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## Homework Statement

Derive the basic relationship that the Antoine equation represents. Most importantly, explain the underlying condition when the Antoine equation applies and the underlying assumptions for the Antoine equation to be valid.

## Homework Equations

Clausius-Clapeyron Equation: dP

_{sat}/dT=ΔH/TΔV

Antoine Equation: lnP

^{sat}=A-B/(T+C)

## The Attempt at a Solution

Assume ΔV=V

_{gas}-V

_{liq}≈Vgas

From the Clausius-Clapeyron Equation, dP

_{sat}/dT=ΔH/(T*nRT/P)=ΔH/R * P/T

^{2}

Rearrange: dP

_{sat}/P=ΔH/R * dT/T

^{2}

Perform the integration, lnP

_{sat}=A-ΔH/RT=A-B/T, A, B are the constant

I think this should be the basic relationship of the Antoine Equation, even though C is not involved in the equation, as Antoine Equation is an empirical relationship.

However, I don't know what kind of conditions and assumptions I should make before using the Antoine Equation, and they are not explicitly stated in my textbook. Should I consider ΔV=V

_{gas}-V

_{liq}≈V

_{gas}as one of the assumptions?

Any help will be appreciated!