Question

The temperature at which the average velocity of oxygen becomes equal to that of methane at 327ºC is​

Answer 1

Answer:

(image from Kinetic Temperature)

There’s a lot of problems with this question, no doubt starting with the fact that a single molecule doesn’t have an “average speed”- only groups of molecules do. And we don’t have any idea what pressure the gas is, or how close oxygen gas molecules will act toward ideality. But it’s clear that the question is a homework problem of some form, so it probably does have an intended answer. Likely, it requires rotely remembering some kind of formula, probably for ideal gases. As such, you can look up said formulas. For example:

(image from Root Mean Square, Average, Median Velocity of Gas Calculator)

So the question is asking T where c(rms)=c(ave). Square both sides, and reduce the constants on both sides (M and R), and you get

3*27 = 8x/π, x=31.8C

So, the problem rests with you- why is this answer incorrect?

Well, first I could use Kelvin.

3*300.15K = 8x/π, x= 353.6K or 80.45C.

So the units of measure matter, and you need to use absolute temperature units like Kelvin or Rankine to get the right answer. In all likelihood, the question is an attempt to trip up the student relying on rote memorization or cribbing from internet sources, like I just did. They want you to understand the underlying properties of a Maxwell-Boltzmann distribution, rather than memorize a bunch of formulas for computing various types of averages, means, etcetera.

Explanation: