Vapor Pressure 101 - How to describe phase equilibria (Vaporization, Absorption)
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Lauth, Jakob Günter (SciFox)
The vapor pressure is the equilibrium partial pressure over a condensed phase. The vapor pressure mainly depends on the volatility of the compound and temperature. The vapor pressure curve of a pure substance, which begins at the triple point and ends at the critical point, can be described using Clausius-Clapeyron equation . With a solute present, the vapor pressure is lower than with the pure solvent. Vapor pressure reduction is proportional to the concentration of the solute and described by Raoult s 1st law. When we dissolve a gas in a liquid, the amount of gas dissolved is proportional to the partial pressure of the gas above the liquid - that's Henry's law.
 Liquids can evaporate, gases can condense. How do pressure and temperature affect these phase transitions? Welcome to FisCAM Basics, our topic today, vapor pressure, a special case of a phase equilibrium. Monoculars change from one phase to another. What is vapor pressure anyway? Consider an evacuated vessel at 20 centigrade and putting liquid water into it. First of all, the pressure in the vessel will be zero. However, the water will start to evaporate and the pressure above the liquid phase will increase. Water partial pressure will build up in the gas phase. For example, in this situation, 1.15 kilopascals. As this state does not correspond to equilibrium rate, water will continue to evaporate. The partial pressure will rise further until at 2.3 kilopascals, the pressure above the liquid phase will remain constant. We are now at equilibrium in phase equilibrium. The partial pressure over a condensed phase at equilibrium is called vapor pressure. The vapor pressure of water at 20 centigrade is 2.3 kilopascals. We mark vapor pressure with an asterisk. The vapor pressure strongly depends on temperature. At zero centigrade, it is 0.6 kilopascals and at 100 centigrade, 101.3 kilopascals. That's exactly one atmosphere. Well, 100 centigrade is a standard boiling point of water. It's defined to be the temperature at which the vapor pressure is equal to the external pressure. If we set the partial pressure of water in relation to the vapor pressure of water, we get the relative humidity phi. This relative humidity is 100%. The air is saturated in water vapor when the vapor pressure is reached. In the second picture, phi equals 50% humidity in the first picture, 0%. We can even oversaturate the gas phase with water vapor. Then phi will exceed 100%. However, this is a metastable state. Vapor pressure is a special case for a phase equilibrium. With these equilibria, a component can move between two phases. In this case, what is the condition for equilibrium? We can look at the whole thing thermodynamically. That equilibrium when the water feels equally fine in both phases. More scientifically speaking, when its stability is the same in both phases. You might remember that Gibbs free energy or chemical potential is a measure for instability. So this is the thermodynamic condition. The chemical potential of water in one phase is equal to the chemical potential of water in the other phase. We can also consider the question kinetically. There is equilibrium if the rate of evaporation shown here in green color is the same as the rate of condensation shown here in blue color. We have a so-called dynamic equilibrium. Everything happens macroscopically, but microscopically we have a forward and reverse process taking place at the same rates. Of course, vapor pressure depends on the compound we are dealing with. Water has a lower vapor pressure than a volatile low boiler like ethanol. The vapor pressure is kind of a measure for the tendency of a substance to escape from the liquid phase. As already mentioned, the vapor pressure mainly depends on temperature. With rising the temperature, vapor pressure increases exponentially as we will see shortly. The vapor pressure also depends on the purity of the phase. If we add another component to water and form a homogeneous mixture, the vapor pressure drops. The vapor pressure also depends to a very small extent to whether we have a flat surface or a curved surface. Over very small droplets, vapor pressure will be larger than over a flat surface. Vapor pressure also increases with an additional inert gas on the high pressure. You remember our three-dimensional PVT phase diagram? Where do we find vapor pressure in this diagram? It is this green region in which liquid and gas are present at the same time. If we project this phase diagram onto the Pt surface, the two-phase region is reduced to a line and we get the typical Pt phase diagram of a pure substance. We see three lines, that is, the vapor pressure curve, the sublimation pressure curve and the melting pressure curve. These three lines intersect at one point, the so-called triple point. The triple point for water is 0.01 centigrade and 0.6 kilopascals. The triple point marks the beginning of the vapor pressure curve. The vapor pressure curve becomes steeper with increasing temperature and ends at the critical point. The critical point of water is 374 centigrade and 22,000 kilopascals. From this diagram, we can depict the boiling point of the liquid for any pressure. The standard boiling point of water at 101 kilopascals is 100 centigrade. At 20 centigrade, the vapor pressure of water is 2.3 kilopascals. If we had an external pressure of 2.3 kilopascals, water would boil at 20 centigrade. There have been many attempts to describe the vapor pressure curve mathematically. In the equation named after them, Clausius and Clapeyron derived the relation between two points on the vapor