The first order rate constant for the decomposition of ethyl iodide by the reaction C 2 H 5 I g ⟶ C 2 H 4 g + HI g at 600 K is 1 . 60 × 10 - 5 s - 1 . Its energy of activation is 209 kJ / mol . Calculate the rate constant of the reaction at 700 K

Given that: T 1 = 600 K , k 1 = 1 . 60 × 0 - 5 s - 1 T 2 = 700 K , k 2 = ? , E a = 209 kJ / mol By the Arrhenius equation, log k 2 k 1 = E a 2 . 303 R T 2 - T 1 T 1 × T 2 Substituting the values, log k 2 k 1 = 209 × 1000 J mol - 1 2 . 303 × 8 . 314 Jk - 1 mol - 1 700 - 600 600 × 700 k = 209000 19 . 147 100 420000 = 2090 19 . 147 × 42 log k 2 k 1 = 2 . 6 k 2 k 1 = antilog ( 2 . 6 ) k 2 = k 1 × 398 . 12 Substitute the value of k 1 k 2 = 1 . 60 × 10 - 5 × 398 . 12 k 2 = 0 . 00636 k 2 = 6 . 36 × 10 - 3 s - Hence, the answer.

The value of rate constant for a second order reaction is 6 . 7 × 10 - 5 mol - L s - at 298 K and 1 . 64 × 10 - 4 mol - L s - at 313 K . Find the Arrhenius frequency factor A and activation energy of the reaction.

Given that: k 1 = 6 . 7 × 10 - 5 mol - 1 L - 1 s - , T 1 = 298 K k 2 = 1 . 64 × 10 - 4 mol - 1 L - 1 s - , T 2 = 313 K By the Arrhenius equation, log k 2 k 1 = E a 2 . 303 R T 2 - T 1 T 1 T 2 Substituting the values, log 6 . 7 × 10 - 5 1 . 64 × 10 - 4 = E a 2 . 303 × 8 . 314 313 - 298 313 × 298 log ( 0 . 4 ) = Ea × 15 19 . 147 × 93274 1 . 8 = E a 8 . 4 × 10 - 6 E a = 46279 J mol - 1 E a = 46 . 279 kJ mol - 1 We know, the rate constant by Arrhenius equation is given by: k = Ae - E a RT Taking log on both sides, we have log k = log A - E a RT log e log k = log A - E a 2 . 303 RT log A = logk + E a 2 . 303 RT log A = log ( 6 . 7 ) + 46279 2 . 303 × 8 . 314 × 298 = 0 . 8260 + 8 . 239 log A = 9 . 065 A = Antilog ( 9 . 065 ) A = 8649 . 48 collisions s - Hence, solved.

If a first order reaction has activation energy of 25000 cal and a frequency factor of 5 × 10 12 sec - 1 , at what temperature will the reaction rate have a half-life of 1 minute? [Hint. k = 0 . 693 t 1 / 2 for a first order reaction.]

A first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants. The Arrhenius equation is k = Ae ( - E a / R T ) where A = frequency exponential factor e - Ea / RT the fraction of collisions that have enough energy to overcome the activation barrier (i.e., have energy greater than or equal to the activation energy ) at temperature T. As we know , k = Ae - Ea / RT and k = 0 . 693 t 1 / 2 c onverting half - time 1 min = 60 sec ; Activation Eneegy 25000 Cal into kJmol - we get 104 . 6 kJ / mol So , 0 . 693 t 1 / 2 0 = Ae - Ea / RT Substituting , 0 . 693 / 60 = 5 × 10 12 e - 104 . 5 / RT T = 370 K

If a first order reaction has activation energy of 25000 cal and a frequency factor of 5 × 10 12 sec - 1 , at what temperature will the reaction rate have a half-life of 80 days? [Hint. k = 0 . 693 t 1 / 2 for a first order reaction.]

A first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants. The Arrhenius equation is k = Ae ( - E a / R T ) where A = frequency exponential factor e-Ea/RT the fraction of collisions that have enough energy to overcome the activation barrier (i.e., have energy greater than or equal to the activation energy ) at temperature T. As we know , k = Ae - Ea / RT and k = 0 . 693 t 1 / 2 converting half - time 80 min = 60 x 80 sec = 4800 Activation Energy 25000 Cal into kJmol - we get 104 . 6 kJ / mol So , 0 . 693 t 1 / 2 0 = Ae - Ea / RT Substituting , 0 . 693 / 4800 = 5 × 10 12 e - 104 . 5 / RT T = 277 K

The rate constant for the decomposition of a hydrocarbon 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?

