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# The rate constant of a second order reaction is ${10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}}$ . The rate constant when expressed as $cc.{molecule^{ - 1}}.{\min ^{ - 1}}$ is:A. $9.96 \times {10^{ - 22}}$B.$9.96 \times {10^{ - 23}}$C.$9.96 \times {10^{ - 21}}$D.$9.96 \times {10^{ - 24}}$

Last updated date: 07th Aug 2024
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Hint: We are given the rate constant of a second order reaction to be ${10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}}$. 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 ${10^{ - 2}}lit.mol{e^{ - 1}}.{\sec ^{ - 1}}$ to find the required answer.

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

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

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 $6.022 \times {10^{23}}$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.
Always remember that one mole has $6.022 \times {10^{23}}$particles , one litre is equal to ${10^3}c{m^3}$. 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.