# Why does adding solutes to pure water lower the the specific heat?

We found that water with salt, sugar, or baking soda dissolved in it cools faster than pure water.
Water has a very high specific heat; how do these solutes lower it?

We heated a beaker (300ml) of water to 90° C and let it cool, checking the temperature every 5 minutes. We repeated the experiment adding a tablespoon of salt. At each 5 minute interval, the temperature was higher for pure water than for salt water. Same result with baking soda and sugar.

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Slower cooling means higher specific heat, doesn't it? –  gigacyan Dec 19 '10 at 18:28
I like the question, but please settle lower/slower problem. –  Marek Dec 19 '10 at 18:45
Also please describe better the experiment: do you measure the cooling from the boiling point or from 100 degrees? It matters because obviously the cooling down is exponential, and as such $\frac{\mathrm{d}T}{\mathrm{d}t}$ varies at different temperatures. –  Sklivvz Dec 19 '10 at 22:29
@gigcyan, @marek: fixed, thanks –  Anne Laks Dec 19 '10 at 22:36
One could argue that this is a chemistry question but to me it seems like asking about the physical explanation behind a chemical phenomenon. I like it. –  David Z Dec 20 '10 at 2:27

I believe the reason is due to the solution trapping water molecules in a cage around it. The reason water has a high specific heat is because it can rotate freely around its center of mass, there is a large number of degrees of freedom that can randomly vibrate and rotate in the pure water. When you have molecules in solution, they trap several water molecules close to them in a lowest-energy stiff configuration, and these molecules are like a tiny rigid body where thermal motion is not possible, because the quantum of oscillation frequency is higher than kT. This reduces the specific heat by an amount directly proportional to the solute.

This is probably strongest with salt, since the charged ionic solutes will produce a very strong cage. I would expect the effect with alcohols to be weaker, sugars weaker still, since I think the charged groups are less charged in these in order.

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The obvious answer for at least part of this simply concerns the new substance.

Water has a fairly high specific heat. It is greater than that of sugar, salt, baking soda, etc. The specific heat of the combination (solution) of these two is somewhere between that of either one alone (probably a weighted average by mass) simply by merit of the temperature change occurring to both substances rather than just one

However I suspect this answer is incomplete. There could be another phenomena in play to explain the cooling differences, perhaps associated with how the solute changes the temperature of phase changes (ie higher boiling pt, lower freezing)

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Yes, this is the same feeling I have. I wonder to what degree those phenomena in the last paragraph are important. Perhaps dissociation of the water molecules into $H_2$, $O_2$ and creation of some new compounds also has to be taken into account. But I am not sure whether this increases or decreases the specific heat. Anyone cares to elaborate? –  Marek Dec 20 '10 at 8:07
@Marek: the only way to convert water to $H_2$ and $O_2$ is stick electrodes in it. Dissociation to $H^+$ and $OH^-$ does not depend (in the first order) of salt concentration. –  gigacyan Dec 20 '10 at 21:21
yes. it is the salts that dissociate into electrolytes. Water dissociation occurs either electrically or in the base/acid manner that gigacyan describes –  jon_darkstar Dec 20 '10 at 21:23
Thanks @gigacyan, @jon. –  Marek Dec 20 '10 at 21:31
It is not the correct explanation, because the salt was added to the water, it wasn't an equal volume of salt water –  Ron Maimon May 3 '12 at 5:26

If your description of the experiment is accurate then the result you got is unexpected. It is true that specific heat capacity of salt solution (per mass unit) is lower than of pure water, you can estimate it as $$C_{p} = wC_{p}^{salt}+(1-w)C_p^{H_2O}$$ where w is the mass fraction of salt. However, as you describe it, you didn't keep the mass constant but increased it by adding some salt to a fixed volume of water so your total heat capacity should be the sum of the heat capacity of water (which is the same for all samples) and that of salt, sugar or baking soda.

Since w in your experiment was around 0.04, the effect you were measuring was quite small and could easily be smaller then the experimental error. This error consists of the accuracy of measuring volume of water, of measuring temperature, of timing. The easiest way to reduce these errors is to repeat each experiment several times in random order and see if the results are consistent.

Update: I found a plot of specific heat of soda solutions and I calculated heat capacity for two cases: a) 300 ml of pure water and b) 300 ml of water + 12.5 g of soda = 312.5 g of 4% soda solution. The heat capacity of pure water sample would be 1254 J/K and that of water with soda 1276 J/K - as I expected, it is higher but the difference is less than 2%.

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We repeated the experiments several times, and with different solutes: sugar and baking soda. The differences in rate of cooling were small but consistent. –  Anne Laks Dec 20 '10 at 19:54
@Anne: Do I understand it correctly that you had 300 ml of water in both cases? Meaning that you compared cooling of 300 g pure water versus 312 g salty water? –  gigacyan Dec 20 '10 at 21:19
300 ml of water; 1 tablespoon = 15 ml of salt. Also tried 3 tablespoons of sugar, also 1 tablespoon baking powder. –  Anne Laks Dec 20 '10 at 21:50
@Anne: did you prepared new water solution for every repetition or did you reuse the same one? Also, try to calculate specific heat based on your observations. Do do this, plot log(T) vs time and make a linear fit. The slope of the line is inversely proportional to the heat capacity. Use heat capacity of pure water as a reference and calculate values for other solutions. It would help if you new the mass of added salt but you can use a cooking table for an estimation (1 tbsp of salt is 12.5 g) –  gigacyan Dec 21 '10 at 8:18
I prepared a new water solution each time we tried a new solute. –  Anne Laks Dec 22 '10 at 0:16