Liquids & Solids, cont.
- freezing/melting point: temperature at which solid and liquid are in equilibrium.
- heat of fusion/crystallization
- supercooling (occurs because its hard to "seed" crystals - will see later when solids are discussed)
- Glasses: supercooled "solid" liquids.
- Heating/cooling curves, below.
- due to van der Waals forces and long molecules
- due to strong H-bonding (ethylene glycol, HOCH2CH2OH has a viscosity much like high MW syrup)
- Surface Tension: due to attraction of molecules of liquid for each other (diagram).
- detergents/surfactants and wetting (water striders, ducks etc.)
Weak bonds range from about 10% as strong as a covalent or ionic bond to <1% as strong. Note the examples in the table below:
|Example||Average Strength, kcal/mol (kJ/mol)||Range**|
|Dipole-induced dipole*||CH4 ClCH3||0.1-0.2 (0.4-4)||1/r6|
|Hydrogen bond||3-8 (12-30)|
Thus for hydrocarbons, which are essentially completely non-polar, we see a very low boiling point for methane (CH4) of - 161°C and a fairly regular increase in boiling point as carbons are added (ethane, C2H6 - 88°C; butane, C4H10 - 0.5°C; hexane, C6H14 69°C; octane, C8H18 126°C; etc.) until very large molecules such as paraffin (about 100 C's) and polyethylene (>1,000 C's) are essentially non-volatile. Note also though, in these very large molecules the forces holding the substance together have become significant due to the very large contact areas.
Hydrogen bonds are a special case of weak bonds. Note that they are significantly stronger (>100 fold) than the other weak bonds at about 4-10% as strong as a covalent bond. Hydrogen bonds only occur when a hydrogen bound to a small, very electronegative atom is brought close to another small, very electronegative atom. Essentially this means that we only see hydrogen bonds between hydrogens bound to N, O, or F (second Period electronegative elements) and N, O, or F. So we can have O-H O, O-H N, O-H F, N-H O, N-H N etc. hydrogen bonds. This is because hydrogen bonds involve dipole-dipole interactions, but they also have covalent character (about 10% of the sharing we see in true covalent bonds) which requires that the participating atoms be small enough to get close enough to allow such partial sharing. (Grp IVA-VIIA bp plot, text Fig 10.4, p 427:
Hydrogen bonding accounts for much of the special properties of water, such as its very high boiling point (261°C higher than methane with only a 10% increase in MW), high viscosity, high heat capacity etc. which in turn are due to the strong bonds between the individual molecules so they stick together.
Examples of water excluding non-polar substances to force the formation of biomembranes, separate out oils etc.
Occurs when rate of evaporation = rate of condensation. Must have some liquid (or solid for sublimation) present. (Figure 10.39, p 460)
Quantitative variation of vapor pressure with temperature:
Plot (Pvap vs. T; upward curve) Figure 10.42, p 462
public domain image via Wikipedia Creative Commons
Plot (lnPvap vs 1/T; linear with negative slope, T = K) Figure 10.42, p 4462
For the linear plot can find the equation (y = ax + b):
This expression is known as the Clausius-Clapeyron Equation.We can use this equation to find useful information such as the boiling points of liquids at different elevations (and thus pressures).
Example: Find the boiling point of water at 10,000 ft elevation if the atmospheric pressure is 508.4 mmHg. Hvap = 4.39 x 104 J/mol.
How do we solve this? If we take the difference between the two situations we get:
ln P1 - ln P2 = -Hvap/R (1/T1 - 1/T2) + b - b
reaarranging and recalling that log a - log b = loga/b
ln P1/ P2 = Hvap/R (1/T2 - 1/T1)
1/T2 - 1/T1 = (R/Hvap) (ln P1/ P2)
putting in numbers
1/T2 = (8.315 JK-1mol-1/ 4.39 x 104 J/mol) ln (760 mmHg / 508.4 mmHg) + 1/373.15 K
1/T2 = 7.62 x 10-5 + 2.68 x10-3 = 2.76 x 10-3
T2 = 362.7 K = 89.7 °CNotice that we can also use the data from vapor pressures (or boiling points) at two pressures to calculate a value for Hvap!
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© R A Paselk
Last modified 22 April 2013