For the reaction N2 O5( g) ⟶2 NO2( g)+(1)/(2) O2( g) the rate constant k at 25^∘ C is 3.46 ×10^-

Name: Problem 61, Chapter 13: Chemistry: The Molecular Science
Uploaded: 2021-11-10T20:04:56-08:00
Duration: 1 min 44 s
Channel: David Collins
Description: For the reaction N2 O5( g) ⟶2 NO2( g)+(1)/(2) O2( g) the rate constant k at 25^∘ C is 3.46 ×10^-5 s^-1 and at 55^∘ C it is 1.5 ×10^-3 s^-1 . Calculate the activation energy, Ea.

step 1 To calculate the activation energy from two rate constants at two different temperatures, we nee

Question

For the reaction $$\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})$$ the rate constant $k$ at $25^{\circ} \mathrm{C}$ is $3.46 \times 10^{-5} \mathrm{~s}^{-1}$ and at $55^{\circ} \mathrm{C}$ it is $1.5 \times 10^{-3} \mathrm{~s}^{-1} .$ Calculate the activation energy, $E_{\mathrm{a}}$.

   For the reaction
$$\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})$$
the rate constant $k$ at $25^{\circ} \mathrm{C}$ is $3.46 \times 10^{-5} \mathrm{~s}^{-1}$ and at $55^{\circ} \mathrm{C}$ it is $1.5 \times 10^{-3} \mathrm{~s}^{-1} .$ Calculate the activation energy, $E_{\mathrm{a}}$.

Chemistry: The Molecular Science

John W. Moore,… 3rd Edition

Chapter 13, Problem 61

Instant Answer

Solved by Expert David Collins

11/10/2021

Step 1

Step 1: We start by using the Arrhenius equation in the form: $$\ln \left(\frac{k_1}{k_2}\right) = \frac{E_a}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$ where $k_1$ and $k_2$ are the rate constants at temperatures $T_1$ and $T_2$ respectively, $E_a$ is the Show more…

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For the reaction $$\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})$$ the rate constant $k$ at $25^{\circ} \mathrm{C}$ is $3.46 \times 10^{-5} \mathrm{~s}^{-1}$ and at $55^{\circ} \mathrm{C}$ it is $1.5 \times 10^{-3} \mathrm{~s}^{-1} .$ Calculate the activation energy, $E_{\mathrm{a}}$.

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Key Concepts

Arrhenius Equation

The Arrhenius equation describes the quantitative relationship between the rate constant of a reaction and the temperature. It shows that as temperature increases, the rate constant increases exponentially, reflecting the increased fraction of molecules that have enough energy to overcome the activation energy barrier.

Rate Constant

The rate constant is a proportionality factor in the rate law that quantifies the speed of a reaction. It is influenced by both the activation energy and the temperature, and its temperature dependence is described by the Arrhenius equation.

Activation Energy

Activation energy is the minimum amount of energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products and is a fundamental parameter in chemical kinetics, influencing how much the reaction rate increases with temperature.

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