What Is the Partial Pressure of Methyl Isonitrile After 12.8 Hours?

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Discussion Overview

The discussion revolves around calculating the partial pressure of methyl isonitrile after a specified time, given a rate constant and initial pressure. The context includes aspects of chemical kinetics, particularly focusing on first-order reactions and the application of logarithmic equations in solving the problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant notes the need for concentration data to solve the problem, expressing uncertainty about how to begin.
  • Another participant states that partial pressure is proportional to concentration, suggesting that assuming a first-order reaction might be necessary.
  • A different participant highlights the lack of information about the reaction type, speculating that it could involve rearrangement to acetonitrile and questioning the assumption of first-order kinetics.
  • One participant presents a solution using the first-order reaction equation, calculating the partial pressure to be 10 torr, but raises a concern about solving the problem without a calculator.
  • Another participant agrees with the calculation and emphasizes that it would be unreasonable to expect students to solve such problems without calculators unless they involve simple numbers.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the assumptions needed for the calculation, particularly about the reaction order and the lack of specific details about the reaction. There is no consensus on how to approach the problem without a calculator, as opinions vary on the expectations for such assessments.

Contextual Notes

The discussion reveals limitations in the provided information, including the absence of the reaction type and the units of the rate constant, which are critical for determining the reaction order and solving the problem accurately.

brake4country
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Homework Statement


The rate constant for the conversion of methyl isonitrile is 5 x 10^-5. A scientist has a container containing this substance with a partial pressure of 100 torr. After 12.8 hours (46,000 seconds), what is the partial pressure of methyl isonitrile gas inside the container?

Homework Equations


PV = nRT

The Attempt at a Solution


I tried to attempt this problem using concentrations but they were not given. I have no idea where to start...
 
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Partial pressure is directly proportional to the concentration, so as long as there is no change in volume/total pressure they can be used interchangeably (simple conclusion of the Avogadro's law). But I have a different problem - I don't see how to solve, unless you are expected to assume first order reaction.
 
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Yes it sounds you are supposed to assume this. If we'd been told the units of the rate constant that would have told us. Bad! But if the OP knows what the question will have that answered.

We're not even told what the reaction is. Again from the absence of information we'd guess probably just rearrangement to acetonitrile. Again quite plausibly but not necessarily that is just a monomolecular internal movement that could be first order.
 
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Yes, I just realized that the book has this equation: log [A]t=-kt/2.303 + log[A]0 for a first order reaction. So this is a first order reaction. This looks like plug and chug:

log[A]t = -(5x10-5)(46000)/2.303) + log [100]
log[A] = -1+2 = log[A} = 1 therefore, the answer is 10 torr.

My other question is that I had to use a calculator for this problem but the test does not allow calculators. How best to approach this type of problem without a calculator? Thanks in advance!
 
brake4country said:
Yes, I just realized that the book has this equation: log [A]t=-kt/2.303 + log[A]0 for a first order reaction. So this is a first order reaction. This looks like plug and chug:

log[A]t = -(5x10-5)(46000)/2.303) + log [100]
log[A] = -1+2 = log[A} = 1 therefore, the answer is 10 torr.

My other question is that I had to use a calculator for this problem but the test does not allow calculators. How best to approach this type of problem without a calculator? Thanks in advance!

In general you can't. It would not be reasonable to ask you do so and it will not happen - unless the problem had nice round numbers like this one. It was reasonable to expect you to know the log of 100 and the antilog of 1.

You would find it kinda useful often if you mastered an art of mentally converting 1st order rate constants to half-lives.

So would I. :biggrin:
 

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