Rate constant and partial pressure

In summary: 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
  • #1
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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  • #2
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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  • #3
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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  • #4
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!
 
  • #5
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:
 

1. What is a rate constant?

A rate constant, also known as a rate coefficient, is a proportionality constant that relates the rate of a chemical reaction to the concentrations of the reactants. It is a measure of the reaction's speed and is specific to a particular reaction at a specific temperature.

2. How is the rate constant determined?

The rate constant can be determined experimentally by measuring the initial rate of reaction at different concentrations of reactants and plotting the data on a graph. The slope of the graph is equal to the rate constant. It can also be calculated using the Arrhenius equation, which takes into account the temperature dependence of the rate constant.

3. What factors affect the rate constant?

The rate constant is affected by temperature, concentration of reactants, and the presence of a catalyst. A higher temperature usually leads to a higher rate constant as molecules have more energy to overcome the activation energy barrier. Higher concentrations of reactants also increase the rate constant as there are more collisions between molecules. A catalyst can also lower the activation energy, thus increasing the rate constant.

4. What is the relationship between rate constant and partial pressure?

The rate constant is directly proportional to the partial pressure of reactants in a gaseous reaction. This is because an increase in partial pressure leads to an increase in the number of collisions between gas molecules, effectively increasing the reaction rate. However, this relationship is only valid for reactions where the partial pressure is the only variable affecting the rate constant.

5. Can the rate constant change during a reaction?

The rate constant is usually considered to be constant during a reaction, as long as the temperature and concentration of reactants remain constant. However, for some reactions, the rate constant may change due to factors such as a change in temperature or the presence of a catalyst. Therefore, it is important to determine the rate constant experimentally for each specific reaction and conditions.

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