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

A container at $$30~^\circ\pu{C}$$ contains $$\ce{HNC_{(g)}}$$ reacting to form $$\ce{HCN_{(g)}}$$. Knowing that the specific reaction constant is $$4.4\cdot10^{-4}~\pu{s-1}$$ and that you initially have $$\pu{1 g}$$ 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 $$\pu{1.5 hrs}$$ (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 $$30~^\circ\pu{C}$$?
• 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, 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 