pressure curve and the enthalpy of vaporization delta H sub VAP. The Antoine equation, which uses three empirical Antoine vectors A, B and C, is even more popular for the calculation of vapor pressures. It gives very precise results for vapor pressures but does not have as nice a thermo-economical background as the equation of Clausius and Clapeyron. With the help of Clausius-Clapeyron's equation, we may also evaluate a vapor pressure curve to get the enthalpy of vaporization. We have to plot the logarithm of the vapor pressure against the rectibrocal of the absolute temperature, the so-called Clausius-Clapeyron plot, and then usually get a nice straight line with a negative slope. By simply multiplying the slope of the curve by the negative of the universal gas constant R, we may calculate the enthalpy of vaporization, the heat of vaporization. Liquid water has a vapor pressure of 2.3 kPa at 20 centigrade. We cool the water down to zero centigrade and then measure a vapor pressure of 0.61 kPa. If we are careful, we succeed in cooling down the liquid water below zero centigrade and at negative 10 centigrade, we measure a vapor pressure of only 0.29 kPa. This vapor pressure of undercooled, metastable liquid water corresponds to the red curve. Solid ice at negative 10 centigrade has a lower vapor pressure, namely 0.26 kPa. The black curve corresponds to the vapor pressure of solid ice. Low vapor pressure means that the system is less unstable. At zero centigrade, ice and liquid water have the same vapor pressure. At zero centigrade, both phases are equally stable. In fact, vapor pressure is a direct measure of instability. It tells us how comfortable a component feels in the liquid phase. What happens when we dissolve another component in solvent water? First of all, we have to clearly describe the composition of the mixture. If we take, for example, 1 kg of water as solvent, abbreviated with A and 1 mol of sugar as solute, abbreviated with B, we will get a homogeneous mixture, AB. We may calculate the mol fraction x of this mixture, the amount of substance of the solute divided by the total amount of substance. In our case, that would be 1.8% per mol sugar. Molarity is also popular to specify concentration. We have to divide the amount of the solute by the total volume. Molarity should not be confused with molality. We calculate molality by dividing the amount of the solute by the mass of the solvent A. Molarity and molality are approximately the same for very diluted solutions. We get such a diluted solution if we dissolve 10 grams of CO2 in 1 kg of water. We get a molarity of 0.23 moles per liter and a molality of 0.23 moles per kilogram. How does the vapor pressure of a solution compare to the vapor pressure of a solvent? Let's take, for example, this IcT, which is a solution of sugar in water. There is a phase equilibrium between the gas phase and the liquid phase in respect to the solvent and we can formulate it very simply. Water molecules can change between the liquid phase and the gas phase. We may formulate kind of a law of mass action. C sub water in the gas phase over C sub water in the liquid phase is a constant. You remember the concentration conventions in thermodynamics. The concentration of a gas phase must be formulated as a pressure in bars. The concentration of a liquid as a mole fraction. This is in fact Raoult's first law, which states the concentration of water above over the concentration of water below is a constant. If we dissolve a gas in water, for example carbon dioxide and lemonade, then we deal with another phase equilibrium because the solute B in RKCO2 can switch between two phases. Again, the equilibrium can be described in a way analogous to the law of mass action. The pressure of CO2 in the gas phase divided by the mole fraction of CO2 in the liquid phase is a constant. This is the so-called Henry's law of absorption and just like Raoult's first law, it says that the concentration ratios in gas and liquid phase result in a constant. We can use Henry's law to calculate the pressure in a lemonade bottle. We need the mole fraction of CO2 in the liquid phase, that's 0.4% per mole. We need Henry's constant, this is 175 MPa for CO2 in water at 20 centigrade. And this will result in a considerable pressure of 0.7 MPa or 7 bar in the gas phase. For the sake of completeness, we can also mention another phase equilibrium here, namely the distribution equilibrium, which was described by Walter Nernst. We start with two non-missable liquids, for example water and oil, and we are adding a third component that can switch between these two solvents, that can pass the phase boundary, for example acetic acid. Again, we use kind of the law of mass action and state that the concentration of acetic acid in the organic phase divided by the concentration of acetic acid in the aqueous phase is a constant. Nernst's distribution law is important for the separation process of extraction. Let's summarize. The vapor pressure is the equilibrium partial pressure over a condensed phase. The vapor pressure mainly depends on the volatility of the component and the temperature. The vapor pressure curve of a pure substance, which begins at the triple point and ends at the critical point, can be described using Clausius-Clapeyron's equation. With a solute present, the vapor pressure is lower than with a pure solvent. Vibrant pressure reduction is proportional to the concentration of the solute and described by Raoult's first law. When we dissolve a gas in a liquid, the amount of gas dissolved is proportional to the partial pressure of the gas above the liquid, that's Henry's law. More information about the topic will be found in the book and in the lecture. Thanks for watching.
