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Standard XII

Chemistry

Half life

At 380∘C, t...

Question

At $380^{\circ}$ C, the half-life period for the first-order decomposition of $H_{2} O_{2}$ is 360 min. The energy of activation of the reaction is 200 kJ mol $^{- 1}$ . Calculate the time required for 75% decomposition at $450^{\circ} C$ ?

20.4 minutes

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21.6 minutes

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26.7 minutes

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30.2 minutes

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Solution

The correct option is A 20.4 minutes
As we know,

$k = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{360} = 0.001925$

and $E_{a} = 200$ kJ mol $^{- 1}$

$ln \frac{k_{2}}{k_{1}} = ln \frac{t_{1 / 2 (1)}}{t_{1 / 2 (2)}} = - \frac{E_{a}}{R} \times (\frac{1}{T_{2}} - \frac{1}{T_{1}})$

On substitution we get,

$t_{1 / 2 (2)} = 0.693 / k = 10.2$ min at $450^{0}$ C

So time required for 75% decomposition is $2 t_{1 / 2} = 20.4$ min.

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Similar questions

Q. At

380^{\circ} C

, the half-life period for the first order decomposition of

H_{2} O

is 360 min. The energy of activation of the reaction is 200 kJ

m o l^{- 1}

. Calculate the time required for 75% decomposition at

450^{\circ} C

Q. At

380^{o} C

, the half-life period for the first order decomposition of

H_{2} O_{2}

is 360 min. The energy of activation of the reaction is

200 k J m o l^{- 1}

. The time required for 25% decomposition at

450^{o} C

in minutes (nearest integer) is :

Q. At

380^{\circ} C

, the half-life period for the first order decomposition of

H_{2} O_{2}

360 m i n

. The energy of activation of the reaction is

200 k J / m o l^{1}

. Calculate the time required for

75

% decomposition at

450^{\circ}

.
Use :

[\frac{1}{653} - \frac{1}{723}] = 1.48 \times 10^{- 4}, e^{14.8} = 2.67 \times 10^{6}

Q. A first order reaction,

A \to B

, requires activation energy of 70 kJ

m o l^{- 1}

. When a 20% solution of A was kept at

25^{\circ} C

for 20 minutes, 25% decomposition took place. What will be the percent decomposition in the same time in a 30% solution maintained at

40^{\circ} C

? Assume that activation energy remains constant in this range of temperature.

Q. A first order reaction,

A \to B,

requires activation energy of

70 k J m o l^{- 1}

. When a solution of A was kept at

25^{\circ} C

for 20 minutes, 25 percent decomposition took place. What will be the percent decomposition in the same time if solution maintained at

40^{\circ} C

? Assume that activation energy remains constant in this range of temperature.

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At 380∘C, the half-life period for the first-order decomposition of H2O2 is 360 min. The energy of activation of the reaction is 200 kJ mol−1. Calculate the time required for 75% decomposition at 450∘C?

The correct option is A 20.4 minutesAs we know,k=0.693t1/2=0.693360=0.001925and Ea=200 kJ mol−1lnk2k1=lnt1/2(1)t1/2(2)=−EaR×(1T2−1T1)On substitution we get,t1/2(2)=0.693/k=10.2 min at 4500CSo time required for 75% decomposition is 2t1/2=20.4 min.

At $380^{\circ}$ C, the half-life period for the first-order decomposition of $H_{2} O_{2}$ is 360 min. The energy of activation of the reaction is 200 kJ mol $^{- 1}$ . Calculate the time required for 75% decomposition at $450^{\circ} C$ ?