How to derive partial gas equation? If the following gasses are to mix, what is the partial pressure of neon?
  
  


The correct answer is 0.1. I cannot figure out how my professor derived this equation. From the ideal gas law, all I can arrive to is this:

$P_x = \frac{P_tV_t}{V_x}$

This gives me an answer of 4.4, which is obviously incorrect.

I've determined the equation he used is as follows:

$P_x = \frac{P_xV_x}{V_t}$

which gives the correct answer of 0.1. How did he arrive to this answer?
The total pressure of the system is:

$\frac{1.0\times0.5+1.0\times0.4+2.0\times0.2}{1.0+1.0+2.0}=1.3/4=0.325$

i.e. just the sum of the $PV$s divided by the sum of the $V$s.  Then $0.325$ is the sum of the partial pressures by the Law of Partial Pressures.  So this at least suggest that the individual partial pressures are near $0.1$.

Can you figure out how to parcel out the individual pressures from here?