[Sebs]

Hello everyone and thanks in advance for your help.
I've this simple question which I'm not sure if I solved correctly. Can anyone tell me where did I go wrong? Also, I can't seem to figure out how to solve the second part. Any ideas?


A container at 30∘C contains HNC(g) reacting to form HCN(g). Knowing that the specific reaction constant is 4.4⋅10⁻⁶ s^-1 and that you initially have 1 g of HNC: how many moles of each gas are in the container after one hour and a half? What's the yield of the reaction at that point? (when one our and a half has passed)


So I started this way: I know it's a first order reaction because the constant is in 1/seconds. Also, even if it's a reversible reaction we can ignore that fact because the reaction time is so slow it doesn't make a difference. Knowing that, my equation to know the concentration after 90 minutes is simple:

ln[A] = -kt ln[A]₀   ----------->  [A] = [A]₀ * e^(-kt)

So I have to get the concentration first. In order to do that, I need to know the volume, so I plug the data in the ideal gas law assuming a pressure of 101 kpa. I know that 1 gram of HNC contains 1/27 moles of HNC, therefore:

PV = nRT
V = (1/27mol * 8.31 * 303K) / 101 kpa
V = 0.94 liters


After that I calculate molarity

1/27mol
-------      =   0.0394 liters/mol.
0.94 liters


Then I put those values on my Rate law equation (90 minutes = 5400 seconds):

[A] = 0.0394 mol/liter * e^(-4.403 1/seconds * 10^-4 * 5400seconds)
[A] = 0.03847 mol/liter concentration of HNC after 90 minutes

After that I know by simple math:

0.0394 concentration ______ 1/27 (~0.037) moles
0.03847 concentration _____ X = 0.03616 moles of HNC after 90 minutes.

To know the amount of HCN I just have to substract them:

1/27 - 0.03616 = ~ 0.00088 moles/liter of HCN after 90 minutes!

Reversing the molarity to know moles is silly cause I truncated the result so if I multiply
0.00088 * 0.94 = ~0.00085 still, so It's safe to say that I have ~0.00085 moles of HCN after 90 minutes.

So If I did everything right that's it. However, I've no clue how to answer the yield question. There's no way to find out the theoretical yield, cause the reaction is reversible (which we are ignoring here). Am I right? Is this a part of yield that I don't know about?


Thanks a lot in advance!!

[Borek]

I have just skimmed, two things caught my attention:

1. I don't think you have to assume pressure nor use ideal gas equation. In the equation

[tex][A] = [A]_0 e^{-kT}[/tex]

volume cancels out, and you are left with just

[tex]n_A = n_{A0} e^{-kT}[/tex]

2. Theoretical yield is most likely related to 100% conversion (even if the reaction never goes there).

[Sebs]

Thank you very much for the answer!

Okay I understood what you said about yield, and according to that then the yield is 2.23%. Great!

You make a really good point about volume. However something bothers me: if volume cancels out where should I put the 30 degrees I'm given as information? Is it there just to confuse me?

Thanks a lot!!

[Borek]

Apparently it is of no use here.

[Sebs]

You've helped me a lot. Thank you very much!!!