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.
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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.
where Δ
H_{vap} 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:
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
H_{vap} , can be determined by using the Clausius-Clapeyron equation:
Since we have two vapor pressure-temperature values (
T_{1} = 34.0 °C = 307.2 K,
P_{1} = 10.0 kPa and
T_{2} = 98.8 °C = 372.0 K,
P_{2} = 100 kPa), we can substitute them into this equation and solve for Δ
H_{vap} . Rearranging the Clausius-Clapeyron equation and solving for Δ
H_{vap} 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.
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
The eyes of some reptiles are sensitive to 850 nm light. If the minimum energy to trigger the receptor at this wavelength is 3.15 x 10-14 J, what is the minimum number of 850 nm photons that must hit the receptor in order for it to be triggered?
A teaspoon of the carbohydrate sucrose contains 16 calories, what is the mass of one teaspoo of sucrose if the average number of calories for carbohydrate is 4.1 calories/g?
4. On the basis of dipole moments and/or hydrogen bonding, explain in a qualitative way the differences in the boiling points of acetone (56.2 °C) and 1-propanol (97.4 °C), which have similar molar masses
Which of the following will increase the percent of HF that is converted to the fluoride ion in water? (a) addition of NaOH (b) addition of HCl (c) addition of NaF