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Theory |
If a pure substance (which have only one component), exists in two phases, the degree of freedom is one in the formula:
Where C is the component, P is the number of phases, and F is the degree of freedom. In this scenario, C = 1 and P = 2, so:
However, if temperature is specified (thus using up the degree of freedom), then the two phases (liquid and gas) can exist simultaneously only at a certain pressure namely vapor pressure.
The vapor pressure of the liquid is located in the isoteniscope. This pressure can be measured using the mercury manometer (which is connected to the U-tube through the condenser) and can be calculated using the formula:
Where Pb is the corrected barometric pressure, Pv is the vapor pressure, and DP is the absolute value of the pressure difference between the two manometer logs.
However, before Pv can be calculated, corrected barometric pressure must be known.
To calculate corrected barometric pressure, the following formula is used:
Where Pb is the corrected barometric pressure, Tcorr is the temperature correction, and Gcorr is the gravitation correction.
To get the temperature correction, one must look for the tabulated values of Temperature corrections in the table located within the lab, and calculate the correct Temperature correction using the formula of interpolation:
By substituting pressure correction as y and pressure as x, we get:
Where Tcorr is the temperature correction, P1 and P2 is the pressure range from table in lab, and DP1T and DP2T is the pressure correction of the corresponding pressure P1 and P2.
The second part of the correction is based on the gravitation correction. Gravitation correction can be calculated by averaging the gravity correction of the corresponding latitude range (ex. If latitude is 51, one must average the gravitation correction values of latitude 50 and 52)
After Pv is taken care of, one can look at the concept of latent heat of vaporization.
Latent heat of vaporization is the energy to convert a unit mass of a substance from liquid phase to gas phase at constant temperature. Latent heat of vaporization usually bears the symbol DHv. There are two ways to calculate the latent heat of vaporization: Trouton’s rule and Clausius-Clapeyron equation
Note: From now on, P = Pv
Trouton’s Rule
Based on Trouton’s Rule, latent heat of vaporization shows a relationship with the normal temperature of the liquid. According to Trouton’s Rule,
 [1]
Where Tb is the normal boiling point measured in Kelvin and DHv is the corresponding latent heat of vaporization. This formula is used to estimate DHv when there is a given boiling point.
Please note that Trouton’s rule is accurate within a five percent range.
Clausius-Clapeyron equation
Another method of finding latent heat of vaporization is through Clausius-Clapeyron equation. The Clausius-Clapeyron Equation formula is:
 [1]
Where dP/dT is the slope of the vapor pressure curve, DHv is the heat of vaporization, Vg is the specific volumes of the vapor, Vl is the specific volumes of the liquid, and T is the absolute temperature.
The function of the Clausius-Clapeyron equation was to state that the slope of the curve of vapor pressure could be calculated from the DHv in the above formula. Assumptions can be made that the specific volume of the liquid phase can be ignored due to its relatively small number, and that Vg=RT/P (From the ideal gas law). When the previous formula replaces Vg-Vl, the formula then changes to:
  [1]
If the formula is integrated, it will turn into:
 [1]
Which in turn leads to:
 [1]
Where DHv is the latent heat of vaporization, R is the gas constant (8.314 kJ/molK), T is the temperature, ln(P) is the natural logarithm of vapor pressure, and C is a constant
There is another constant beside C, and that is the constant A. Constant A can be found by finding the slope of the graph when the x-axis is 1/Temperature and the y-axis is ln(P),
The slope formula is:
Where m is the slope of the graph (constant A), Dy is the difference between two y coordinates on the line of best fit of the graph, and Dx is the difference between two corresponding x coordinates on the line of best fit of the graph.
If A can also be found with this formula:
 (Reference Eqn. 7.33, Note: A is C1 in reference)
Then by substituting A into the equation  , we get:
 [2]
Normal boiling point is the temperature at which the vapor pressure of a pure substance is one standard atmosphere. The normal boiling point uses the formula  , but the P is set to 1atm, which is 101.325kPa.
If a binary mixture (which have two components), exists in two phases, the degree of freedom is one in the formula:
Where C is the component, P is the number of phases, and F is the degree of freedom. In this scenario, C = 2 and P = 2, so:
To calculate the number of moles of the components in the binary mixture, one can use the formula:
This formula is derived using the method of cancellation units, which in the end leaves the units in kmol.
If one wants to find the mole fraction of the a substance within its composition, the corresponding formula is used:
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