Energy to separate one molecule of water from a single neighbour

[johnconnor]

Question:

The amount of heat required to convert 1g of ice into vapour is approx. 3000J. Estimate the energy required to separate one molecule from a single neighbour, assuming that in ice, each H₂O molecule has four nearest neighbours. [M_r(water) = 18)

My reasoning:

3000 x 2 / [1/18 mole x N_A x 4] = 4.5 E-20 J

Because each molecule is attracted to 4 other molecules -- hence the product of the number of water molecules with 4. And since I'm looking for the energy required to separate one molecule from a single neighbour, I multiplied the division by 2.

Is this reasoning valid? Haven't we ignored the unused bonds of the water molecules at the outermost part of the ice cube? How significant is it to take into consideration those unused bonds?

If the reasoning is wrong, could anyone please point to me the proper way of attempting the question (rather than getting a fortuitous answer)?

 

[johnconnor]

Anyone?

 

[johnconnor]

Bump?

 

[Infinitum]

I think the reasoning is almost correct. I don't understand why you multiplied by two, though. Each molecule has four neighbors. And the term you get without multiplying the two, is the binding energy between them for each neighbor.

Also, there are no 'outermost bonds'. It is somewhat like a football structure, closed on itself, so each ice molecule is joined to four others.

 

[asteriatic]

I would say that your reasoning is valid to some extent, but it is not the complete picture. The energy required to separate one molecule of water from its nearest neighbor depends on various factors such as temperature, pressure, and the strength of the bonds between the molecules.

To get a more accurate estimate, we would need to consider the energy required to break the hydrogen bonds between the water molecules. In ice, each water molecule is surrounded by four other water molecules, and each of these bonds would need to be broken in order to separate a single molecule from its neighbor.

Moreover, the strength of these bonds also varies depending on the temperature and pressure. At lower temperatures, the bonds are stronger, and more energy would be required to break them. So, the estimate you have calculated may not be accurate for all conditions.

Additionally, as you have mentioned, there are also unused bonds at the outermost part of the ice cube, which would require additional energy to break. However, these bonds are not as strong as the ones between the nearest neighbors, so their contribution to the overall energy required may be relatively small.

To get a more precise estimate, we would need to consider all these factors and use a thermodynamic approach to calculate the energy required to separate one molecule from its neighbor. This would involve considering the enthalpy and entropy changes of the system, which would give us a more accurate estimate of the energy required.

In conclusion, while your reasoning is valid to some extent, it is not the complete picture. To get a more accurate estimate, we would need to consider all the factors mentioned above and use a thermodynamic approach.

 

[asteriatic]

Your reasoning is valid in terms of the calculation, however, it is important to consider the unused bonds of the water molecules at the outermost part of the ice cube. While they may not directly contribute to the separation of one molecule from a single neighbour, they still play a role in the overall energy required for the process.

In order to get a more accurate estimate, it would be necessary to take into account the energy required to break these unused bonds as well. This could be done by factoring in the surface energy of the ice cube, which would account for the energy needed to break the bonds at the outermost layer.

It is also important to note that this calculation is an estimation and may not accurately reflect the actual energy required for this process. There may be other factors at play that could affect the energy needed, such as the temperature and pressure of the system.

In order to get a more precise answer, it would be necessary to conduct experiments or use more advanced calculations that take into account all the variables involved. However, your approach and reasoning is a good starting point for estimating the energy required to separate one molecule from a single neighbour.