Which equation relates the natural log of vapor pressure ratio to temperature difference during phase transitions?

Which equation relates the natural log of vapor pressure ratio to temperature difference during phase transitions?

• A. k = A e^(-Ea/RT)
• B. ln((P2^sat)/(P1^sat)) = (-ΔHvap)/R (1/T2 - 1/T1)
• C. P = RT/(V - b) - a/V^2
• D. ΔP = 8 μ L Q /(π r^4)

Answer: (B)

Vapor pressure along a phase boundary follows the Clausius–Clapeyron relation. When the enthalpy of vaporization is treated as roughly constant, integrating d(ln P^sat)/dT = ΔHvap/(R T^2) yields a linear form in 1/T: ln(P2^sat/P1^sat) = -ΔHvap/R (1/T2 - 1/T1). This directly connects the natural log of the vapor-pressure ratio at two temperatures to the reciprocal temperature difference, with ΔHvap the latent heat of vaporization and R the gas constant. The other expressions correspond to different topics—Arrhenius behavior of reaction rates, a real-gas equation of state, and a flow-pressure relation, none of which describe how vapor pressure changes with temperature during a phase change.

Vapor pressure along a phase boundary follows the Clausius–Clapeyron relation. When the enthalpy of vaporization is treated as roughly constant, integrating d(ln P^sat)/dT = ΔHvap/(R T^2) yields a linear form in 1/T: ln(P2^sat/P1^sat) = -ΔHvap/R (1/T2 - 1/T1). This directly connects the natural log of the vapor-pressure ratio at two temperatures to the reciprocal temperature difference, with ΔHvap the latent heat of vaporization and R the gas constant. The other expressions correspond to different topics—Arrhenius behavior of reaction rates, a real-gas equation of state, and a flow-pressure relation, none of which describe how vapor pressure changes with temperature during a phase change.