 Liquids can evaporate, gases can condense.  How do pressure and temperature affect these phase transitions?  Welcome to FisCAM Basics, our topic today, vapor pressure, a special case of a phase  equilibrium.  Monoculars change from one phase to another.  What is vapor pressure anyway?  Consider an evacuated vessel at 20 centigrade and putting liquid water into it.  First of all, the pressure in the vessel will be zero.  However, the water will start to evaporate and the pressure above the liquid phase will  increase.  Water partial pressure will build up in the gas phase.  For example, in this situation, 1.15 kilopascals.  As this state does not correspond to equilibrium rate, water will continue to evaporate.  The partial pressure will rise further until at 2.3 kilopascals, the pressure above the  liquid phase will remain constant.  We are now at equilibrium in phase equilibrium.  The partial pressure over a condensed phase at equilibrium is called vapor pressure.  The vapor pressure of water at 20 centigrade is 2.3 kilopascals.  We mark vapor pressure with an asterisk.  The vapor pressure strongly depends on temperature.  At zero centigrade, it is 0.6 kilopascals and at 100 centigrade, 101.3 kilopascals.  That's exactly one atmosphere.  Well, 100 centigrade is a standard boiling point of water.  It's defined to be the temperature at which the vapor pressure is equal to the external  pressure.  If we set the partial pressure of water in relation to the vapor pressure of water, we  get the relative humidity phi.  This relative humidity is 100%.  The air is saturated in water vapor when the vapor pressure is reached.  In the second picture, phi equals 50% humidity in the first picture, 0%.  We can even oversaturate the gas phase with water vapor.  Then phi will exceed 100%.  However, this is a metastable state.  Vapor pressure is a special case for a phase equilibrium.  With these equilibria, a component can move between two phases.  In this case, what is the condition for equilibrium?  We can look at the whole thing thermodynamically.  That equilibrium when the water feels equally fine in both phases.  More scientifically speaking, when its stability is the same in both phases.  You might remember that Gibbs free energy or chemical potential is a measure for instability.  So this is the thermodynamic condition.  The chemical potential of water in one phase is equal to the chemical potential of water  in the other phase.  We can also consider the question kinetically.  There is equilibrium if the rate of evaporation shown here in green color is the same as the  rate of condensation shown here in blue color.  We have a so-called dynamic equilibrium.  Everything happens macroscopically, but microscopically we have a forward and reverse process taking  place at the same rates.  Of course, vapor pressure depends on the compound we are dealing with.  Water has a lower vapor pressure than a volatile low boiler like ethanol.  The vapor pressure is kind of a measure for the tendency of a substance to escape from  the liquid phase.  As already mentioned, the vapor pressure mainly depends on temperature.  With rising the temperature, vapor pressure increases exponentially as we will see shortly.  The vapor pressure also depends on the purity of the phase.  If we add another component to water and form a homogeneous mixture, the vapor pressure  drops.  The vapor pressure also depends to a very small extent to whether we have a flat surface  or a curved surface.  Over very small droplets, vapor pressure will be larger than over a flat surface.  Vapor pressure also increases with an additional inert gas on the high pressure.  You remember our three-dimensional PVT phase diagram?  Where do we find vapor pressure in this diagram?  It is this green region in which liquid and gas are present at the same time.  If we project this phase diagram onto the Pt surface, the two-phase region is reduced  to a line and we get the typical Pt phase diagram of a pure substance.  We see three lines, that is, the vapor pressure curve, the sublimation pressure curve and  the melting pressure curve.  These three lines intersect at one point, the so-called triple point.  The triple point for water is 0.01 centigrade and 0.6 kilopascals.  The triple point marks the beginning of the vapor pressure curve.  The vapor pressure curve becomes steeper with increasing temperature and ends at the critical  point.  The critical point of water is 374 centigrade and 22,000 kilopascals.  From this diagram, we can depict the boiling point of the liquid for any pressure.  The standard boiling point of water at 101 kilopascals is 100 centigrade.  At 20 centigrade, the vapor pressure of water is 2.3 kilopascals.  If we had an external pressure of 2.3 kilopascals, water would boil at 20 centigrade.  There have been many attempts to describe the vapor pressure curve mathematically.  In the equation named after them, Clausius and Clapeyron derived the relation between  two points on the vapor pressure curve and the enthalpy of vaporization delta H sub VAP.  The Antoine equation, which uses three empirical Antoine vectors A, B and C, is even more popular  for the calculation of vapor pressures.  