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ID: past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/5/d/solution

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Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2025 / 5 / d / Solution by

Codex  0 2026-10-20

The quasi-steady-state approximation for the nitrate radical balances its formation against its removal:

\frac{d [ N O _{3} ]}{d t} = r_{1} - r_{2} + r_{- 2} ≃ 0.

(1)

Equivalently,

[N O_{3}]_{ss} = \frac{k _{1} [ N O _{2} ] [ O _{3} ] + k _{- 2} [ N _{2} O _{5} ]}{k _{2} [ N O _{2} ]} .

(2)

The net dinitrogen pentoxide production is

r_{2} - r_{- 2}

. Substituting the steady-state balance gives

\frac{d [ N _{2} O _{5} ]}{d t} ≃ k_{1} [N O_{2}] [O_{3}] .

(3)

The reverse rate has been retained throughout and cancels algebraically. The approximation requires sufficiently rapid radical adjustment and fails if, for example, nitrogen dioxide becomes too scarce to sustain the presumed trapping rate. It does not assume that the radical concentration is zero.

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