The boiling points of liquids are the temperatures at which their equilibrium vapor pressures equal the pressure of the surrounding atmosphere. Normal boiling points are those corresponding to a pressure of 1 atm (101.3 kPa.)
A boiling point at reduced pressure
A typical atmospheric pressure in Leadville, Colorado (elevation 10,200 feet) is 68 kPa. Use the graph in
[link] to determine the boiling point of water at this elevation.
Solution
The graph of the vapor pressure of water versus temperature in
[link] indicates that the vapor pressure of water is 68 kPa at about 90 °C. Thus, at about 90 °C, the vapor pressure of water will equal the atmospheric pressure in Leadville, and water will boil.
Check your learning
The boiling point of ethyl ether was measured to be 10 °C at a base camp on the slopes of Mount Everest. Use
[link] to determine the approximate atmospheric pressure at the camp.
The quantitative relation between a substance’s vapor pressure and its temperature is described by the
Clausius-Clapeyron equation :
where Δ
Hvap is the enthalpy of vaporization for the liquid,
R is the gas constant, and ln
A is a constant whose value depends on the chemical identity of the substance. This equation is often rearranged into logarithmic form to yield the linear equation:
This linear equation may be expressed in a two-point format that is convenient for use in various computations, as demonstrated in the example exercises that follow. If at temperature T
1 , the vapor pressure is P
1 , and at temperature T
2 , the vapor pressure is T
2 , the corresponding linear equations are:
Since the constant, ln
A , is the same, these two equations may be rearranged to isolate ln
A and then set them equal to one another:
which can be combined into:
Estimating enthalpy of vaporization
Isooctane (2,2,4-trimethylpentane) has an octane rating of 100. It is used as one of the standards for the octane-rating system for gasoline. At 34.0 °C, the vapor pressure of isooctane is 10.0 kPa, and at 98.8 °C, its vapor pressure is 100.0 kPa. Use this information to estimate the enthalpy of vaporization for isooctane.
Solution
The enthalpy of vaporization, Δ
Hvap , can be determined by using the Clausius-Clapeyron equation:
Since we have two vapor pressure-temperature values (
T1 = 34.0 °C = 307.2 K,
P1 = 10.0 kPa and
T2 = 98.8 °C = 372.0 K,
P2 = 100 kPa), we can substitute them into this equation and solve for Δ
Hvap . Rearranging the Clausius-Clapeyron equation and solving for Δ
Hvap yields:
Note that the pressure can be in any units, so long as they agree for both
P values, but the temperature must be in kelvin for the Clausius-Clapeyron equation to be valid.
Check your learning
At 20.0 °C, the vapor pressure of ethanol is 5.95 kPa, and at 63.5 °C, its vapor pressure is 53.3 kPa. Use this information to estimate the enthalpy of vaporization for ethanol.
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
