MOLE TEASER

Here is an extract from the diary of Adrian Supermole
"I was given a hydrated acid ethanedioate of vanadium(hua xue jia n+) of formula: VxHy(C2O4)z.wH2O

With a total of five unknowns I expected to have to do five expts.In each of my expts.I took 1.348 g of the compound:

Expts.1 On heating in a stream of nitrogen to dehydrate,without any oxidation by oxygen in the air,my sample lost 0.432 g.

Expts.2 Asecond sample was made up to 200 cm^3 solution and 1.168 g of calcium ethanedioate monohydrate was formed when excess calcium chloride solution was added.

Expts.3 By now I had a hunch that I knew the formula,and did only one further test with a solution made up as in expt.2.I knew that acidified potassium permanganate would oxidise ethanedioate ions to CO2 and at the same time oxidise V(n+) ions to oxidation state +5.Sure enough,20.00 cm^3 of my solution required exactly 28.00 cm^3 of 0.0200 mol dm^-3 KMnO4 after acidification.I then knew n,x,y,z and w without having to do any further experiments."

What did the odious Supermole find?

Solution:
expt.2:The amount of the VxHy(C2O4)z.wH2O=1.168/146/z=0.008/z
expt.1:The amount of the VxHy(C2O4)z.wH2O=0.432/18/w=0.024/w
so 0.008/z=0.024/w w=3z
expt.3 In the reaction,the Mn(+7) ions become Mn (+2) ions,
the total electrons it need = 0.028*0.02*5=0.0028mole
Also in the reaction the C(+3) ions in ethanedioate ions become C(+4) in CO2.
the total electrons it offer=(0.008/z)*(20/200)*z*2=0.0016mole
So when V(+n) become V(+5)
the total electrons it offer=0.0028-0.0016=0.0012mole
Hence 0.0012=(0.0008/z)*x*(5-n) 1.5z=x*(5-n)

The mass of VxHy(C2O4)z=(51x+1*y+88z)*(0.008/z)=1.348-0.432
So 51x+y=26.5z

From the formula VxHy(C2O4)z we also know:nx+y=2z

Now we get:w=3z; 1.5z=x*(5-n); 51x+y=26.5z; nx+y=2z
So n=2 and x:y:z:w=1:2:2:6

Hence the answer:n=2;x=1;y=2;z=2;w=6