Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 109 - General Chemistry - Spring 2011

Lecture Notes 31: 11 April


Equilibrium Vapor Pressure

Occurs when rate of evaporation = rate of condensation. Must have some liquid (or solid for sublimation) present. (Figure 10.39, p 460)

Recall that:

Quantitative variation of vapor pressure with temperature:

Plot (Pvap vs. T; upward curve) Figure 10.42, p 462

plot of water vapor pressure vs. temperature

public domain image via Wikipedia Creative Commons


Plot (lnPvap vs 1/T; linear with negative slope, T = K) Figure 10.42, p 4462

plot of ln (vapor pressure) vs. 1/T

For the linear plot can find the equation (y = ax + b):

equation of line for plot of  ln (vapor pressure) vs. 1/T

where a = the slope = -deltaHvap/R and R = 8.315 JK-1mol-1. So

Clausius-Clapeyron equation

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. deltaHvap = 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 = -deltaHvap/R (1/T1 - 1/T2) + b - b

reaarranging and recalling that log a - log b = loga/b

ln P1/ P2 = deltaHvap/R (1/T2 - 1/T1)


1/T2 - 1/T1 = (R/deltaHvap) (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 °C

Notice that we can also use the data from vapor pressures (or boiling points) at two pressures to calculate a value for deltaHvap!

Heating & Cooling Curves

A consideration of vapor pressure etc leads to the behaviors of substances with increasing (or decreasing) temperture (see Fig 10.44, p 464 of Zumdahl 5th ed):

plot of heating curve for water

Solids and Crystals

Solids:Recall earlier definition - solids have fixed or definite shapes and volumes. By this definition solids are strictly limited to the crystalline solids. (The amorphous (noncrystalline) solids discussed in our text are what we have discussed as supercooled liquids.)


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© R A Paselk

Last modified 11 April 2011