Question

a) Combining the barometric distribution with the Clausius-Clapeyron equation, deduce an equation that relates the boiling point of a liquid to the temperature of the atmosphere, temperature (Ta) and altitude (h). In b) and c) suppose ta = 20 ° C. 
b) For water, tb = 100 ° C at 1 atm and ΔH vap = 40,670 kJ / mol. What is the boiling point on the top of a mountain with h = 4754 m? 
c) For diethyl ether, tb = 34.6 ° C at 1 atm and ΔH vap = 29.86 kJ / mol. What is the boiling point on the mountain top of b).

Answer 1

a) Combination of barometric distribution with the Clausius-Clapeyron equation can be written as follows.

(1/T_h) = {-Mgh/(ΔH_vapT_b)} + 1/T_a

Here, M = molar mass of air = 0.029 kg/mol

g = acceleration due to gravity = 9.8 m/s²

h = altitude = 4754 m

T_a = temperature of atmosphere = 20 ^oC = (20+273.15) K = 293.15 K

T_b = boiling point at 1 atm

T_h = boiling point on the altitude h.

b) (1/T_h) = {-0.029 kg/mol​ * 9.8 m/s² * 4754 m/(40670*10³ kg m² s^-2/mol * 373.15 K)} + 1/293.15 K

i.e. T_h = 293.16 K = 20.01 ^oC

c) (1/T_h) = {-0.029 kg/mol​ * 9.8 m/s² * 4754 m/(29.86*10³ kg m² s^-2/mol * 307.75 K)} + 1/293.15 K

i.e. T_h = 306.35 K = 33.2 ^oC