Name: Methods of Determination of Order of Reactions
Uploaded: 2019-07-19
Duration: 2 min 47 s
Description: There are various methods to ascertain the order of reactions. Let’s watch the video and learn some of the important methods for the determination of the ord...

Question

Two reactions, (i)

A \to

Products, (ii)

B \to

Products, follow first order kinetics. The rate of reaction (i) is doubled when the temperature is raised from

300 K

to

310 K

. The half- life of this reaction at

310 K

is

10 \min

. At the same temperature,

B

decomposes twice as fast as

A

. Calculate the energy of activation for reaction (i) and calculate the rate constant of reaction (ii), at

300 K

.

Accepted Answer

Given : $T_{1} = 300 K$ and $T_{2} = 310 K$

$k_{2} = 2 k_{1}$ .

Solution : $\log_{10} (\frac{k_{2}}{k_{1}}) = \frac{E_{a}}{2.303 R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})$

Value of gas constant $(R) = 8.314 J {mol}^{- 1} K^{- 1}$ .

Putting the given values in the formula : $\log_{10} (\frac{2 k_{1}}{k_{1}}) = \frac{E_{a}}{2.303 \times 8.314} (\frac{1}{300} - \frac{1}{310})$

$\log_{10} (2) = \frac{E_{a}}{2.303 \times 8.314} (\frac{310 - 300}{310 \times 300}) 0.301 = \frac{E_{a}}{19.15} (\frac{10}{93000}) E_{a} = \frac{536.06 \times 1000}{10} = 53.6 \times 10^{3} J {mol}^{- 1}$

The value of activation energy comes out be $53.6 kJ {mol}^{- 1}$ .

Activation energy for the second reaction = $\frac{53.6 kJ {mol}^{- 1}}{2} = 26.8 kJ {mol}^{- 1}$ .

Calculation of rate constant of second reaction : $k = \frac{0.693}{t_{\frac{1}{2}}} = \frac{0.693}{10} = 0.0693 \min^{- 1}$ .

Arrhenius equation can be given as : $logk = logA - \frac{E_{a}}{2.303 RT}$

$\log 0.0693 = logA - \frac{26 . . 8 \times 1000}{19.15 \times 310} - 1.159 = logA - 4.514 logA = 3.335$

Rate constant for the first reaction can be calculated as : ${logk}_{A} = logA - \frac{E_{a}}{2.303 RT}$

${logk}_{A} = 3.335 - \frac{53600}{19.15 \times 300} {logk}_{A} = 3.335 - 9.329 = - 5.994 k_{A} = 2.49 \times 10^{- 3} \min^{- 1}$

Experiment	$[A] M$	$[B] M$	Initial rate $mol L^{- 1} s^{- 1}$
$1$	$0.50$	$0.5$	$1.6 \times 10^{- 4}$
$2$	$0.50$	$1.0$	$3.2 \times 10^{- 4}$
$3$	$1.00$	$1.0$	$3.2 \times 10^{- 4}$

$t / s$	$0$	$30$	$60$
${CH}_{3} {OCH}_{3} / mol L^{- 1}$	$0.60$	$0.30$	$0.15$

Important Questions on Chemical Kinetics

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