Doubts on Diffusion/ Effusion of gases at different pressures
"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.

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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.