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I recently encountered units of energy written as $``\mathrm{kJ}/\mathrm{mol}"$ or $`` \mathrm{kcal} / \mathrm{mol} "$. I'm aware of the meanings of $`` \mathrm{kJ} "$ and $`` \mathrm{mol} " , $ however, I don't understand what they mean when put together like this.

Questions:

  1. How does the qualifier $`` / \mathrm{mol} "$ modify the meaning of a unit of energy like $\mathrm{kJ}$ or $\mathrm{kcal}$?

  2. Can $\mathrm{kJ}/\mathrm{mol}$ or $\mathrm{kcal} / \mathrm{mol}$ be converted into $\mathrm{kJ}$ or $\mathrm{kcal}$?

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If you have n moles of a substance and it receives Q kJ of heat, how much heat does each mole of the substance receive? What are the units of this?

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kcal/mol is a unit of energy density, more precisely energy number density. kcal is a unit of energy, and mol is a unit of number.

You may be more familiar with energy volume densities, like J/m$^3$ or J/mL. It might be easier to think of energy per molecule. That's a second kind of number density. It's the same idea as a volume density, but instead of measuring the energy content per volume of a substance, we measure the energy content per particle of the substance.

You could define the energy per 10 particles, or the energy per million particles, or the energy per $6\times 10^{23}$ particles.

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It's the same thing as pricing gasoline in dollars per gallon, or whatever currency you have per whatever volume unit you are using in your country - typically (some currency) per liter in most parts of the world that use at least a substantial fragment of the SI unit system in their daily life activities. Such values tell you the amount of currency you are expected to fork over if you want to buy one unit - here a gallon or liter - of gasoline for your vehicle. If you want to buy more units than that, you have to fork over X times that amount for X such units.

Likewise in this case, with a thermodynamic quantity such as, say, enthalpy of vaporization or energy required to raise temperature by one kelvin, it is telling you the "cost" in energy to achieve that physical result on a mole-by-mole basis, that is, if you have X moles of the substance you want to subject to transformation, you will need to supply X times the given amount in terms of energy to carry that out, and possibly (indeed surely) more given inefficiencies in whatever systems you will be using.

E.g. if gas is priced at \$3.00/gal and I need to buy 10 gal, then I need \$3 x 10 = \$30 of gas. Likewise if it "costs" $45\ \mathrm{kJ/mol}$ in activation energy to trigger a certain chemical reaction, then if I have 10 mol of whatever stuff I want to cause to undergo the reaction, I have to inject 45 x 10 = 450 kJ of energy into that - typically in the form of heat - to make it happen.

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