How many times faster will nitrogen dioxide gas effuse than sulfur trioxide?

1 Answer
Truong-Son N.
May 10, 2018

Gases have speeds proportional to #sqrt(1/M)#, such as the root-mean-square speed

#v_(RMS) = sqrt((3RT)/M)#.

So, the ratio of effusion speeds is simply the ratio of the speeds:

#v_2/v_1 = sqrt(M_1/M_2)#

This is known as Graham's law of effusion. We know that #"NO"_2# has a molar mass of #"46.005 g/mol"# and #"SO"_3# has a molar mass of #"80.062 g/mol"#. Thus,

#v_2/v_1 = sqrt("46.005 g/mol"/"80.062 g/mol")#

#= 0.758#

The lighter gas is faster... From this result, calculate the factor to which #"NO"_2# is faster than #"SO"_3#. Which gas is #1# and which gas is #2#?

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