The decomposition of N2 O5 has an activation energy of 103 kJ / mol and a frequency factor of 4

step 1 So here we're given an example of a specific reaction with an activation energy of 103 kilojoule

The decomposition of N2 O5 has an activation energy of 103...

The decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ has an activation energy of $103 \mathrm{~kJ} / \mathrm{mol}$ and a frequency factor of $4.3 \times 10^{13} \mathrm{~s}^{-1}$ What is the rate constant for this decomposition at (a) $25^{\circ} \mathrm{C}$ and (b) $373 \mathrm{~K}$ ?

The decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ has an activation energy of $103 \mathrm{~kJ} / \mathrm{mol}$ and a frequency factor of $4.3 \times 10^{13} \mathrm{~s}^{-1}$ What is the rate constant for this decomposition at
(a) $25^{\circ} \mathrm{C}$ and
(b) $373 \mathrm{~K}$ ?

Key Concepts

Temperature Effects in Kinetics

Temperature plays a crucial role in chemical kinetics by affecting the kinetic energy of molecules. In the Arrhenius equation, temperature is expressed in Kelvin to ensure consistent energy units. A rise in temperature increases the fraction of molecules exceeding the activation energy, thereby accelerating the reaction rate. Conversely, lower temperatures result in slower reaction rates due to a lower proportion of high-energy particles.

Rate Constant

The rate constant is a proportionality factor in the rate equation that quantifies the intrinsic speed of a chemical reaction at a given temperature. It is directly influenced by both the activation energy and the frequency factor, and its value is determined using the Arrhenius equation. The rate constant provides insight into how fast a reaction proceeds under specific conditions.

Frequency Factor

The frequency factor, or pre-exponential factor, in the Arrhenius equation represents the frequency of collisions and the orientation of reactant molecules that are effective for a reaction to occur. It embodies the idea that even when reactants have sufficient energy to overcome the activation barrier, their collisions must be properly oriented to result in a reaction.

Activation Energy

Activation energy is the minimum energy that reacting molecules must possess for a successful collision leading to a chemical reaction. It acts as a barrier that must be overcome for reactants to convert into products. In the context of the Arrhenius equation, a higher activation energy results in a lower reaction rate because fewer molecules have the necessary energy to react at a given temperature.

Arrhenius Equation

The Arrhenius equation is a fundamental expression in chemical kinetics that relates the rate constant of a reaction to the temperature, the activation energy, and a frequency factor. It is expressed as k = A exp(-Ea/RT), where k represents the rate constant, A is the frequency or pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the absolute temperature in Kelvin. This equation highlights how temperature and energy barriers influence the speed of a chemical reaction.

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