Thermodynamics Question

[maxx52188]

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2A -> B + C

This is a first order reaction



True or false, the rate of consumption of A is half the rate of disappearance of A.

The answer is true, and I have no reasons that it is.

 

[bxadook]

First off, wouldn't rates of consumption be equal to rates of disappearance?? Forgive me if I am wrong. The only way I can think of finding out the answer to this problem algebraically is by this method.

The rate of consumption of A is determined by the coefficient 2. The rate is negative due to consumption. So here we go. We can use the rate law expression since they tell us that the reaction order is first overall.
Using rate law:
rate = k[A] (I don't understand how this could be "disappearance" it is a positive value, this is where I am also confused. Are you sure it is not appearance?)
And using a related rates expression:
rate = -d[A]/2dt (I think this would be consumption, because it is a negative rate.)

You can set these two rates equal to each other:

-d[A]/2dt=k[A]


And you can clearly see that one of the rates is half of the other.

Hope this helps.. 👍

 

[maxx52188]

First off, wouldn't rates of consumption be equal to rates of disappearance?? Forgive me if I am wrong. The only way I can think of finding out the answer to this problem algebraically is by this method.

The rate of consumption of A is determined by the coefficient 2. The rate is negative due to consumption. So here we go. We can use the rate law expression since they tell us that the reaction order is first overall.
Using rate law:
rate = k[A] (I don't understand how this could be "disappearance" it is a positive value, this is where I am also confused. Are you sure it is not appearance?)
And using a related rates expression:
rate = -d[A]/2dt (I think this would be consumption, because it is a negative rate.)

You can set these two rates equal to each other:

-d[A]/2dt=k[A]


And you can clearly see that one of the rates is half of the other.

Hope this helps.. 👍

well heres the thing. I now remember my professor saying there was a grammatical error in the true or false section, so this much be it.

Now im even more confused...how can we have a rate of APPEARANCE if this is a degregation?

Are we assuming we flipped the equation and are now comparing A like this?

B + C -> 2A
vs.
2A -> B + C

Cause then what you said makes total sense,

 

[bxadook]

Yeah, I was somewhat confused from what you could tell..
But you can always have a rate of appearance, even though this is a degradation. You can infer that this is possible due to the conditions of equilibrium. A reaction in chemical equilibrium has not stopped. It is balanced by the forward and reverse reactions. Therefore it is theoretically possible to determine the rates of consumption vs the rates of appearance, obviously that rate would have to be determined by its position relative to equilibrium (Q) during the reaction.

Or maybe it could be determined by a simple change in rate expression like:

rateoverall = (rate consumption) - (rate appearance) Dont use this by the way it is just an idea hehe. And obviously in this case rate consumption > rate appearance. Hence the rate is negative.

Kind of getting ahead of MCAT material, but this is just my 2 cents.

 

[maxx52188]

Yeah, I was somewhat confused from what you could tell..
But you can always have a rate of appearance, even though this is a degradation. You can infer that this is possible due to the conditions of equilibrium. A reaction in chemical equilibrium has not stopped. It is balanced by the forward and reverse reactions. Therefore it is theoretically possible to determine the rates of consumption vs the rates of appearance, obviously that rate would have to be determined by its position relative to equilibrium (Q) during the reaction.

Or maybe it could be determined by a simple change in rate expression like:

rateoverall = (rate consumption) - (rate appearance) Dont use this by the way it is just an idea hehe. And obviously in this case rate consumption > rate appearance. Hence the rate is negative.

Kind of getting ahead of MCAT material, but this is just my 2 cents.

Cool dude, thanks so much...and i just realized this isnt thermodynamics...jesus finals has me in shambles.

 

[addo]

as a side note, this is a kinetics question. Thermodynamics deals with equilibrium, while kinetics deals with rates. An important distinction to keep in mind for the mcat, it has come up several times in practice questions ive done.