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Name: Wee Keng Y.
Status: educator
Age: 30s
Location: N/A
Country: N/A
Date: 4/21/2004

When we solve problems involving heating of aqueous solutions, we assume the specific heat capacity of the solution to be that of water, while taking the mass of the solution as the sum of mass of water and mass of solute. Why is that so? Why do we ignore heat capacity of the solute but not its mass? Does heat capacity of a solute, e.g. salt, change when it goes from solid phase to a dissolved form?

Well, I do not think we ignore the heat capacity of the solute. We simply tend to assume that, per unit volume, it's about the same as water, when it is dissolved in water. This is never exactly true, but it is kind of close. I think there is an embedded assumption that usually we are not doing very high precision work with heat capacities of solutions. It is too complicated to accomplish, and rarely bothered with.

Specific heat is usually cited in heat capacity per unit mass.

Do yourself a favor and make a table for several pure substances including specific heat, and mass density, and a calculated column of heat capacity per unit volume, and another column of heat capacity per atom. (or mole of atoms) These numbers change much less, from substance to substance, than the heat capacity per unit mass.

And the changes which they do exhibit, make more sense. You can clearly see the difference between monatomic gasses He, Ne, Ar, etc. and diatomic gasses such as H2, N2, O2. The mass of each atom does not matter. Only the average number of degrees of freedom enjoyed by each atom matters. Monatomic atoms can move in X, Y, and Z, but because they are slippery spheres, their rotations cannot matter. So they have 3 degrees of freedom, and 3 units of thermal mass per atom. Diatomic gasses can additionally rotate in 2 directions. (The on-axis rotation is slippery, cannot matter.) So they have 5 degrees of freedom, and 5 units of thermal mass per atom. 6 degrees of freedom per atom is the nominal maximum.

For adjacent atoms joined by firm molecular bonds, some vibrations are suppressed at room temperature, so some degrees of freedom are lost. For rigidly packed crystals, whole molecules can become unable to rotate, so degrees of freedom are lost. Heat capacity per atom, and per unit volume, is lost with them.

Water has approximately a full set of active degrees of freedom. Ions constrained in a crystal have fewer. When broken into individual atoms and weakly linked to water molecules around them (hydration), They are likely to gain a full set of degrees of freedom. so the heat capacity of the solute does change when dissolved, probably increasing and probably becoming close to that of water, per atom and per unit volume.

Atomic sizes change rather slowly as a function of atomic number and mass. So the atom count density of most solids and liquids varies much less than the mass density. Check it out. That is why I keep equating per unit volume and per atom. It is not exactly true, but if you want to re-scale things to look for relevant changes rationally, this tends to help.

Notice that when you add 2kg/1Liter salt to 2kg/2Liter of water, you will have 4 kg of solution. The volume is another matter, poorly conserved. When you assume the specific heat of the solution to be equal to that of water, do you measure the solution by weight or volume?

If you ever do wish to do very precise thermal capacity work with solutions, I think you will need to measure the thermal capacity for concentration of each solute. It will vary linearly for low concentrations, but near saturation it may be non-linear. Then you will need to integrate over changes in concentration that occur when you mix chemicals.

Most people have avoided getting into all that.

Jim Swenson

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