# 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.

• 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
• As above comments stated it increases its specific heat also note that it generally increases its saturation point and freezing point at a certain pressure. Also, normally a saturated liquid remains constant in temperature while undergoing a phase change, however a solution does not remain constant in temperature. These phenomena are all of the same nature so when you modify the question you may include these as well – Cem Dec 19 '10 at 22:37
• 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.

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)

• 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
• 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%.

• 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
• It is difficult for me to understand why you observed such a behavior without seeing all the data. When people publish their results in scientific journals, they try to be as specific as possible to avoid any misunderstandings. Maybe you could post a plot of temperature versus time so that we could see how big was the difference that you observed. – gigacyan Dec 22 '10 at 18:37
• The effect of salt etc. on the heat capacity is probably negligible, and the question in the header may be misleading.
• Cooling down water in a beaker is usually driven by convection. Liquid on top of the solution in the beaker cools quickly, and then has a higher density than the hot liquid at the bottom. The cold liquid falls down, hot comes up, cools, falls down and so on.
• Convection depends on the density gradient in the liquid. The solute may reduce convection, since the density difference, which drives the convection, may be different for different solutions.
• The quantity to look at is the density as a function of temperature (or equivalently the thermal expansion coefficient) for salt solutions vs. the respective data for pure water.
• This question should play a role in the heat exchange of seawater and people should have discussed it there before.

I find a useful way to think about specific heat is this:

How much heat does the substance contain at room temperature? If it contains a lot of heat, adding or subtracting a small amount of heat will not make much of a difference. However, if it only has a little energy, removing the same amount will make a big difference, causing it to to cool or heat quickly.

Salt/ sugar water contains less heat than water, so it cools and heats quickly.

The ions "trapping" water molecules plays a role, but there is another, more simple explanation: the dissolved substance also physically gets in the way. Imagine a bunch of children running around in a space. Now imagine you added some rather fat people at random spots. The children would bump into them, and slow down.

Roughly speaking, heaver substances have a lower specific heat, take a look at this graph: http://periodictable.com/Properties/A/SpecificHeat.html

The more massive molecules move more slowly, hence less energy, hence, adding or subtracting energy is a big deal. However, this explanation is simplified. If heavy molecules moved at a speed proportioned to their mass, they could still move in the same pattern as light ones. However, they don't. Everything else being equal, heavier molecules are bigger, which means they run in to each other more. Its not actually the speed but the size that is most important.

Final answer: Salt and sugar water have large molecules in them that slow movement.

I think that the reason why water has a very high specific heat capacity is due to the presence of hydrogen bonding between each individual water molecule (polarity). These hydrogen bonds are capable of storing energy from heating, and so when water is heated, some heat energy becomes the bond energy and is stored, therefore much more energy is needed to heat up a specific volume of water by a degree and vice versa.

When solutes are present, hydrogen bonds break as the permanent dipole - permanent dipole interactions change to ion-dipole interactions where, as mentioned above, solute ions/ polar substances surround each water molecule. This causes each water molecule to lose its attractive forces with each other due to the net loss of hydrogen bonds with each water molecule.

Finally, as such, the reduced number of hydrogen bonds mean that less energy can be stored in them, reducing the specific heat capacity of water.

P.S this is just a conjecture

I’d +1 gigacyan, But I’m Under 15 rating and can’t. But I think there is an answer that was missed because you jumped right into specific heat being the reason.

Instead I’d argue that an increase in thermal conductivity is more important. http://www.dtic.mil/dtic/tr/fulltext/u2/752491.pdf Table 2 in this link has the figure for saline’s thermal conductivity. You will need to find water’s t. C. To see if I’m right. Double check me, but I see almost 10x the thermal conductivity for saline (598.5) vs. water (62) at about 30 degrees C. Yes, this isn’t the 90 degrees C in ur exp.

You did not explain the methodolgy you used. So, I cannot assess for possible errors. That said, I doubt any errors would affect the results much since you got similar results for different solutes/suspensions.