# How to calculate the concentration after a certain timespan from the specific reaction constant?

I've been going crazy with this question for the past 4 hours. I can't find much help in google because it's not a traditional "find the velocity of the reaction" question. It's fine if you don't give me the answer, just teach me how to get there:

A container at $30~^\circ\mathrm{C}$ contains $\ce{HNC_{(g)}}$ reacting to form $\ce{HCN_{(g)}}$. Knowing that the specific reaction constant is $4.4\cdot10^{-4}~\mathrm{s}^{-1}$ and that you initially have $1~\mathrm{g}$ of $\ce{HNC}$: how many moles of each gas are in the container after one hour and a half?

I'm pretty sure that the reaction is reversible here. However, I have no idea how to calculate how many moles of each gas will there be after $1.5~\mathrm{h}$ (even if it was not reversible).

I have many doubts: Did they skip the concentration because there's only one reactant? Does $K$ take into account the $30~^\circ\mathrm{C}$? What's the equation for "change of concentration over time" here?!

How can I figure out how many moles of $\ce{HNC}$ and $\ce{HCN}$ the container will have after 90 minutes?

EDIT: Thanks for the comments! I get your points and edited the post. However, how can I figure out how many moles of $\ce{HCN}$ I have after 90 minutes ignoring the fact that it's a reversible reaction?.

• Where did you get the idea that the reaction formed an equilibrium at equal amounts of HNC and HCN? In truth, the equilibrium is quite favoured towards products; hydrogen isocyanide is a rather unstable molecule. For this problem, you don't really need to think about chemical equilibrium at all (or equivalently, assume the equilibrium constant is infinite). – Nicolau Saker Neto May 15 '14 at 3:42
• I think that because it is such a slow reaction that you don't reach equilibrium in 90 minutes. The provided rate is for the specified temperature of 30°C. For a first approximation, I would treat it as only a forward reaction to see what the concentrations would be. If the HCN concentration is still small (in comparison), I would go with that. – LDC3 May 15 '14 at 3:42
• Okay thanks a lot! I understand. However, how can I figure out how many moles of HCN I have after 90 minutes? – Sebs May 15 '14 at 4:16
• Because the rate constant is $4.4\times 10^{-4} s^{-1}$, it tells us that it is a first order reaction. If you look at this section in Wikipedia, you should see the direction to go. en.wikipedia.org/wiki/Rate_equation#First-order_reactions – LDC3 May 15 '14 at 5:19 