Water boils at 100 °C at 1.00 atm pressure. At what temperature will water boil in Alma, Colorado, elevation 10,361 feet, where the atmospheric pressure is 0.527 atm (For water, AHvap = 40.7 kJ/mol)
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![### Boiling Point of Water at Different Atmospheric Pressures
Water boils at 100 ºC at 1.00 atm pressure. At what temperature will water boil in Alma, Colorado, at an elevation of 10,361 feet, where the atmospheric pressure is 0.527 atm? (For water, ΔHvap = 40.7 kJ/mol)
**Solution Approach:**
To solve this problem, you can use the Clausius-Clapeyron equation, which describes the relationship between the vapor pressure and temperature of a substance:
\[
\ln \left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{vap}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)
\]
Where:
- \( P_1 = \) initial pressure (1.00 atm)
- \( P_2 = \) final pressure (0.527 atm)
- \( \Delta H_{vap} = \) enthalpy of vaporization (40.7 kJ/mol)
- \( R = \) gas constant (8.314 J/mol·K)
- \( T_1 = \) initial boiling temperature (373 K or 100 ºC)
- \( T_2 = \) final boiling temperature (unknown)
**Steps:**
1. Convert temperatures to Kelvin.
2. Rearrange the Clausius-Clapeyron equation to solve for \( T_2 \).
3. Insert the given values and solve for the unknown temperature, \( T_2 \).
This process will allow us to determine the boiling point of water at the specified atmospheric pressure in Alma, Colorado.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbca33481-84f0-4d0e-9458-2fdcb949c0ec%2F5e29961c-b059-4f53-b84f-b99b05648346%2F8guplz8_processed.jpeg&w=3840&q=75)
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