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Multiple Choice
Denver, Colorado is about 1600 m above sea level, where atmospheric pressure is lower than . As a result, the boiling point of water in Denver is closest to which value?
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Verified step by step guidance
1
Understand that the boiling point of a liquid is the temperature at which its vapor pressure equals the external atmospheric pressure.
Recognize that at higher altitudes, such as Denver (1600 m above sea level), atmospheric pressure is lower than 1 atm, which lowers the boiling point of water compared to sea level.
Use the Clausius-Clapeyron equation to relate the change in boiling point to the change in pressure:
\[\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)\]
where \(P_1\) and \(T_1\) are the vapor pressure and boiling point at standard conditions (1 atm and 373 K), \(P_2\) is the atmospheric pressure at Denver, and \(T_2\) is the boiling point at Denver.
Gather or estimate the atmospheric pressure at Denver (less than 1 atm, approximately 0.83 atm) and use the known enthalpy of vaporization of water (\(\Delta H_{vap}\)) and the gas constant \(R\) to solve for \(T_2\).
Convert the temperature \(T_2\) from Kelvin to Celsius by subtracting 273.15, which will give the boiling point of water at Denver's altitude, expected to be lower than 100°C.