How much heat is given off when a human body burns, for example, Uncle Owen and Aunt Beru?
Example Combustion reaction:
2C8H18 + 25O2 → 16CO2 + 18H2O
A body is:
Taking 100 grams of a human body, that's:
Since water doesn't burn very well, I'm going to subtract the oxygen and hydrogen that is in water
A human body is 60% water.
60 g H2O x 1mol/18.015 g = 3.331 moles of water
That's
So,
In our 100 gram chunck of a human body, there are:
Multiply these all by four, and you get:
So, the molecule we get is:
C6H13O3
This stuff makes up 33% of the human body, we're saying for the purposes of solving this problem.
For simplicity, I'm going to assume the all the carbon present in the human body comes from this compound, which is a very inaccurate assumption, but in Physical Chemistry you can assume whatever you want.I'm also going to assume that the heat of formation of this compound is -750.9 kJ/mol, since a compound of similar size has that heat of formation. And it has a formula weight of 134.2 g/mol, which isn't an assumption at all.
Finding the heat of combustion using this equation:
CaHbOc
heat of combustion = 393.51a + 142.915b + (heat of formation of CaHbOc)
heat of combustion = [393.51 x 6 + 142.915 x 14 + 750.9]kJ/mol
And the answer I got was:
Uncle Owen:
190 lb ÷ 2.2 = 86kg
Aunt Beru:
140 lb ÷ 2.2 = 64kg
1,081,000kJ + 754,000kJ = 1,835,000kJ!
Wow! Together they put off as much heat as 12 gallons of burning gasoline!
65% oxygen
18% carbon
10% hydrogen (by wieght)
65g O/15.9994 g/mol O = 4.063 moles of oxygen
18g C/12.011 g/mol C = 1.499 moles of carbon
10g H/1.0079 g/mol H = 9.921 moles of hydrogen
That's 60 grams of my 100 gram sample
6.662 moles of hydrogen
3.331 moles of oxygen
4.063 mol O - 3.331 mol O = 0.732 mol O
9,921 mol H - 6.662 mol H = 3.259 mol H
0.732 moles of oxygen
1.499 moles of carbon
3.259 moles of hydrogen
that can be burned
2.928 moles of oxygen
5.996 moles of carbon
13.036 moles of hydrogen
heat of combustion for C6H14O3 = 5,111 kJ/mol
86kg x 33% = 28.38kg of C6H14O3
28,380g ÷ 134.2g/mol = 211.48 moles of C6H14O3
211.48 mol x 5,111 kJ/mol = 1,081,000 kJ
64kg x 33% = 19.80kg of C6H14O3
19,800g ÷ 134.2g/mol = 147.54 moles of C6H14O3
147.54 mol x 5,111kJ/mol = 754,000 kJ