Doubts on Diffusion/ Effusion of gases at different pressures Let's start with a question:  


  "One mole of nitrogen gas at 0.8 atm takes 38 s to diffuse through a pinhole, whereas one mole of an unknown compound of Xenon with fluorine at 1.6 atm  takes 57 s to diffuse through the same hole. Calculate the molecular formula of the compound."  


It is a question where pressures of the gases are not similar. Could be solved quite easily, if we calculate the rates of diffusion ($r_{N_2}$ and $r_{un}$) of each gas separately as no. of moles of the respective gas diffused per unit time, find the ratio of the rates and then equate this ratio, with another ratio found using pressures and molar masses of the given gases, i.e, with 
$$\frac{r_{N_2}}{r_{un}}= \frac{p_1}{p_2}\sqrt{\frac{M_{un}}{M_{N_2}}}$$, ($M_{un}$ and $M_{N_2}$ are molar masses of the unknown gas and nitrogen gas respectively) and finally find the no. of fluorine atoms attached with xenon from the value of molar mass of the unknown gas.

It's fine that way. But we also know that, volumes of a gas diffused per unit time gives us rate of diffusion too. And in the question above, the volumes (in case they were given instead of moles) would have been different because of different pressures. Consequently, the first ratio (the ratio involving volume and time) would have been different compared to the ratio involving moles and time. And that would have affected the final value of molar mass and thus messed up our solution.
So my question is, what would be the actual cause of such a situation? And how to fare in those situations?
"But we also know that, volumes of a gas diffused per unit time gives us rate of diffusion too. And in the question above, the volumes (in case they were given instead of moles) would have been different because of different pressures."


If you wanted to measure the effused gas in terms of volume, you had to somehow calculate this volume from the number of moles effused. This volume has nothing to do with the volume or the pressure inside the vessel from which the gas effused.

[edit]

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

From the number of particles that escaped to the right, you could calculate a volume, given an arbitrary pressure (e.g. standard pressure). With this you could express the rate of diffusion in units of volume per time unit.