NOCl decomposes as: 2 NOCl ⟶2 NO+Cl2, and has k=9.3 ×10^-5 L mol^-1 s^-1 at 100^∘ C and k=1.0

step 1 There's multiple parts to this question. First, given the chemical reaction and the rate constan

NOCl decomposes as: 2 NOCl ⟶2 NO+Cl2, and has k=9.3 ×10^-5...

NOCl decomposes as: $2 \mathrm{NOCl} \longrightarrow 2 \mathrm{NO}+\mathrm{Cl}_{2},$ and 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 $E_{2}$ 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 describes how the rate constant of a chemical reaction depends on temperature, showing that the rate increases exponentially as the temperature increases. It is expressed as k = A exp(-Ea/RT), where k is the rate constant, A is the frequency factor or pre?exponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature. This equation is a central concept in chemical kinetics, linking the microscopic molecular behavior to macroscopic reaction rates.

Activation Energy

Activation energy is the minimum energy barrier that must be overcome for reactants to transform into products. It is an indicator of the sensitivity of the reaction rate to temperature changes; higher activation energies result in a greater change in the rate constant with temperature according to the Arrhenius equation. Determining Ea helps in understanding the mechanism and the energy profile of the reaction.

Frequency Factor

The frequency factor (A), sometimes called the pre-exponential factor, represents the frequency of collisions and the proper orientation of molecules for a successful reaction. It is a constant that reflects the number of times reactants approach the activation barrier per unit time, and its value is influenced by factors such as molecular size and the complexity of the reaction. Calculating A is essential for accurately modeling and predicting reaction behavior at different temperatures.

Rate Constant

The rate constant (k) is a proportionality factor in the rate equation that quantifies the speed at which a chemical reaction occurs. Its value is temperature-dependent, as described by the Arrhenius equation. Changes in the rate constant with temperature can provide insights into the energy requirements and mechanistic details of a reaction, making it a key parameter in chemical kinetics.

Transcript

00:01 There's multiple parts to this question.

00:05 First, given the chemical reaction and the rate constant at two different temperatures, you're asked to determine the activation energy.

00:14 The activation energy can be determined by taking the equation in your textbook that has two activation energies and two temperatures as variables and rearranging it to solve for just activation energy.

00:27 That's what i did here, where activation energy is equal to r, natural log of k2 over k1 divided by 1 over t1 minus t2 where these are kelvin temperatures.

00:40 I'll then plug in my values, natural log of the second k value at the higher temperature, divided by the first k value at the lower temperature, and then divide that whole thing by kelvin temperatures.

00:55 We're given temperatures in celsius, so we need to add on 273 to the 100 celsius, and we need to add on 273 to the 130.

01:02 Celsius, and i get ea of 98 ,900 joules per mole, or 98 .9 kilojoules per mole.

01:12 It then wants us to calculate the frequency factor at 373 kelvin.

01:19 So we'll use a different form of the uranus equation.

01:22 The different form of the uranus equation is one over the frequent, it can be rearranged, so one over the frequency factor is equal to e to the negative ea over rt divided by the rate constant.

01:37 Well, ea, i determined up here.

01:39 The temperature they told me to use is 373, and then the k value will be the k value at 373.

01:49 That also is provided...

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