How can I find the ratio of molecular masses using the ideal gas equation?


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> A person evacuated a cylinder and filled in $4~\mathrm{g}$ of gas A at $25~\mathrm{^\circ C}$. Pressure was found to be $1~\mathrm{atm}$. Another person filled another $8~\mathrm{g}$ of gas B in the cylinder at the same temperature. The final pressure was found to be $1.5~\mathrm{atm}$. What is the ratio of molecular masses of A and B (assuming ideal gas behaviour)? 
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I tried to do it this way:


Taking the molecular mass of A as $x\ \mathrm{g}$ and that of B as $y\ \mathrm{g}$, I formed the respective ideal gas equations but the required terms ($x$ and $y$) just cancelled out. 


$$N(a) = 4/x ;\quad N (b) = 8/y$$  

So$$V (a) = \frac{4 \times 22.4}{x};\quad V (b) = \frac{8 \times 22.4}{y}$$


So, ideal gas equation for A:
$$1 X \frac{4 \times 22.4}{x} = \frac {4 \times R \times 25} x$$
Here $x$ cancels out. Similarly $y$ cancels out in its equation.  

This is the problem I am facing. 


Another thing I want to know is that the total pressure (i.e $1.5~\mathrm{atm}$), will that be the sum of the individual pressures of gases A and B?




The ideal gas equation is $PV = nRT$


But for this problem V, R, and T are constants. So we can collect terms as:


$\dfrac{P}{n} = \dfrac{RT}{V}$


So $\dfrac{P\_A}{n\_A} = \dfrac{P\_B}{n\_B}$


Now you correctly determined the number of moles of A and B.


$n\_A = \dfrac{4}{\text{MW}\_A}$  

$n\_B = \dfrac{8}{\text{MW}\_B}$


But you need to consider the partial pressures of A and B.



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> The cylinder was empty before A was added, and after A was added the pressure was 1 atmosphere. So the partial pressure of A is 1 atmosphere.
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> Before B is added the pressure is 1 atmosphere and after B is added the pressure is 1.5 atmospheres. So the partial pressure of B is 0.5 atmospheres.
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$P\_A = 1$  

$P\_B = 0.5$


Now substituting into our simplified equation


$\dfrac{1}{\frac{4}{\text{MW}\_A}} = \dfrac{0.5}{\frac{8}{\text{MW}\_B}}$


$\dfrac{8}{\text{MW}\_B} = \dfrac{2}{\text{MW}\_A}$


$\dfrac{\text{MW}\_A}{\text{MW}\_B} = \dfrac{2}{8} = \dfrac{1}{4}$


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Ideal gas equation is PV = nRT
Here R is constant temperature is constant mentioned in question and also the volume is constant as volume of gas equals to the volume of cylinder (volume of gas= space occupied by it)


So in ideal gas equation n and P are variables rest are constant equation can be modified as,


P1/n1 = P2/n2


P1=1
n1=4/x
n2
P2=1.5


By solving we get n2=6/x


It is total moles of gas filled in cylinder 
i.e. 4/x + 8/y


6/x = 4/x +8/y
Multiplying equation by x we get
6=4+8x/y


x/y = 1/4


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