> Chem 102 at my college
> We are studying "Chemical Equilibrium" now. We have to write a paragraph by Friday explaning what would happen to this system: A cube of ice is placed in a beaker and water is poured in until the level of the water is at the very top of the beaker. (The ice will be sticking about 1/3 of the way out of the water.) The beaker is at room temperature. So, the question is: What happens to this system as the ice melts?
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> Here is what I know so far: Ice is less dense than water, so as the ice cube melts the water level will fall. But I am also thinking (since we are studying equilibria) that it has something to do with the water vapor also. Our professor didn't tell us if the beaker was covered or not, so I'm not exactly sure what will happen to the system as vapor is produced. Also I don't know the point at which vapor will start to form - I have a feeling that we need to know this.
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> Ga"any help would be so totally appreciated"halia

Hey. It's actually a little difficult to approach your professor's question without knowing 'what' level of chemical equilibria systems you have been studying. For example, dynamic equilibria using Le Châtelier's Principle? Thermodynamic equilibria using heats of reaction and enthalpy? A physical chemistry consideration of Gibb's free energy and entropy? It's possible to do a vapour pressure calculation but if you use Le Châtelier to describe it, it will only be a hand-waving argument. (One of my instructors once joked, "If you can't express it in figures, it's not chemistry -- it's opinion.")

The provided parameters of this ice-water system are somewhat imprecise. As you've already noted, you aren't given whether the system is open or closed. You aren't told the initial temperature of the water in the system. The beaker is at room temperature, so I assume the immediate environment is also ambient. What's a bit strange is the assertion that the ice cube is floating 1/3 higher than the water level. Is this a normal ice cube, or one that has an internal air pocket, perhaps?

But for what it's worth, my two cents: as the ice cube melts in (presumably) room temperature water, the entropy disorder of the system is increasing. The melting reaction is endothermic (it is drawing energy from the surrounding air in order to melt the ice); and I think the enthalpy is also increasing. If the cube occupies a large enough volume, it will also decrease the total temperature of the water in the beaker a significant fraction of the way towards 0ºC. This endothermicity is a stress put on the system which, by decreasing the temperature, will cause a smaller proportion of H20 molecules to exchange into vapour phase at the surface of the liquid; but at the same time since the cube itself is *melting*, it is increasing its immediate vapour pressure (according to Le Châtelier's principle, the total rate of evaporation [water vapour pressure] vs. vapour condensation will be unbalanced until a new equilibrium is established.) I would think (read: I'm guessing) that the average temperature of the ice cube/water system will most likely decrease somewhat towards zero, and will not begin to rise until the ice is completely melted. Convection currents inside the water will bring 'strings' of melted cold water to the bottom of the beaker and cause the warmer (less dense) water to float upwards to the top, where it will melt the ice cube even faster.

As for the water level in the beaker: as the temperature drops, the water level also should drop -- technically speaking -- because the average density of the water-in-water system is decreasing. And as Don says, the water level will rise once more after the ice is completely melted. However, for most practical purposes, the water level does not change. That's because the density of water at 25ºC is 0.9970479 g/cm3; at 17ºC it's 0.9987779; and at 3.98ºC it's 1.0000 g/cm3. At 0ºC it has slightly decreased again to 0.9998425 g/cm3. These differences in density are so miniscule that to the naked eye there will be no change in water level. The only big difference occurs when all the water actually freezes into pure ice at 0ºC, where it has a expanded and lighter density of 0.917 g/cm3.

Anyway water chemistry is a complex and fascinating topic, and I'm sorry to have to use a hand-waving argument to describe it. There isn't any other substance which can exist naturally, in large quantities, in all three phases (solid, liquid, and gas) at the same time in a narrow temperature range.

Wolf "curious to see what answer your professor was looking for" spirit