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DETERMINATION OF SATURATED VAPOR PRESSURE OF ORGANIC LIQUIDS
2.1. Introduction
Saturated vapor is in dynamic equilibrium with the liquid from which it has been formed. The state of dynamic equilibrium means that two opposite processes, namely the evaporation of liquid and vapor condensation, take place at the interface in the same time and at the same rate. When interpreting this phenomenon it is declared that the number of liquid molecules transforming into vapor in a time unit is equal to the number of vapor molecules condensing on the liquid surface.
Vapor pressure in the state of equilibrium is called saturated vapor pressure. According to the phase rule, a one-component and two-phase system is a one-variable system. Hence, at a specified temperature the vapor pressure over the liquid surface is precisely determined. At the same time this means that changes in the saturated vapor pressure are related by a functional relation to temperature changes. This is presented quantitatively by the Clausius-Clapeyron equation
(2.1)
where p saturated vapor pressure of pure liquid [Pa],
i molar enthalpy of evaporation EMBED Equation.3 ,
vp molar volume of vapor EMBED Equation.3 ,
vc molar volume of liquid EMBED Equation.3 .
Under the assumption of vp >> vc, stability of and in narrow ranges of temperature and vapor satisfying the perfect gas equation of state, the integrated form of equation (2.1) is presented by equation (2.2)
(2.2)
where p0 and p are the saturated vapor pressure at temperature T0 and T, respectively, and R is the universal gas constant.
Taking p0 and T0 as constant values, we have
(2.3)
where A and B are constant for a given liquid.
More precise formulas used in practice are Antoine (2.4) and Nernst (2.5) equations:
(2.4)
(2.5)
To find the values of saturated vapor pressure by means of equations (2.3), (2.4) or (2.5) we should know constants A and B or a, b, c, or A, C and E for a given substance.
Besides the effect of temperature which is presented in equations (2.3) to (2.5), the value of saturated vapor pressure depends also on the shape of liquid surface and the presence of inert gas in the gas phase.
It was found experimentally that the saturated vapor pressure is higher over convex liquid surfaces (with the center of curvature lying within the liquid phase r > 0) than over a flat surface (r = 0) at the same temperature. A decrease of saturated vapor pressure appears over concave liquid surfaces (with the center of curvature lying outside the liquid r < 0).
This mechanism can be explained in the following way. Molecules on the liquid surface, when it is convex, are less associated with the liquid interior than in the case of flat or concave surfaces. Therefore, energy input needed for their passage into the vapor phase is small. Thus, at the same temperature, there will be more molecules in the vapor phase and hence the saturated vapor pressure over the convex liquid surface will be higher.
A quantitative relation between the change of saturated vapor pressure p and curvature radius r is derived on the basis of energy balance.
Taking p as the saturated vapor pressure over the flat liquid surface, and p+p as the saturated vapor pressure at the same temperature over a spherical droplet, for the differential fluid weight one can determine work dL required to transfer it from the droplet to the flat surface.
This transition constitutes of three stages:
liquid evaporation from a droplet with molar volume vc to saturated vapor at pressure p+p and molar volume vp1,
isothermal vapor expansion from pressure p+p to pressure p and molar volume vp2,
isothermal vapor condensation under pressure p to molar volume vc.
According to the described parts of the process, the total work dL is
(2.6)
where M molecular weight of the liquid EMBED Equation.3 ,
m liquid mass [kg].
After developing equation (2.6), making necessary simplifications and observing that (p+p)vp1 = pvp2, we get
(2.7)
Work presented by equation (2.7) is equal to the work of changing the surface which is done by surface tension
(2.8)
A decrease of ball mass m EMBED Equation.3 by dm (4r2dr) causes a change in the droplet surface A (4r2) by dA (8rdr), i.e.
(2.9)
Substituting equation (2.9) to (2.8) and comparing to equation (2.7), we have after transformation
(2.10)
Due to the fact that the value of equation EMBED Equation.3 is only slightly higher than unity, without the risk of a serious mistake we can write
(2.11)
Hence, finally we have
(2.12)
For the convex surface (r>0) we have p>0, for the concave surface (r<0) we get p<0 and for the flat surface ( EMBED Equation.3 ) we have p = 0.
The presence of inert gas in the vapor phase is reduced to two cases. In the first case, when the inert gas partly dissolves in the liquid, the saturated vapor pressure decreases. In the second case, when the gas does not dissolve in the liquid, the saturated vapor pressure increases. This is due to the fact that the presence of foreign molecules hinders the access of vapor molecules to the interface and reduces the likelihood of condensation. At the same time collisions of inert gas molecules with the liquid surface contribute to increasing the energy of molecules on the surface and their detachment from the liquid phase.
In the presence of the inert gas, at the temperature T, the total pressure p over the liquid is given by the formula:
(2.13)
where p saturated vapor pressure over pure liquid,
p0 inert gas pressure.
In the case of total pressure imposed on the liquid P > p, at given temperature T the saturated vapor pressure p can be calculated from the equation:
(2.14)
where p saturated vapor pressure when the liquid is under the pressure P = p + p0,
p saturated vapor pressure over the pure liquid,
vc molar volume of liquid at temperature T and pressure P EMBED Equation.3 ,
R universal gas constant EMBED Equation.3 .
The saturated vapor pressure can also be determined graphically by comparing with saturated vapor pressure of the reference liquid.
Such methods for determination of pressure use similarity of physicochemical properties. Two techniques should be mentioned here: Duhring and Cox methods.
The first one is based on the linear relationship between boiling points of two different liquids, however with similar structure and chemical properties, but at the same pressure
(2.15)
where Ti boiling point of tested liquid [K],
Tj boiling point of reference liquid [K],
A1, B1 constants.
