Enthalpy of reaction P4 -> Pn

[brunetteangel]

The problem is this:

 

Calculate how much heat is being released in the reaction of white phosphorus turning into red phosphorus if the mass of white phosphorus is 1000 kg. Standard enthalphy of this reaction is -16,73 kJ/mol.

 

Now, I tried solving it using proportion, like this:

 

P4 -> Pn

 

123,89g ... -16,73kJ

1.000.000g ... x

 

But when I calculate x, I get 135.033,6543 kJ, and the solution at the back of the book is different, it's 5,4 * 10^5 kJ. Can someone please tell me where I made mistakes? Thanks.

Edited January 14, 2012 by brunetteangel

[Fuzzwood]

There is an exact *4 difference between your and the answer in the book.

[brunetteangel]

I know. I get the right solution when I multiply the standard enthalpy by 4, so my proportion looks like this:

 

123,89g... -66,92kJ

1.000.000g ... x

 

Then x turns out to be 540156,5905 kJ, and that is the right solution, but I don't know how to explain why I multiplied the standard enthalpy.

I know that red phosphorus has chain structure, and that the chain can consist of n phosphorus atoms, and that's why it's formula is Pn.

But in this reaction, I have P4 (so that's 4 phosphorus atoms) turning into Pn, red phosphorus. Does that mean that the chain of red phosphorus has to consist of 4 atoms of phosphorus, too?