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AP Chemistry
5.6 Reaction Energy Profile
5.5 Collision Model
AdvancedMCQProportional AnalysisConceptual19.7k
A student investigates the kinetics of the gas-phase decomposition of dinitrogen pentoxide at three different temperatures under identical initial concentrations:

\[ 2\text{ N}_2\text{O}_5\text{(g)} \rightarrow 4\text{ NO}_2\text{(g)} + \text{O}_2\text{(g)} \]

The initial rate data collected by the student are shown in the table below.

TrialTemperature (\(\text{K}\))Initial Rate (\(\text{M}\cdot\text{s}^{-1}\))
1\(300\)\(1.2 \times 10^{-4}\)
2\(310\)\(2.4 \times 10^{-4}\)
3\(320\)\(4.8 \times 10^{-4}\)

Between Trial 1 and Trial 2, the absolute temperature increases by approximately \(3.3\%\) (from \(300\text{ K}\) to \(310\text{ K}\)), whereas the initial reaction rate increases by \(100\%\) (a factor of \(2.0\)). Which of the following proportional relationships and explanations correctly accounts for the observation that the rate ratio \(\dfrac{\text{Rate}_{310\text{ K}}}{\text{Rate}_{300\text{ K}}} = 2.0\)?

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