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Question: The rate constant of a second order reaction is \({10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}}\) . Th...

The rate constant of a second order reaction is 10−2lit.mole−1.sec⁡−1{10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}} . The rate constant when expressed as cc.molecule−1.min⁡−1cc.{molecule^{ - 1}}.{\min ^{ - 1}} is:
A. 9.96×10−229.96 \times {10^{ - 22}}
B.9.96×10−239.96 \times {10^{ - 23}}
C.9.96×10−219.96 \times {10^{ - 21}}
D.9.96×10−249.96 \times {10^{ - 24}}

Explanation

Solution

We are given the rate constant of a second order reaction to be 10−2lit.mole−1.sec⁡−1{10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}}. We will try to find the relation and convert moles into a number of molecules, litres into cubic centimetre and second into minutes. And finally we will put it in 10−2lit.mole−1.sec⁡−1{10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}} to find the required answer.

Complete step by step answer:
As the rate constant of a second order reaction is given 10−2lit.mole−1.sec⁡−1{10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}}and we have to find the rate constant of the second order reaction in the unit cc.molecule−1.min⁡−1cc.{molecule^{ - 1}}.{\min ^{ - 1}} . We know that
1L=103cm3 1mol=6.022×1023 1sec⁡=160min⁡  1L = {10^3}c{m^3} \\\ 1mol = 6.022 \times {10^{23}} \\\ 1\sec = \dfrac{1}{{60}}\min \\\
We will have to put the required units of volume , mole and time in 10−2lit.mole−1.sec⁡−1{10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}} to find the answer in cc.molecule−1.min⁡−1cc.{molecule^{ - 1}}.{\min ^{ - 1}}, We will have to do it carefully so that we can avoid calculation error. So:
10−2lit.mole−1.sec⁡−1 =10−2.103cc6.022×1023molecule.160min⁡=9.96×10−22cc.molecule−1.min⁡−1  {10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}} \\\ = \dfrac{{{{10}^{ - 2}}{{.10}^3}cc}}{{6.022 \times {{10}^{23}}molecule.\dfrac{1}{{60}}\min }} = 9.96 \times {10^{ - 22}}cc.{molecule^{ - 1}}.{\min ^{ - 1}} \\\
From the above explanation and calculation it is clear to us that

The correct answer of the given question is option: A. 9.96×10−229.96 \times {10^{ - 22}}

Additional information:
The Rate constant is a proportional constant of the equation which expresses the Relation between the rate of the chemical equation and the concentrations of the reactants of the chemical equation. One mole of a substance contains 6.022×10236.022 \times {10^{23}}particles. This is a special number and it is also known as the Avogadro’s number or Avogadro constant. It is named after the great scientist Amedeo Avogadro. Amedeo Avogadro was from Italy.

Note:
Always remember that one mole has 6.022×10236.022 \times {10^{23}}particles , one litre is equal to 103cm3{10^3}c{m^3}. One minute has sixty seconds. Always try to avoid silly mistakes and calculation errors while solving the numerical. To convert a given value in it’s different unit, always use the concept of units and dimensions as used in the above question.