Question

An excited ozone molecule, O3*, in the atmosphere can undergo one of the following reactions,O3* → O3 (1) fluorescenceO3* → O + O2 (2) decompositionO3* + M → O3 + M (3) deactivation,where M is an inert molecule, the rate constant for the fluorescence reaction is k1, the rate constant for the decomposition reaction is k2, and the rate constant for the deactivation reaction is k3. Write a simplified expression for the fraction, X, of ozone molecules undergoing deactivation in terms of the rate constants. (Use the following as necessary: k1, k2, k3, cO for [O3*], and cM for [M].)

Answer 1

The simplified expression for the fraction is
`\text {X} = \frac{ {k_3 * cM} }{k_1 +k_2 + k_3 }`

Step-by-step explanation:

From the given information:

O3* → O3 (1) fluorescence

O + O2 (2) decomposition

O3* + M → O3 + M (3) deactivation

The rate of fluorescence = rate of constant (k₁) × Concentration of reactant (cO)

The rate of decomposition is = k₂ × cO

The rate of deactivation = k₃ × cO × cM

where cM is the concentration of the inert molecule

The fraction (X) of ozone molecules undergoing deactivation in terms of the rate constants can be expressed by using the formula:

`\text {X} = \frac{ \text {rate of deactivation} }{ \text {(rate of fluorescence) +(rate of decomposition) + (rate of deactivation) } } }`

`\text {X} = \frac{ {k_3 * cO * cM} }{ {(k_1 * cO) +(k_2 * cO) + (k_3 * cO * cM) } }`

`\text {X} = \frac{ {k_3 * cO * cM} }{cO (k_1 +k_2 + k_3 * cM) }`

`\text {X} = \frac{ {k_3 * cM} }{k_1 +k_2 + k_3 }` since cM is the concentration of the inert molecule