I was doing this question and I was wondering if my process and conclusion were valid...

Consider an equimolar mixture (equal number of moles) of two diatomic gasses (A2 and B2) in a container fitted with a piston. The gasses react to form one product (which is also a gas) with the formula AxBy. The density of the sample after the reaction is complete (and the temperature returns to its original state) is 1.50 times greater than the density of the reactant mixture.

a) Specify the formula of the product, and explain if more than one answer is possible based on the given data.

b) Can you determine the molecular formula of the product with the information given or only the empirical formula?

This was my process for (a):

1/2xA2 (g) + 1/2yB2 (g) :rarrow: AxBy (g)

Let z = initial moles of A2
Let z = initial moles of B2
Let a = used moles of A2
Let b = used moles of B2
Let c = produced moles of AxBy
Let ni = initial number of moles
Let nf = final number of moles
Let ?i = initial density of mixture
Let ?f = final density of mixture
Let m = mass of mixture
Let T = temperature
Let P = pressure
Let Vi = initial volume of container
Let Vf = final volume of container

?f = m/Vf
?i = m/Vi
?f = 1.5?i = 1.5m/Vi
1.5m/Vi = m/Vf
1.5Vf = Vi

ni = z + z = 2z
nf = c + 2z - a - b

a mol A2 × 1 mol AxBy/0.5x mol A2 = c mol AxBy
a/x = 1/2c
b mol B2 × 1 mol AxBy/0.5y mol B2 = c mol AxBy
b/y = 1/2c

a/x = b/y

PVi = niRT
1.5PVf = 2z × 8.31 × T
PVf/T = 11.08z

PVf = nfRT
PVf = (c + 2z - a - b) × 8.31 × T
PVf/T = 8.31(c + 2z - a - b)

11.08z = 8.31(c + 2z - a - b)
4/3z = c + 2z - a - b
-2/3z = c - a - b

Now, let B2 be the limiting reagent in the following reaction, that is b = z, and y > x...

Let z = 1 mole, and x = 1...

Find x:y...

-2/3z = c - a - b
-2/3z = c - a - z
-1/3z = c - a
1/3 = c - a
1/3 = 2a/1 - a
1/3 = a

a/x = b/y
1/3 = 1/y
y = 3

Therefore, the ratio of x:y is 1:3 respectively. Likewise, if one were to assume that A2 was the limiting reagent, then the ratio of x:y would be found to be 3:1 respectively.

As such, AxBy can be either AB3, or A3B.

(b) Not enough information is given in order to determine the molecular formula of the compound. As such, only the empirical formula can be calculated.

If anyone could let me know if this looks like the correct working and logic, that would be greatly appreciated!

Thank you,