Determining Liters of ethane burned to convert H20 to steam

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Homework Statement


The Heat of combustion of Ethane is 373 kcal/mole. Assuming that 60% of the heat is useful , how many liters of ethane,, measured at standard temperature and pressure, must be burned to convert 50.0kg of water ar 10.0C to steam at 100.0C? One mole of a gas occupies 22.4 liters at precisely 0C and 1atm.

Homework Equations


PV=nRT Q=mcΔT

The Attempt at a Solution


Qburned=Q heat up

=mL + mcΔT

540g/C(50g)+ 50(1cal/gC)(100-10)
Q=31500 cal

n= Q/heat of combustion(60%)
n=0.1407mol

PV=nRT
V=0.1407mol(8314j/kmolK)(273K)/1atm

V=3193680 L

The book has it at 315000. Is there something wrong here? I feel like I am missing a term or left something out?
 
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Discussion

You calculated Qburned per 50 grams. Did you convert this to per 50 kg somewhere?
 
Why use PV=nRT when you're given 22.4 L/mol?
 
Ahh that's where the error comes from. I forgot that it is per mole
 
NascentOxygen said:
You calculated Qburned per 50 grams. Did you convert this to per 50 kg somewhere?
I did I believe. It should be in my note pad