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.