# How can I calculate the energy of a solution by knowing all of it's elements?

How can I calculate the energy of a solution by knowing all of it's elements?

For example:

If I have 2 liters of salting water $\mathbf{NaCl_{(aq)}+H_2O_{(l)}}$ contains 1.5 g of salt, how can I determine the internal energy stored in it?

• It would be helpful if you would put some of the ideas you've already thought about into your question. That way, others aren't just giving you the answer, they are helping you reason it out. Aug 11, 2013 at 2:14
• You need to precisely specify what form of energy you're referring to. If you mean internal energy, then measuring it directly is impossible for any real system, one can only calculate the change in internal energy that occurs due to heat transfer and work done on/by the system in the course of moving from one state to another. Aug 11, 2013 at 2:18
• @MohammadFakhrey, that's food energy, which is only one specific measure of energy, namely the heat energy released during the process of metabolism. Salt water has zero food energy, as it's not consumed in the process of cellular respiration. Aug 11, 2013 at 12:10
• @bobthechemist, funny how that one section claims a computer simulation can be used to "determine" an intrinsically uncertain quantity of a real system. Approximate might be an apter choice of word. Otherwise somebody should go resurrect Joule, Boltzmann, Carnot, Kelvin, et al. post haste to let them know we can now measure the precise velocities and positions of individual microscopic particles. Aug 12, 2013 at 23:22
• @GregE. well at we know that through this process that entropy is heading in the right direction; all of them must be spinning in their graves. Aug 12, 2013 at 23:24

Since you ask specifically for internal energy, would it be that you already have some ideas?

So what is internal energy? It is the energy due to the interaction among the species plus the energy due to the interaction between the species and any external field. That is, the energy it takes to "assemble" the system.

Then for gaseous species, it would be mainly the bonding energies of the molecules. Those are usually inferred from experiments. And you can look up tables in textbooks and IUPAC website.
For ionic crystals, you would reason this way: first ionize the species and them find the Columb interaction among them in crystal. Ionization energies are measured. Columb interaction is probably calculated and is a nightmare to calculate.
The further problem is from NaCl(s) to (aq) where the solvation involves quite a bit of interactions between the ions and water. For the case of Na+ Cl-, water molecules do not form regular cages around them, even though we CAN study the ideal case of regular cages. I think there has been some minimal models which can possibly guide a simulation study for the solvation energy. Though I don't think there has been any simulation study or any theoretical study that is sufficient to predict solvation energy. I can be wrong. On the other hand, direct measurement should at least be able to measure the heat change during solvation.

So in digression, I don't think you can find the complete energy too well.

You can't calculate the internal energy of any real thing. The reason is that the total internal energy is the sum of all kinetic and potential energies of every particle in the system - there is no way to know that. You could calculate it for a simulated system of particles.

What you can do for real systems is figure out the change in energy. If you can compare it to a "ground state" (a state we define as having zero energy) then you can measure the change using the law of conservation of energy. For a system closed to mass transfer:

$\Delta E = q + w$

Change in energy is equal to heat transfer plus work done on or by the system.

Heat is a thermal transfer of energy (kinetic energy of molecules) and work is a mechanical transfer of energy (potential energy of molecules) and we can measure both on the macroscopic scale. Since those are the only two ways to transfer energy, we know that if we account for both, we also have the total energy change.

Incidentally, this is the reason that you almost always see $\Delta$ in front of $G$, $H$, and $E$ in thermodynamics. There is no "universal" ground state for energy, and so we have to look at changes in those quantities to solve practical problems. Entropy, $S$ is a little different - we can define a universal zero entropy state, and so when you see $S$ used in practice, it really means "entropy relative to the zero entropy point" - which is a perfect crystal at absolute zero.