# Calculating the rate constant

#### jpe1

Hi Guys,
Ive got the following equation 2CH4 + O2 -> C2H4 + H2O. I need to find the rate constant, but don't know the activation energy so cant use the Arrhenius equation. I tried using the Eyring equation but dont have the values for the enthalpy and entropy of activation. Does anyone know how to solve this?

#### jpe1

Hi Guys,
Ive got the following equation 2CH4 + O2 -> C2H4 + H2O. I need to find the rate constant, but don't know the activation energy so cant use the Arrhenius equation. I tried using the Eyring equation but dont have the values for the enthalpy and entropy of activation. Does anyone know how to solve this?

In addition to this I know the reaction is running at 1073K.

#### studiot

To obtain the rate constants for this reaction you need a mechanism because this is a catalysed reaction which leads to a multistep analysis.

I note that there have been several papers in the last 10 years, studying this reaction with different catalysts.
Unfortunately I no longer have access to the professional databases holding these papers so can only see the abstracts.

At a pinch you could try the simplest catalysed reaction sequence

$$\displaystyle C + R\mathop \mathbin{\lower.3ex\hbox{\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}}} \limits_{{k_{ - 1}}}^{{k_1}} CR\mathop \to \limits^{{k_2}} C + P$$

Where C refers to the catalyst, R to the reactants and P to the products.

and

$$\displaystyle {K_s} = \frac{{{k_{ - 1}} + {k_2}}}{{{k_1}}}$$

is the Michaelis rate contant.

Edit, Dan can you help with the mathmL it doesn't seem to want to parse?

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#### jpe1

To obtain the rate constants for this reaction you need a mechanism because this is a catalysed reaction which leads to a multistep analysis.

I note that there have been several papers in the last 10 years, studying this reaction with different catalysts.
Unfortunately I no longer have access to the professional databases holding these papers so can only see the abstracts.

At a pinch you could try the simplest catalysed reaction sequence

$$\displaystyle C + R\mathop \mathbin{\lower.3ex\hbox{\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}}} \limits_{{k_{ - 1}}}^{{k_1}} CR\mathop \to \limits^{{k_2}} C + P$$

Where C refers to the catalyst, R to the reactants and P to the products.

and

$$\displaystyle {K_s} = \frac{{{k_{ - 1}} + {k_2}}}{{{k_1}}}$$

is the Michaelis rate contant.

Edit, Dan can you help with the mathmL it doesn't seem to want to parse?View attachment 318
Hi
Thank you for getting back to me. I hadn't considered Mechelis Menton. Ive rewritten K_s in terms of concentration as I dont have values for k1, k_-1 or k2 and got:
K_s = ([C]^3[P] [R]^2)/ [CR]^3 where [R] = [CH4]^2 [O2] and [P] = [C2H6] [H2O]^2
I am unsure how to work out the concentration of CR. Ill add in some numbers to explain my issue better.
If I have 1 mol of cataylst, 10 moles of CH4 and 5 moles of O2 per 1m^3, this gives the concentrations as [C]=1, [CH4] =10, [O2]=5. If 95% of the reactants are used up, then this means the outlet stream has the composition of the outlet as 1 mol Catalyst, 0.5 mol CH4, 0.25 mol O2, 4.75 mol C2H6 and 9.5 mol H2O. as the volume will still be one the conc of the product will be [4.75] [9.5]^2.
The only thing I need now is the concentration of CR, how do if calculate this as I dont have values for k1, k_-1 or k2?

#### topsquark

Forum Staff
I should probably update the LaTeX forum with this.

I had to look this up on the net. Most of the coding is simpler if you use certain packages but I don't know if we use any of them or not.

This is the basic element.
$$\displaystyle A \overset{U}{\underset{D} \rightleftarrows} X$$
A \overset{U}{\underset{D} \rightleftarrows} X

$$\displaystyle C + R \overset{k_1} {\underset{k_{-1}} \rightleftarrows} CR \overset{k_1}{ \rightarrow} C + P$$
C + R \overset{k_1} {\underset{k_{-1}} \rightleftarrows} CR \overset{k_1}{ \rightarrow} C + P

-Dan

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