The average life time of methane in the atmosphere, is | TestHub

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Methane is an important greenhouse gas since it absorbs infrared radiation. To calculate its concentration in the atmosphere, one needs to know the processes that release methane into the atmosphere and what happens to it in atmosphere.

While it is produced from a variety of natural and human-related sources, it is mainly consumed by reaction with the hydroxyl radical, which is a simple elementary reaction:

$C H_{4} +^{.} O H \to C H_{3} \cdot + H_{2} O$

with a rate constant equal to $4 \times 1 0^{6} M^{- 1} s^{- 1}$ .

It is also known that in the atmosphere, $^{.} O H$ radicals are constantly produced and removed, so their concentration is approximately constant and is equal to $1 \times 1 0^{- 15} M$ . Similar to methane, isoprene is also released in significant amounts and has absorbing power. It is also removed in a similar manner with a rate constant equal to $2 \times 1 0^{11} M^{- 1} s^{- 1}$ .

Also, the average lifetime of a reactant following first-order kinetics is $t_{a vg} = 1/ K$ . Using this information, answer the questions that follow.

The average life time of methane in the atmosphere, is

Options:

Answer:

B

Solution:

Given:

$k = 4 \times 1 0^{6} M^{- 1} s^{- 1}$

$[O H] = 1 \times 1 0^{- 15} M$

Pseudo first-order constant:

$k^{'} = k [O H]$

$k^{'} = 4 \times 1 0^{6} \times 1 0^{- 15}$

$k^{'} = 4 \times 1 0^{- 9} s^{- 1}$

Average lifetime:

$t_{a vg} = \frac{1}{k ^{'}}$

$t_{a vg} = \frac{1}{4 \times 1 0 ^{- 9}}$

$t_{a vg} = 2.5 \times 1 0^{8} sec$

$t_{a vg} = 25 \times 1 0^{7} sec$

Stream:JEESubject:ChemistryTopic:Chemical KineticsSubtopic:First Order Reactions

⏱ 2mℹ️ Source: QB

Chemistry - Chemical Kinetics Question with Solution | TestHub

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