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

step 1 The activation energy and the rate constant are related to each other via our heinous equation w

For the reaction N2 O5( g) ⟶2 NO2( g)++(1)/(2) O2( g) the...

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, $E_{1}$

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, $E_{1}$

Key Concepts

Temperature Dependence of Reaction Rates

Temperature affects chemical reaction rates by altering the kinetic energy of the molecules involved. As temperature increases, more molecules have sufficient energy to overcome the activation energy barrier, resulting in a higher rate constant and, consequently, a faster reaction. This temperature dependence is quantitatively described by the Arrhenius equation, making it a central concept in the study of reaction kinetics.

Rate Constant

The rate constant is a proportionality factor in the rate law of a chemical reaction that quantifies the speed at which the reaction proceeds. It is influenced by factors such as temperature and the activation energy of the reaction. The precise value of the rate constant at a given temperature can be determined experimentally and is crucial for predicting reaction behavior under various conditions.

Activation Energy

Activation energy is the minimum amount of energy required for the reactants to undergo a transformation into products. It represents the energy barrier that must be overcome for a reaction to proceed. A higher activation energy implies that fewer molecules possess the necessary energy to react at a given temperature, leading to a slower reaction rate, while a lower activation energy corresponds to a faster reaction rate.

Arrhenius Equation

The Arrhenius equation is a fundamental relationship in chemical kinetics that describes how the rate constant of a reaction depends on temperature and activation energy. It is typically written in the form k = A exp(-E_a/(RT)), where k is the rate constant, A is the pre-exponential factor or frequency factor, E_a is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation serves as the basis for understanding how temperature influences the speed of chemical reactions.

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