The decomposition of NOCl, 2 NOCl ⟶2 NO+ Cl2, has k=9.3 ×10^-5 L mol^-1 s^-1 at 100^∘ C and k

step 1 So in this question, we're given the decomposition of NOCL, and we're going to use the Glazius -

The decomposition of NOCl, 2 NOCl ⟶2 NO+ Cl2, has k=9.3...

The decomposition of $\mathrm{NOCl}, 2 \mathrm{NOCl} \longrightarrow 2 \mathrm{NO}+$ $\mathrm{Cl}_{2}$, has $k=9.3 \times 10^{-5} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $100^{\circ} \mathrm{C}$ and $k=$ $1.0 \times 10^{-3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $130^{\circ} \mathrm{C}$. What is $E_{\mathrm{a}}$ for this reaction in $\mathrm{kJ} \mathrm{mol}^{-1}$ ? Use the data at $373 \mathrm{~K}$ to calculate the frequency factor, $A$. What is the rate constant at $473 \mathrm{~K}$ ?

The decomposition of $\mathrm{NOCl}, 2 \mathrm{NOCl} \longrightarrow 2 \mathrm{NO}+$
$\mathrm{Cl}_{2}$, has $k=9.3 \times 10^{-5} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $100^{\circ} \mathrm{C}$ and $k=$
$1.0 \times 10^{-3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $130^{\circ} \mathrm{C}$. What is $E_{\mathrm{a}}$ for this
reaction in $\mathrm{kJ} \mathrm{mol}^{-1}$ ? Use the data at $373 \mathrm{~K}$ to calculate the frequency factor, $A$. What is the rate constant at $473 \mathrm{~K}$ ?

Key Concepts

Arrhenius Equation

The Arrhenius Equation relates the rate constant of a reaction to the temperature and activation energy using the formula k = A exp(–Ea/(RT)). This equation is fundamental in chemical kinetics for understanding how temperature changes affect the speed of a reaction, and it can be linearized to determine kinetic parameters from experimental data.

Activation Energy

Activation energy (Ea) is the minimum energy that reacting molecules must possess to undergo a chemical transformation. It reflects the sensitivity of a reaction’s rate to temperature changes and can be determined from the slope of a plot of ln k versus 1/T using the Arrhenius Equation. Lower activation energies generally lead to faster reactions under given conditions.

Frequency Factor

The frequency factor (A) in the Arrhenius Equation represents the rate at which collisions occur with the correct orientation to trigger a reaction. It is an important parameter that, together with activation energy, determines the overall rate constant. Calculating A helps to understand the intrinsic reactivity of the chemical process independent of the energy barrier.

Rate Constant

The rate constant (k) is a proportionality factor in the rate law that quantifies how quickly a reaction proceeds. In the context of the Arrhenius Equation, it is influenced by both the frequency factor and the activation energy. Understanding k is crucial for predicting the behavior of chemical reactions under various temperature conditions.

Temperature Conversion and Dependence

Accurate kinetic calculations require using the absolute temperature scale (Kelvin) since the Arrhenius Equation is based on absolute temperature. Converting temperatures from degrees Celsius to Kelvin is essential for correctly applying the equation and predicting how changes in temperature will affect the reaction rate.

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