Question

Estimate the boiling point of water in Leadville, Colorado, elevation 3170 m. To do this, use...

Estimate the boiling point of water in Leadville, Colorado, elevation 3170 m. To do this, use the barometric formula relating pressure and altitude: P=P0×10−Mgh/(2.303RT) (where P = pressure in atm; P0 = 1 atm; g = acceleration due to gravity; molar mass of air, M= 0.02896 kg mol−1 ; R = 8.3145 J mol−1 K−1; and T is the Kelvin temperature). Assume the air temperature is 10.0 ∘C and that ΔHvap= 41 kJ mol−1 H2O.

Homework Answers

Answer #1

First we get the pressure:

P = 1 atm * 10^(-(0.02896 kg/mol * 9.81m/s2 * 3170 m)/(2.303 * 8.3145 J/molK * 283K))

Units cancel out as J/mol over J/mol, so:

P = 1 atm * 0.682 = 0.682 atm

We now have a point of comparison, which is the normal boiling point at sea level (1 atm), and we will get the new point with the pressure obtained, using clausius clapeyron:

ln (P1/P2) = deltaHvap / R * (1/T2 - 1/T1)

ln (1atm / 0.682 atm) = 41 kJ/mol / 0.0083145 kJ/mol * (1/T2 - 1/373.15)

0.382726 = 4931.14 * (1/T2 - 0.00268)

7.7614 x 10-5 = 1/T2 - 0.00268

0.0027576 = 1/T2

T2 = 362.63 K = 89.48 ºC

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