To find the values of numerical coefficients A1 and B1 in equation (2.15), we should know for two different pressures the corresponding two pairs of boiling points of the tested and reference liquids. The boiling points of reference liquid are found in the dependence of saturated vapor pressure on temperature given in the tabularized form or as a diagram. In this way two equations are obtained in which unknown coefficients are A1 and B1.
The knowledge of coefficients A1 and B1 allows us to draw relation (2.15) in the system of rectangular coordinates (Tj, Ti). Each point on the straight line representing equation (2.15) determines boiling points of the reference and tested liquids which have the same saturated vapor pressure in this point.
Hence, determination of the saturated vapor pressure of a liquid tested at any temperature Ti1 consists in a graphic determination of reference liquid temperature Tj1, and then reading the pressure value pj1 = pi1 from tables or diagram pj = f(Tj).
The principle and procedure in the Cox method are analogous to the Duhring method. So, to be able to use equation (2.16) for two different boiling points it is necessary to know two corresponding pairs of saturated vapor pressures of the tested and reference liquids and the dependence of saturated vapor pressure of the reference liquid on temperature.
Practical use of these methods is possible when in addition to the relation pj = f(Tj) we have two experimental values for the tested liquid (in the Duhring method boiling point, in the Cox method saturated vapor pressure).
The aim of the exercise is to determine experimentally the dependence of saturated vapor pressure of an organic liquid on temperature and to compare the so specified values to literature data.
Fig. 2.1. Schematic of: a) valve z position, b) measuring apparatus: 1 measuring flask, 2 thermometer, 3 reflux condenser, 4 manometer, 5 manostat, 6 safety flask
2.3. Measuring apparatus
The measuring apparatus is shown schematically in Figure 2.1. Its main element is a glass measuring flask (1) with a thermometer (2) placed in it to measure temperature equilibrium. The flask is heated electrically. The heating is controlled by an autotransformer. Vapor produced from the tested liquid flows into the reflux condenser (3) where it condenses and returns to the measuring flask. The measuring flask is connected through the condenser to mercury manometer (4). Manostat (5) is used to stabilize pressure. Through the valve z and safety flask (6) the apparatus is connected to a vacuum pump.
2.4. Measurement methods
2.4.1. Preliminary procedure preceding the measurements
Check if liquid to be tested is in the measuring flask. If it is not, pull out the thermometer carefully and through a funnel pour so much liquid that the thermometer ball is completely immersed in it. To prevent liquid overheating add a pinch of crushed kaolin to the flask.
Check the tightness of the apparatus. The valve z should be in position 1 (the measuring flask connected to the vacuum pump at cut-off atmosphere) and produces vacuum of 300-400 mm Hg. Then, turn the valve left and set in position 3 (the vacuum pump connected to the atmosphere, the measuring flask cut off from the atmosphere and the vacuum pump). Observe stability of the manometer deflection. Negative pressure in the flask should remain at a constant level for about 4-5 minutes which shows a sufficient tightness of the installation. Next, turn the vacuum pump off. The pump should always be turned off with valve z in position 3. This position provides a connection of the vacuum pump to the atmosphere and prevents suction of water into the measuring section.
Turn on the cooling water flow through the reflux condenser.
2.4.2. Procedure during the measurements
Turn on electric heating and then control it so that the liquid is in the state of delicate boiling. This operation should be carried out under atmospheric pressure. When temperature t gets stable, write down indications of the thermometer (the manometer does not show naturally any pressure difference h) and the value of atmospheric pressure P on the barometer. These values are the data of the first measurement.
Perform the next measurement at the pressure lower than atmospheric. For this purpose, with the valve z set in position 1 turn on the vacuum pump to obtain in the apparatus the pressure by about 30-40 mm Hg lower than atmospheric. Next, cut off the measuring section from the water pump by turning the valve z left to position 3. At the same time observe liquid in the measuring flask to prevent overheating. To do this decrease electric heating in an adequate way. When in the new conditions the temperature t and pressure difference h are stabilized in the manometer during boiling of the liquid in the measuring flask, these value are the data for the next measurement.
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The last measurement should be performed in vacuum conditions specified by the tutor (you are absolutely not allowed to increase the vacuum in the system above the specified level, otherwise the manometric fluid will get to the apparatus). It should be taken into account that the measurements can be carried out starting with the highest vacuum up to the atmospheric pressure.
2.4.3. Procedure after the measurements
Turn off the heating of liquid.
When the final measurement was performed under reduced pressure, the valve z was in position 3. Hence, the vacuum pump should be turned off by closing water supply to it. Next vacuum in the system should be eliminated by turning the valve z right to position 2 (the vacuum pump cut off, the system connected to the atmosphere).
2.5. Safety note
The exercise can start only when approved by the tutor.
Handle the tested organic liquids carefully because of their flammability and toxicity.
Carefully supply the atmospheric air to the apparatus while equalizing pressure during vacuum elimination, so as to avoid sudden motion of the manometric fluid, which could cause penetration of mercury into the system or to the outside.
Handle glass parts of the apparatus carefully (the risk of breaking).
Inform the tutor of any disturbances in the operation of the apparatus.
2.6. Description of results
While analyzing results of the measurements the measuring data given in Table 2.1 are used. Results of calculations are also written in this table.
The following calculations and diagrams are made:
The diagram of relation p = f(t) is prepared.
The diagram of relation EMBED Equation.3 is prepared.
Using the linear regression method the coefficients A and B in equation (2.3) are defined.
On the diagrams mentioned in points 1 and 2 literature data are plotted for comparison.
2.7. Table of measurements and calculation results
Table 2.1
No.HPatmplog ptT EMBED Equation.3 AB[mm Hg][mm Hg][mm Hg][C][K] EMBED Equation.3
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