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In European countries, they use $\ce{NaCl}$ or $\ce{KCl}$ to melt ice during the winter season. In Asian Countries, they use $\ce{NaCl}$ to keep the ice without melting, for example in ice cream and beer boxes.

I asked my chemistry teacher about this and his answer was,

when you add ions to the ice, its melting point goes (i.e. freezing point of water) to -9 to -19 degree Celsius, depending on the amount of ions. The reason behind that is, when water becomes ice its water molecules re-arrange to specific shapes (see the link for the video at bottom). After we put ions to it, ions disturb that shape as they come in-between the water molecules. If water wants to be ice again, it should be like -9 degree Celsius because of these ions disturbing them to rearrange as a solid.

I also asked my Physics teacher about this and his answer was,

When we put salt into water, its temperature goes down to somewhere around $\pu{-6 ^\circ C}$, so that it takes more time to come to $\pu{0 ^\circ C}$ and begins melting

Link to the videos are as follows,

Could you give me a correct explanation for this question?

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The apparent contradiction is resolved as follows: in both cases, addition of salt makes ice melt faster, which is important in the street and negligible in a beer box (or an old style cold bath used in the lab). But in doing so, it also causes the temperature of the ice and its surroundings to go well below $0^\circ\rm C$, which is important in the lab and negligible in the street.

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  • $\begingroup$ also liquid has more surface area with the icebox than ice does, so adding the salt helps increase surface area by melting the solid water to liquid water $\endgroup$ – jeremy Jan 16 '16 at 4:38
  • $\begingroup$ only the initial melting directly after adding salt will be faster but melting the bulk of the ice will be slower. @Ivan Neretin $\endgroup$ – M.ghorab Jan 16 '16 at 14:19
  • $\begingroup$ Would it? Well, anyway, suppose there is no bulk, just a thin layer of ice all over the street, and you want to get rid of it. Then you may benefit from that initial faster melting. $\endgroup$ – Ivan Neretin Jan 16 '16 at 17:03
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The main difference is, that in order to melt the ice, you add the salt to the ice itself, where it lowers the melting point and thus (if the ambient temperature is only just below zero). Melts away the ice from the road.

On the other hand to keep ice cream cold, you add ice+salt around the ice cream that you want to prevent from melting.

This has three effects that help you cool your drink/ice cream faster to a lower temperature:

  1. The melting point of the ice around your ice cream is below zero. This means that the temperature on the outside of your ice cream box cannot rise above zero until all the ice on the outside is molten and the temperature of your ice cream is kept below zero for that duration. The reason for this is, that it takes energy to break up the structure of solid ice. This is the same effect that keeps your coke at zero degrees until the last of your ice cubes has melted (and is the reason why adding more ice than necessary just reduces the effective volume of your container and does not help to keep your drink cool).

  2. As your teacher correctly pointed out, when salt dissolves in water, the temperature of the water is lowered (because of the entropy vs. enthalpy of dissolving crystalline salt). However, as pointed out in the comments, this effect is small compared to the others.

  3. Your drink/ice cream is cooled faster because the very cold salty water (ideally with some ice cubes still swimming in it) around the bottle transports the heat away from your drink faster than some ice cubes touching the bottle would.

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  • $\begingroup$ When salt ($\ce{NaCl}$) dissolves in water, the temperature stays pretty much the same, because the enthalpy of dissolution is all but negligible. And if you are talking about salts in general, there are examples of any sort: some would make water pretty hot, some pretty cold. $\endgroup$ – Ivan Neretin Jan 15 '16 at 14:14
  • $\begingroup$ I did not specify how strong that effect was. I just looked it up and 1mole of NaCl cools down one litre of water by close to one degree Celsius. So with a solubility of 6 M, you could cool down water by about 6 degrees celsius. This is exactly as the teacher of the OP said and whether this is a lot or not depends on the use case. But considering that this could cool your drink well below freezing and thus make your tongue stick to the glass, I would say this should not be left out. And yes, I was talking about table salt since that was the question. $\endgroup$ – Thawn Jan 15 '16 at 21:08
  • $\begingroup$ Well, yes, technically that's true. However, in any realistic setup some of that cold would be lost for cooling down the reaction vessel, and some would creep away to the surroundings, so you'll hardly be able to literally freeze anything at all. The enthalpy of melting of the ice is two orders of magnitude greater, so I think the word "negligible" (applied to the enthalpy of dissolution) is justified here. $\endgroup$ – Ivan Neretin Jan 15 '16 at 22:02
  • $\begingroup$ Given enough salt and water, I am sure we could make an ice cube. However, this is completely besides the point. I was aiming to give a complete answer and since the op already mentioned this effect, I explained how it applies to his question. You are free to your opinion that it is negligible but please stop giving the impression that my answer was irrelevant. $\endgroup$ – Thawn Jan 15 '16 at 22:25
  • $\begingroup$ By the way, in your own answer, you clearly mention that the decrease in temperature is very relevant in the lab, so I do not get why you are trying to argue that it is negligible now. $\endgroup$ – Thawn Jan 15 '16 at 22:30
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Adding salt or any solute causes freezing point depression as one of the colligative properties of the material.

In the cold climate, when snow is left to accumulate it forms a slippery ice which is dangerous. Workers utilize the freezing point effect and add salt to snow to melt avoiding the danger of the slippery ice.

In the hot climate, when ice in the ice box is left it is going to melt. People utilize the freezing point (or melting point) depression effect of salt to ice to melt it at the depressed melting (or freezing) point (below the usual $\pu{0 ^\circ C}$). This can be described as a preemptive protective step to the ambient temperature effect, since the ambient temperature will melt the ice at a relatively high point (the usual $\pu{0 ^\circ C}$). This means a high rate of heat transfer and corresponding rapid melting to the remainder of the bulk of the ice, the salt-water will cover the ice with a layer of relatively cold water (below the usual $\pu{0 ^\circ C}$) which confers a slow rate of heat transfer and corresponding slow melting.

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  • $\begingroup$ I don't believe this to be correct. See @Thawn's answer. Salt is added to the ice surrounding the ice box to increase surface area with the ice box + to lower the temp of the water (ice) surrounding it (b/c dissolving salt in water will decrease the temperature of the water) $\endgroup$ – jeremy Jan 16 '16 at 4:35
  • $\begingroup$ Increasing the surface area by melting and lowering temperature by endothermic reaction are true effects but are of minor importance, the most important effect is melting the ice in new depressed melting(or freezing)point and keeping it in contact with salt-water to retard it's melting, by means of colder water contact and continuous effect of melting point depression but with gradually decreasing magnitude due to dilution of the salt by the melting ice. $\endgroup$ – M.ghorab Jan 16 '16 at 14:14
  • $\begingroup$ would the salty water not just dissolve more salt in the surface of the solid water, melting that ice until all ice was liquid? $\endgroup$ – jeremy Jan 16 '16 at 18:00
  • $\begingroup$ dissolution stops by the production of sufficient water by melting, it doesn't continue to the end of melting, except in case of salt has diffused in the ice or elsewhere. $\endgroup$ – M.ghorab Jan 16 '16 at 18:27
  • $\begingroup$ Okay, interesting. good to know $\endgroup$ – jeremy Jan 16 '16 at 18:28

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