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Strength of a hydrogen bond

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1 Strength of a hydrogen bond
How strong is the hydrogen bond between two water molecules? We can estimate this from the heat of sublimation, which is the heat required at constant pressure to turn ice into steam. Ice, solid water, has a tetrahedral structure where each water molecule has 4 hydrogen bonds: two between its two hyrogen atom are attached to the lone-pairs of a neighboring water, and two from attraction of its two lone pairs to the H atoms of adjacent water molecules. In the vapor phase, all hydrogen bonds are broken. Thus, the heat of sublimation, divided by 4, will be a measure of the strength of a hydrogen bond. But we are really interested in the energy of sublimation, which is the heat (or enthalpy) of sublimation minus the additional PV work done by transforming a high density solid into a low density gas. At 240 K, the enthalpy of sublimation of water [H2O(s)➞H2O(g)] is ΔH = kJ/mol (see this website contains a number of useful properties of water)

2 We know that ΔU = ΔH- Δ(PV), or, at constant pressure, ΔU = ΔH- PΔV The density of ice at its melting point is kg/m³, or 916.72/0.0018=5.09e5 mol/m³. The molar volume of ice is the inverse of this number, namely, VM[H2O(s)]=1.964e-6 m³. The molar volume of H2O(g) at 240 K and 1 atm = RT/P = 8.314*240/1.01e5= m³ Thus for the sublimation of H2O at 240 K, ΔV= e-6= m³ Consequently, ΔU =51.139e e5×0.0198= 51139–1998=49.14e3 kJ/mol When we transform ice into water vapor, we are breaking 4 hydrogen-bonds per molecule. Thus, the energy of a hydrogen bond is 49.14/4 = 12.3 kJ/mol

3 Number of hydrogen bonds in liquid water
When ice melts some of the hydrogen bonds are broken. How many, in fact? We can estimate this from the energy of fusion of ice. We know that the heat of fusion of ice at 0˚C is 6.00 kJ/mol at 1.01e5 Pa pressure (1 atm). Since the molar volume of ice and that of water are very similar, the PV work done is melting ice will be very small, so ΔUfus≅ΔUfus = 6.00 kJ/mol We’ve already seen (previous page) that the strength of a hydrogen bond is 12 kJ/mol. Thus, the energy of fusion of water corresponds pretty closely to 1/2 the energy of a hydrogen bond. Consequently, we can say that each molecule in liquid water is joined to the other water molecules by, on the average 3½ hydrogen bonds. Another way of saying this is that the disorder in liquid water results in breaking 1/8 (or 12%) of the hydrogen bonds that were present in ice.


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