AP Chemistry
5.6 Reaction Energy Profile
5.5 Collision Model
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.
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 \(\dfrac{\text{Rate}_{310\text{ K}}}{\text{Rate}_{300\text{ K}}} = 2.0\)?
\[ 2\text{ N}_2\text{O}_5\text{(g)} \rightarrow 4\text{ NO}_2\text{(g)} + \text{O}_2\text{(g)} \]
The initial rate data collected by the student are shown in the table below.
| Trial | Temperature (\(\text{K}\)) | 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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