On top of one of the peaks in Rocky Mountain National Park the pressure of the atmosphere is 500.torr. Determine the boiling point of water at this location. The heat of vaporization of water is 40.7 kJ/mol? Show work for me please! Thank you
Use the Clausius-Clapeyron equation.
The equation require 2 pressure but there is only 1 in this problem
Could I use STP( 760 torr and 273K) to plug in the equation ?
To determine the boiling point of water at a specific location given the pressure, we can use the Clausius-Clapeyron equation.
The Clausius-Clapeyron equation is given by: ln(P1/P2) = (ΔHvap/R) * (1/T2 - 1/T1), where P1 and P2 are the initial and final pressures, ΔHvap is the heat of vaporization, R is the gas constant (8.314 J/(mol K)), T1 is the initial temperature, and T2 is the final temperature.
In this case, we are given the pressure at the location (P2 = 500 torr) and the heat of vaporization of water (ΔHvap = 40.7 kJ/mol = 40,700 J/mol). We also know that the initial pressure of water is the standard atmospheric pressure (P1 = 760 torr) and the boiling point of water at this pressure is 100°C or 373.15 K.
Now, we can rearrange the Clausius-Clapeyron equation to solve for the boiling point at the given pressure:
ln(P1/P2) = (ΔHvap/R) * (1/T2 - 1/T1)
Now substitute the given values:
ln(760/500) = (40,700 J/mol / (8.314 J/(mol K))) * (1/T2 - 1/373.15)
Simplify:
ln(1.52) = 4925.5 * (1/T2 - 1/373.15)
Now, solve for (1/T2 - 1/373.15):
1/T2 - 1/373.15 = ln(1.52) / 4925.5
Now, solve for T2:
1/T2 = ln(1.52) / 4925.5 + 1/373.15
T2 = 1 / (ln(1.52) / 4925.5 + 1/373.15)
Using a calculator, we can evaluate this expression to find the boiling point of water at the given pressure.