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How much energy is produced by burning a 1 ct. diamond?

I'm trying to figure out how much energy to build the diamonds in a biological process. See here: https://worldbuilding.stackexchange.com/questions/15314/are-diamond-berries-possible

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  • $\begingroup$ Still looking for the answer but a question hit my mind: Diamond ignites at 700 to 800 degrees centigrade. Why on Earth would the energy matter if you have to reach those temperatures for the combustion to happen?! Just saying. :P $\endgroup$ – M.A.R. Apr 28 '15 at 17:20
  • $\begingroup$ This is, perhaps, a homework question. $\endgroup$ – Jon Custer Apr 28 '15 at 17:24
  • $\begingroup$ @JonCuster No, no. Not homework. I'm trying to figure out how much energy to build the diamonds in a biological process. See here: worldbuilding.stackexchange.com/questions/15314/… $\endgroup$ – Sam Washburn Apr 28 '15 at 17:25
  • $\begingroup$ @Sam you might add that info to your question. There is some homework policy here. See: Homework policy $\endgroup$ – M.A.R. Apr 28 '15 at 17:35
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    $\begingroup$ OK - the assessed elemental Gibbs free energies are cataloged in 'SGTE Data for Pure Elements', A.T. Dinsdale, CALPHAD 15(4) 317-425. There one finds (at low pressures such as atmosphere) that the free energy of diamond relative to graphite is 1009 + 4.88 T - 0.01 T ln(T) + 135400/T + 33.0E5/T^2 - 9E8/T^3. I'll leave the graphite + oxygen making CO2 part up to you. $\endgroup$ – Jon Custer Apr 28 '15 at 17:45
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Well it looks for me, the question was addressed by a non-Chemist. Hence my attempt to answer this accordingly.

  • You have to know the reaction of the combustion, the starting materials, the product(s), and their relative quantities to balance the reaction equation.
    Your case is described by $\ce{C} + \ce{O2} \rightarrow \ce{CO2}$, with "$\ce{C}$" for carbon (here: in form of diamond), $\ce{O2}$ for oxygen and $\ce{CO2}$ to yield the product, carbon dioxide. And the reaction equation is already balanced, i.e. the number of atoms per type on the left hand side (prior the arrow) equals the number of atoms per type written on the right, too.
  • There is a heat called standard enthalpy of formation, describing how much heat is necessary or liberated to form a compound if one (even theoretically) were to prepare this out of elements. Normally, you look up these tabulated data for all your products and sum this up, and subtract the sum of all these enthalpies of formation of your starting materials.
    In your example, by convention elementary gases (like oxygen, $\ce{O2}$) were attributed a zero value. By means of thermodynamic, diamond is not the most stable form of carbon, and was attributed a value of ${+1.88}{\,\mbox{kJ/mol}}$ (same reference). Carbon dioxide was attributed a value of ${-393.5}{\,\mbox{kJ/mol}}$ (reference) and the energy balance of the reaction equation equals to ${-391.62}{\,\mbox{kJ/mol}}$, i.e. if you would burn 1 mole of diamond. (This is a quantity like dozen, used in chemistry.)
  • Now if we express the quantity of diamond actually burned (mass $m$ of 1 ct) in this above mentioned unity of mole, we need a proportional factor, the molar mass $M$, that happens to be $12{\,\mbox{g/mol}}$ for carbon (reference).

    Now we have the pieces. Hence we calculate the "chemical quantity" ($n$) of carbon deployed as

$n = \frac{m}{M} = \frac{0.2\,\mbox{g}}{12\,\mbox{g/mol}} = 0.017\,\mbox{mol}$

and than multiply this with the above calculated heat of the reaction, i.e

$\mbox{heat} = 0.017\,\mbox{mol} \times (-391.62\,\mbox{kJ/mol}) = -6.527\,\mbox{kJ}.$

So if you burn 1 ct of diamond in oxygen at 25 degree Celsius (about 77 Fahrenheit) and would collect the heat of the product by cooling the $\ce{CO2}$ to the same 25 degrees Celsius, this offers you 6527 Joules (or about 1559 calories).

Notes: The heat calculated here is the reaction enthalpy. The minus sign indicates energy is "liberated" in the course of this reaction. Actually, if all this heat were completely converted into electrical energy, you were able to switch on a light bulb of 60 W for less than 2 minutes (only 108 seconds).
In the beginning of modern chemistry, diamonds actually were burned by concentrated solar power, for example by Lavoisier (here) although to prove their composition.

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