[Rutherford]

I asked few months ago a similar question, but I wouldn't ask this again if I understood it completely then. I've done these problems by memorizing rather than understanding them.

PCl₅ dissociates on PCl₃ and Cl₂. Under 200°C and p=101.325Pa, the density of the gas mixture towards hydrogen is 70.2. How many percents of PCl₅ dissociated on this temperature?
-I was solving it this way:
PCl₅ PCl₃ + Cl₂
x-y        y        y

(1)208.5(x-y)+137.5y+71y=70.2*2
(2)x+y=1
How do I get those equations? Why has x+y to be 1?

[curiouscat]

Why has x+y to be 1?

Because MW is the mass of 1 mole.

PS. Is the answer 47.848.5%? (My eqns. were set a wee bit differently; its easier to start with a basis of 1 gmol PCl5; then you only need one variable x)

How do I get those equations?

[tex]
\rho=\frac{PM}{RT} \\

\frac{M_{mix}}{M_{H_2}}=70.2 \\

MW_{mix}=\displaystyle\sum_{i} MW_i \cdot x_i \\
[/tex]

[Rutherford]

Okay, then I want it to be 2 moles.
x+y=2
417(x-y)+417y=70.2*2
When solved y is bigger than x, so more PCl₅ dissociated than there was at the beginning. Why is it so?

[curiouscat]

Okay, then I want it to be 2 moles.

Ok, fine. Have it be 2 moles.

x+y=2
417(x-y)+417y=70.2*2
When solved y is bigger than x, so more PCl₅ dissociated than there was at the beginning. Why is it so?

Because you set up a wrong equation? Justify writing your second equation.

GIGO. 

[Rutherford]

48.32% is the right answer.
I want to start from the last equation you wrote in your 1st post. x is the molar share of the components of the mixture. The sum of the molar shares must be equal to the number of moles of the gas mixture (1mol has a mass of 140.4g). Now back to the equations I wrote:
x+y=2
417(x-y)+417y=70.2*2*2
Why is again y bigger than x?

[curiouscat]

417(x-y)+417y=70.2*2*2
Why is again y bigger than x?

Still the wrong eq.

Why 417?

[Rutherford]

Right. It should be 208.5 so it is:
x+y=2
208.5(x-y)+208.5y=70.2*2*2
Just to conclude: when I have density towards a gas of a mixture given, using the ideal gas law I get that the molar mass of the mixture divided by the molar of the referent gas is equal to the density. The molar mass is the mass of 1 mole, so I can assume that there was 1 mole of the mixture. Then, using the formula you gave, I can calculate the unknowns.

Thanks again for the help. It is much clearer now. If I maybe get a doubt about this I will revive this topic, but I hope that it won't happen  .