The vapor pressure P of a liquid rises exponentially when it is heated according
ID: 1010436 • Letter: T
Question
The vapor pressure P of a liquid rises exponentially when it is heated according to the equation ln(P_2/P_1) = -delta H/R (1/T_2 - 1/T_1) Here P_2 and P_1 are the vapor pressures of the liquid at the Kelvin temperatures T_2 and T_1 after and before the temperature increase, R is the gas constant 8.3 J K^-1 mol^-1, and delta H is the liquid's enthalpy of vaporization, which for water is 44 kj mol^-1. Calculate the percentage increase in the vapor pressure of water that occurs if the temperature is raised from 15degreeC to 18degreeC. Give several reasons why the amount of outgoing thermal infrared in water's absorption bands may not be increased by exactly the percentage you calculate if the average air/surface temperature is increased to 18degreeC.Explanation / Answer
The equation may also be written as,
ln(P2/P1) = dHv/R[1/T1 - 1/T2]
with,
T1 = 15 + 273 = 288 K
T2 = 18 + 273 = 291 K
dHv = 44 kJ/mol
R = 8.3 J/K.mol
we get,
ln(P2/P1) = 44000/8.3[1/288 - 1/291]
P2/P1 = 1.207
percent increase in vapor pressure from 15 to 18 oC = 1.207 x 100/2.207 = 54.67%
For water other strong intermolecular forces such as hydrogen bonding plays a major role in determining the overall change in vapor pressure with temperature. The interaction between air surface would induce addiitonal effect on changing vapor pressure. As the temperature is changed the net change in amount of H-bonding present in the system differs and that would result in a change in vapor pressure. Thus the precentage which entirely depends upon temperature does not relate to actual vapor pressure of the system.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.