R dt = k R 1 , where k is the rate constant of the first order reaction. Let the initial concentration of the reactant be R 0 mol dm - 3 and the concentration at any time t be R mol dm - 3 . Therefore, the rate of the reaction at a time t is given by - d R dt = k R , on rearranging, d R R = - kdt -----(i) Integrating the equation (i), ∫ d R R = ∫ - kdt ln R = - kt + C ------(ii), where C is the constant of integration. When t = 0 , R = R 0 , therefore, the equation (ii) becomes ln R 0 = 0 + C or ln R 0 = C . Substituting the value of C in the equation (ii), ln R = - kt + ln R 0 kt = ln R 0 R Therefore, k = 2 . 303 t log R 0 R , this is an expression for rate constant for a first order reaction. This can also be written as k = 2 . 303 t log a a - x , where a and a - x represent the concentration of the reactant in the beginning and after a time t respectively.

Write two differences between order of reaction and molecularity.

The differences between order of reaction and molecularity are given below: Molecularity Order (i) This is the number of reacting species that take part in an elementary reaction. (i) The sum of powers to which the reactant concentrations are raised in the rate law equation is known as the order of the reaction. (ii) The molecularity of a reaction is always a whole number. (ii) It can be a whole number, or a fraction, or zero.

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR CHEMISTRY>Chapter -1 - Chemical Kinetics>Gujarat Board-2020>Q 15

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