Kinetics question: calculating rate constants

[annnoyyying]

Homework Statement

I need help for this kinetics question:

Chlorination of butene at 0 degrees c, liquid phase, dichloromethane as solvent.
initial concentration of butene is 0.1M
conversion of 47.71% achieved after 3.1 hours.
an additional 0.5M of hot butene was added at this point, which increased the temperature of the mixture to 10 degrees c
after another 20mins the concentration of the alkene in the mixture is 0.52M.

Determine the value of the rate constant at 0 degrees C and its temperature dependence.

2. Relevant equation
2nd order integral: 1/[A] = 1/[A]0 +kt

3. The Attempt at a Solution
The reaction will form 1,2 - dichlorobutene due to presence of a non-protic solvent and low reaction temperatures.
I'm guessing the overall order of reaction is 2, mainly because the transition state involves a molecule of chlorine and a molecule of butene. However I do not know the order of reaction in respect to each of the reactants.
For the 1st reaction (at 0 degrees);
concentration of butene at 3.1 hrs is 0.05229 M
reaction rate is 2.565e-4 M/min
As the initial concentrations of both reactants are the same, and using the equation for the 2nd order integral the rate constant at 0 degrees would be 0.0491 L/mol . min.
Then I'm stuck after this. To be honest I'm not even sure if my answers/ logic above is even correct...

Thanks in advance!

 

[epenguin]

Homework Statement

I need help for this kinetics question:

Chlorination of butene at 0 degrees c, liquid phase, dichloromethane as solvent.
initial concentration of butene is 0.1M
conversion of 47.71% achieved after 3.1 hours.
an additional 0.5M of hot butene was added at this point, which increased the temperature of the mixture to 10 degrees c
after another 20mins the concentration of the alkene in the mixture is 0.52M.

Determine the value of the rate constant at 0 degrees C and its temperature dependence.

2. Relevant equation
2nd order integral: 1/[A] = 1/[A]0 +kt

3. The Attempt at a Solution
The reaction will form 1,2 - dichlorobutene due to presence of a non-protic solvent and low reaction temperatures.
I'm guessing the overall order of reaction is 2, mainly because the transition state involves a molecule of chlorine and a molecule of butene. However I do not know the order of reaction in respect to each of the reactants.
For the 1st reaction (at 0 degrees);
concentration of butene at 3.1 hrs is 0.05229 M
reaction rate is 2.565e-4 M/min
As the initial concentrations of both reactants are the same, and using the equation for the 2nd order integral the rate constant at 0 degrees would be 0.0491 L/mol . min.
Then I'm stuck after this. To be honest I'm not even sure if my answers/ logic above is even correct...

Thanks in advance!

A pretty horrible question apparently but I question whether you have reported it correctly. For instance the first bolded sentence doesn't mean too much. Please report the question verbatim. Including what you say in the second bolded sentence, if that was given in the problem. Was the 'relevant equation' given in the question? You will have to decide what is meant by the question 'it's temperature dependence' if that was really what was asked, but anyway revise the theory of how chemical reactions depend on temperature.

 

[annnoyyying]

A pretty horrible question apparently but I question whether you have reported it correctly. For instance the first bolded sentence doesn't mean too much. Please report the question verbatim. Including what you say in the second bolded sentence, if that was given in the problem. Was the 'relevant equation' given in the question? You will have to decide what is meant by the question 'it's temperature dependence' if that was really what was asked, but anyway revise the theory of how chemical reactions depend on temperature.

Heres the original:
The chlorination of 1-butene was studied in a batch reactor at 0C in the liquid phase using dichloromethane as solvent. Using 0.1 mol/L of alkene and chlorine, a conversion of 47.71% of the originally present alkene was measured after 3.1 hours of reaction time. At this point an additional 0.5 mol/L of hot alkene was added, increasing the temperature of the reaction mixture to 10C (assume the temperature increase occurred instantaneously). After another 20 minutes the concentration of the alkene in the mixture was measured as 0.52 mol/L.
Determine the value of the rate constant at 0C and its temperature dependence.

The relevant equation wasn't given in the problem. This is the integral equation assuming that it is a 2nd order reaction (before adding hot alkene). Temperature dependence is probably comparing the rate constants calculated from the reaction at 0C and 10C.

Thanks.

 

[epenguin]

I do not have time this morning to check calculations or do much. Especially when questions are so, frankly, poorly framed you must state the assumptions you have to make in your answers. Your assumption of 2nd order reaction is very reasonable. There is a well known equation about halving time for a second order reaction which is all I would have used except they have given you the final concentration not quite half but to a ridiculous precision. But you can use it as a check. Rate constants to my best knowledge always use seconds in units, not any others, though it is not actually wrong to use minutes but you don't want to be the only one. For the second half of the question you will have to state some assumption about the chlorine concentration. (If its all used up in the reaction you cannot calculate any rate constant!)

 

[annnoyyying]

For the second half of the question you will have to state some assumption about the chlorine concentration. (If its all used up in the reaction you cannot calculate any rate constant!)

This is the part where I'm stuck on...
The chlorine concentration is going to be small compared to butene concentration by at least 10 fold.
Assume that the concentration of butene remains relatively constant (i.e. at 0.52M) compared to chlorine. The 2nd order reaction becomes pseudo-first order in respect to chlorine?
Then the rate constant equation becomes:
k = (1/t*)ln([Cl2]0/[Cl2})
Then I would need the final concentration of chlorine, or the fractional conversion, which is not given...

Thank you.

 

[epenguin]

Did you do the check I mentioned and was the result OK?

I suppose the second part is done in the same volume e.g. same full vessel as the first. Then if no chlorine is added, yes you'll have approximately pseudo-first order kinetics.

Surprised you can't see how to work out the final amount of chorine.

 

[annnoyyying]

Did you do the check I mentioned and was the result OK?

I suppose the second part is done in the same volume e.g. same full vessel as the first. Then if no chlorine is added, yes you'll have approximately pseudo-first order kinetics.

Surprised you can't see how to work out the final amount of chorine.

Yes I have checked, its fine.Thank you.

 

[Borek]

Don't worry about steps, look just at totals.

How much butene was put (in total) into the vessel? How much was left? How much reacted?

 

[annnoyyying]

Don't worry about steps, look just at totals.

How much butene was put (in total) into the vessel? How much was left? How much reacted?

0.6M butene in total, 0.52M remaining, 0.08M reacted?
thank you.

 

[Borek]

Wasn't that hard

 

[annnoyyying]

Wasn't that hard

OMG I feel so stupid.
Thank you very much!

 

[epenguin]

Conservation of mass holds aiways and is used all the time in chemistry, not just in problems labelled "stoichiometry". That might be the most important lesson to have learned from this rather academic-sounding excercise in kinetics.

Yes I have checked, its fine.Thank you.

I have heard "I have got it now!" so often here that I have just ammended my sig.