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The reaction 2NO2 → 2NO + O2 obeys the rate law: rate = 1.4 x 10-2[NO2]2 at 500 K . What would be the rate constant at 119 K if the activation energy is 80. kJ/mol? This is a second order reaction, giving k the units of M-1S-1 This will not change with the change in temperature. Do not include units in your answer. Exponential numbers need to be entered like this: 2 E-1 means 2 x 10-1. The rate constant, k, at 119 K equals:

Respuesta :

Answer : The value of rate constant at temperature 119 K is 2.46 E-29

Explanation :

As we are the rate law expression as:

[tex]Rate=1.4\times 10^{-2}[NO_2]^2[/tex]  ..........(1)

The general rate law expression will be:

[tex]Rate=k[NO_2]^2[/tex]       ............(2)

By comparing equation 1 and 2 we get:

[tex]k=1.4\times 10^{-2}[/tex]

Now we have to calculate the rate constant at temperature 119 K.

According to the Arrhenius equation,

[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]

or,

[tex]\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]

where,

[tex]K_1[/tex] = rate constant at [tex]T_1[/tex]  = [tex]1.4\times 10^{-2}[/tex]

[tex]K_2[/tex] = rate constant at [tex]T_2[/tex] = ?

[tex]Ea[/tex] = activation energy for the reaction = 80.0 kJ/mole = 80000 J/mole

R = gas constant = 8.314 J/mole.K

[tex]T_1[/tex] = initial temperature = 500 K

[tex]T_2[/tex] = final temperature = 119 K

Now put all the given values in this formula, we get:

[tex]\log (\frac{K_2}{1.4\times 10^{-2}})=\frac{80000J/mole}{2.303\times 8.314J/mole.K}[\frac{1}{500}-\frac{1}{119}][/tex]

[tex]K_2=2.46\times 10^{-29}=2.46E-29[/tex]

Therefore, the value of rate constant at temperature 119 K is 2.46 E-29

Lanuel

Based on the calculations, the rate constant at a temperature of 119 K is equal to [tex]2.46 \times 10^{-29}[/tex]

Given the following data:

Activation energy = 80.0 kJ/mole = 80000 J/mole

Ideal gas constant = 8.314 J/mole.K.

Initial temperature = 500 K

Final temperature = 119 K.

Rate constant = [tex]1.4 \times 10^{-2}[/tex]

What is the rate law?

Rate law can be defined as a chemical equation that is typically used to relate the initial (forward) rate of a chemical reaction with respect to the concentrations or pressures of the chemical reactants and other constant parameters.

Mathematically, the rate law is given by this formula:

[tex]R = K[A]^x[B]^y[C]^z[/tex]

Where:

  • k is the rate constant.
  • A is the concentration of reactant A.
  • B is the concentration of reactant B.
  • C is the concentration of reactant C.
  • x, y, and z are the order of the reaction.

In order to calculate the rate constant at temperature 119 K, we would apply the Arrhenius equation:

[tex]Log (\frac{k_2}{k_1} )=\frac{E_a}{2.303R} [\frac{1}{T_1} -\frac{1}{T_2}]\\\\Log (\frac{k_2}{1.4 \times 10^{-2}} )=\frac{80000}{2.303 \times 8.314} [\frac{1}{500} -\frac{1}{119}]\\\\Log (\frac{k_2}{1.4 \times 10^{-2}} )=4178.169[-0.006403]\\\\k_2=2.46 \times 10^{-29}[/tex]

Read more on rate constant here: brainly.com/question/24749252

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