Given that: Rate constant, k = 2 . 418 × 10 - 5 s - , at T = 546 K Energy of activation, E a = 179 . 9 kJ / mol Thus, by Arrhenius equation, k = Ae - E a / RT Taking log on both sides, log k = log A - E a 2 . 303 RT log e ∵ log e = 1 log k = log A - E a 2 . 303 R . 1 T log A = log k + E a 2 . 303 R . 1 T = log ( 2 . 418 × 10 - 5 ) + 179 . 9 × 10 3 J / mol 2 . 303 × 8 . 314 × 546 = ( - 5 + 0 . 3834 ) + 17 . 2081 log A = 12 . 5924 s - A = antilog ( 12 . 5924 ) A = 3 . 912 × 10 2 s - Hence, the answer.

HARD

12th West Bengal Board

IMPORTANT

Earn 100

The rate constants of a reaction at $500 K$ and $700 K$ are $0.02 s^{- 1}$ and $0.07 s^{- 1}$ respectively. Calculate the values of $E_{a}$ and A.

Important Questions on Chemical Kinetics

HARD

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 32

The first order rate constant for the decomposition of ethyl iodide by the reaction

C_{2} H_{5} I_{(g)} ⟶ C_{2} H_{4} (g) + {HI}_{(g)}

600 K

1.60 \times 10^{- 5} s^{- 1}

. Its energy of activation is

209 kJ / mol .

Calculate the rate constant of the reaction at

700 K

HARD

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 33

The value of rate constant for a second order reaction is

6.7 \times 10^{- 5} {mol}^{-} L s^{-}

298 K

and

1.64 \times 10^{- 4} {mol}^{-} L s^{-}

313 K .

Find the Arrhenius frequency factor A and activation energy of the reaction.

HARD

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 34

Rate constant $k$ of a reaction varies with temperature according to equation:

$\log k =$ constant $- \frac{E_{a}}{2.303 R} \cdot \frac{1}{T}$

What is the activation energy for the reaction. When a graph is plotted for $\log k$ versus $\frac{1}{T},$ a straight line with a slope $- 6670 K$ is obtained. Calculate energy of activation for this reaction $(R = 8.314 {JK}^{- 1} {mol}^{- 1})$

MEDIUM

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 35

If a first order reaction has activation energy of $25000 cal$ and a frequency factor of $5 \times 10^{12} \sec^{- 1},$ at what temperature will the reaction rate have a half-life of $1$ minute? [Hint. $k = \frac{0.693}{t_{1 / 2}}$ for a first order reaction.]

EASY

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 35

If a first order reaction has activation energy of $25000 cal$ and a frequency factor of $5 \times 10^{12} \sec^{- 1},$ at what temperature will the reaction rate have a half-life of $80$ days?

[Hint. $k = \frac{0.693}{t_{1 / 2}}$ for a first order reaction.]

MEDIUM

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 36

The activation energy for a first order reaction is

60 kJ {mol}^{- 1}

in the absence of a catalyst and

50 kJ {mol}^{- 1}

in the presence of a catalyst. How many times will the rate of reaction grow in the presence of the catalyst if the reaction proceeds at

27 ° C ?

MEDIUM

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 37

For a reaction, the energy of activation is zero. What is the value of rate constant at

300 K,

k = 1.6 \times 10^{6} s^{-}

280 K ?

HARD

12th West Bengal Board

IMPORTANT

NEW SYSTEMATIC MODERN CHEMISTRY>Chapter 4 - Chemical Kinetics>Follow Up Problems>Q 38

The rate constant for the decomposition of a hydrocarbon is

2.418 \times 10^{- 5} s^{- 1}

546 K .

If the energy of activation is

179.9 kJ / mol,

what will be the value of pre-exponential factor?

The rate constants of a reaction at 500 K and 700 K are 0.02 s-1 and 0.07 s-1 respectively. Calculate the values of Ea and A.

Important Questions on Chemical Kinetics

Learn and Prepare for any exam you want !

The rate constants of a reaction at $500 K$ and $700 K$ are $0.02 s^{- 1}$ and $0.07 s^{- 1}$ respectively. Calculate the values of $E_{a}$ and A.