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title: "A student compares two hypothetical bimolecular gas-phase reactions being evaluated for use in a pollutant sensor. The reactant pairs are at the same temperature and have the same initial concentrations. Each successful collision forms one product molecule. The student obtains the following estimates.  | Reaction | Collision frequency, \\(Z\\) (\\(\\text{collisions}\\,\\text{L}^{-1}\\text{s}^{-1}\\)) | Fraction with energy \\(\\ge E_a\\), \\(f_E\\) | Fraction of energetic collisions with a productive orientation, \\(p\\) | |———-|————————————————————————————-|———————————————-|————————————————————————–| | \\(1\\) | \\(2.0\\times10^{12}\\) | \\(1.0\\times10^{-4}\\) | \\(1.0\\times10^{-2}\\) | | \\(2\\) | \\(2.0\\times10^{10}\\) | \\(1.0\\times10^{-2}\\) | \\(1.0\\times10^{-1}\\) |  Which choice correctly compares the initial rates of product formation and explains the comparison?"
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url: "https://nerd-notes.com/ubq/120057/"
date_modified: "2026-08-21T08:41:01+00:00"
---

# A student compares two hypothetical bimolecular gas-phase reactions being evaluated for use in a pollutant sensor. The reactant pairs are at the same temperature and have the same initial concentrations. Each successful collision forms one product molecule. The student obtains the following estimates.

| Reaction | Collision frequency, \(Z\) (\(\text{collisions}\,\text{L}^{-1}\text{s}^{-1}\)) | Fraction with energy \(\ge E_a\), \(f_E\) | Fraction of energetic collisions with a productive orientation, \(p\) |
|———-|————————————————————————————-|———————————————-|————————————————————————–|
| \(1\) | \(2.0\times10^{12}\) | \(1.0\times10^{-4}\) | \(1.0\times10^{-2}\) |
| \(2\) | \(2.0\times10^{10}\) | \(1.0\times10^{-2}\) | \(1.0\times10^{-1}\) |

Which choice correctly compares the initial rates of product formation and explains the comparison?

A student compares two hypothetical bimolecular gas-phase reactions being evaluated for use in a pollutant sensor. The reactant pairs are at the same temperature and have the same initial concentrations. Each successful collision forms one product molecule. The student obtains the following estimates.

| Reaction | Collision frequency, \(Z\) (\(\text{collisions}\,\text{L}^{-1}\text{s}^{-1}\)) | Fraction with energy \(\ge E_a\), \(f_E\) | Fraction of energetic collisions with a productive orientation, \(p\) |
|----------|-------------------------------------------------------------------------------------|----------------------------------------------|--------------------------------------------------------------------------|
| \(1\) | \(2.0\times10^{12}\) | \(1.0\times10^{-4}\) | \(1.0\times10^{-2}\) |
| \(2\) | \(2.0\times10^{10}\) | \(1.0\times10^{-2}\) | \(1.0\times10^{-1}\) |

Which choice correctly compares the initial rates of product formation and explains the comparison?

- **A.** Reaction \(2\) has an initial rate \(10\) times that of reaction \(1\), because the rate depends on \(Zf_Ep\), and the larger energetic and orientation fractions for reaction \(2\) more than offset its lower collision frequency.
- **B.** Reaction \(2\) has an initial rate \(10\) times that of reaction \(1\), because its lower collision frequency allows more energy to be available in each collision, increasing the fraction of successful collisions.
- **C.** The two reactions have equal initial rates, because \(Zf_E\) has the same value for both reactions and every collision with energy \(\ge E_a\) forms products regardless of orientation.
- **D.** Reaction \(1\) has an initial rate \(10\) times that of reaction \(2\), because \(Zp\) is \(10\) times larger for reaction \(1\), and the activation-energy barrier affects only how rate changes with temperature.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120057/*