Question

By using the Clausius-Clapeyron equation, lnP= −ΔHvapRT+C, derive the relationship between the vapor pressures, P1 and P2, and the absolute temperatures at which they were measured, T1and T2.

Answer: ln P1/P2= ___

Answer 1

To find the relationship between vapor pressures P1 and P2 at temperatures T1 and T2, respectively, we derive from the Clausius-Clapeyron equation that ln(P1/P2) equals (ΔHvap/R) multiplied by (1/T2 - 1/T1).

Step-by-step explanation:

To derive the relationship between the vapor pressures P1 and P2, and the absolute temperatures they were measured at, T1 and T2, we use the Clausius-Clapeyron equation, which has the form ln P = -ΔHvap/(RT) + C. Applying this equation to both sets of pressure-temperature conditions, we can write:

ln P1 = -ΔHvap/(R*T1) + C (1)
ln P2 = -ΔHvap/(R*T2) + C (2)

By subtracting equation (2) from equation (1), we eliminate the constant C, since it is the same for both equations:

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

This derived formula shows the relationship between vapor pressures P1 and P2 and their corresponding temperatures T1 and T2.