Useful Equations - The Clapeyron Equation. Gives the rate of change of the vapor pressure with temperature, dp/dT, in terms of the enthalpy of vaporisation, ∆H vap , volume of the liquid, V l , and volume of the vapor, V v , at temperature T and at a pressure equal to the vapor pressure.
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Clausius showed the Clapeyron equation could be simplified by assuming the vapor obeys the ideal gas law and by neglecting the volume of a mole of liquid in comparison with a mole of vapor. For example with water at 100oC the volume of vapor is 30.2 liters and the volume of liquid is 0.0188 liter
C is the integration constant
Using this equation, it is possible to calculate the heat of vaporization or the heat of sublimation from the vapor pressure at two different temperatures.
The approximations involve the assumptions that the vapor is an ideal gas and the heat of vaporization is independent of temperature.
Over wide temperature ranges, plots of log P versus 1/T are somewhat curved because ∆Hvap varies with temperature. It is possible to calculate the heat of vaporization at any temperature from the slope of the curve by drawing a tangent to the curve at the required temperature.
These relationships may be applied to finite changes by replacing the d’s by ∆’s
Although the criteria show whether a change is spontaneous it does not provide any information on the speed (kinetics) of the process.
ΔG = ΔH - T ΔS
This equation is very important because it links the standard Gibbs free energy for a reaction with the value of the equilibrium constant.Chemical Equilibria
= -6.8162 kcal
= -19.28 cal deg-1
= -12,140 cal
= 21.8278 kcal
= 31.3822 kcal