It gives very precise results for vapor pressures but does not have as nice a thermo-economical  background as the equation of Clausius and Clapeyron.  With the help of Clausius-Clapeyron's equation, we may also evaluate a vapor pressure curve  to get the enthalpy of vaporization.  We have to plot the logarithm of the vapor pressure against the rectibrocal of the absolute  temperature, the so-called Clausius-Clapeyron plot, and then usually get a nice straight  line with a negative slope.  By simply multiplying the slope of the curve by the negative of the universal gas constant  R, we may calculate the enthalpy of vaporization, the heat of vaporization.  Liquid water has a vapor pressure of 2.3 kPa at 20 centigrade.  We cool the water down to zero centigrade and then measure a vapor pressure of 0.61 kPa.  If we are careful, we succeed in cooling down the liquid water below zero centigrade and  at negative 10 centigrade, we measure a vapor pressure of only 0.29 kPa.  This vapor pressure of undercooled, metastable liquid water corresponds to the red curve.  Solid ice at negative 10 centigrade has a lower vapor pressure, namely 0.26 kPa.  The black curve corresponds to the vapor pressure of solid ice.  Low vapor pressure means that the system is less unstable.  At zero centigrade, ice and liquid water have the same vapor pressure.  At zero centigrade, both phases are equally stable.  In fact, vapor pressure is a direct measure of instability.  It tells us how comfortable a component feels in the liquid phase.  What happens when we dissolve another component in solvent water?  First of all, we have to clearly describe the composition of the mixture.  If we take, for example, 1 kg of water as solvent, abbreviated with A and 1 mol of  sugar as solute, abbreviated with B, we will get a homogeneous mixture, AB.  We may calculate the mol fraction x of this mixture, the amount of substance of the solute  divided by the total amount of substance.  In our case, that would be 1.8% per mol sugar.  Molarity is also popular to specify concentration.  We have to divide the amount of the solute by the total volume.  Molarity should not be confused with molality.  We calculate molality by dividing the amount of the solute by the mass of the solvent A.  Molarity and molality are approximately the same for very diluted solutions.  We get such a diluted solution if we dissolve 10 grams of CO2 in 1 kg of water.  We get a molarity of 0.23 moles per liter and a molality of 0.23 moles per kilogram.  How does the vapor pressure of a solution compare to the vapor pressure of a solvent?  Let's take, for example, this IcT, which is a solution of sugar in water.  There is a phase equilibrium between the gas phase and the liquid phase in respect to the  solvent and we can formulate it very simply.  Water molecules can change between the liquid phase and the gas phase.  We may formulate kind of a law of mass action.  C sub water in the gas phase over C sub water in the liquid phase is a constant.  You remember the concentration conventions in thermodynamics.  The concentration of a gas phase must be formulated as a pressure in bars.  The concentration of a liquid as a mole fraction.  This is in fact Raoult's first law, which states the concentration of water above  over the concentration of water below is a constant.  If we dissolve a gas in water, for example carbon dioxide and lemonade,  then we deal with another phase equilibrium because the solute B in RKCO2  can switch between two phases.  Again, the equilibrium can be described in a way analogous to the law of mass action.  The pressure of CO2 in the gas phase divided by the mole fraction of CO2 in the liquid phase  is a constant.  This is the so-called Henry's law of absorption and just like Raoult's first law,  it says that the concentration ratios in gas and liquid phase result in a constant.  We can use Henry's law to calculate the pressure in a lemonade bottle.  We need the mole fraction of CO2 in the liquid phase, that's 0.4% per mole.  We need Henry's constant, this is 175 MPa for CO2 in water at 20 centigrade.  And this will result in a considerable pressure of 0.7 MPa or 7 bar in the gas phase.  For the sake of completeness, we can also mention another phase equilibrium here,  namely the distribution equilibrium, which was described by Walter Nernst.  We start with two non-missable liquids, for example water and oil, and we are adding a  third component that can switch between these two solvents, that can pass the phase boundary,  for example acetic acid.  Again, we use kind of the law of mass action and state that the concentration of acetic  acid in the organic phase divided by the concentration of acetic acid in the aqueous phase  is a constant.  Nernst's distribution law is important for the separation process of extraction.  Let's summarize.  The vapor pressure is the equilibrium partial pressure over a condensed phase.  The vapor pressure mainly depends on the volatility of the component and the temperature.  The vapor pressure curve of a pure substance, which begins at the triple point and ends at  the critical point, can be described using Clausius-Clapeyron's equation.  With a solute present, the vapor pressure is lower than with a pure solvent.  Vibrant pressure reduction is proportional to the concentration of the solute  and described by Raoult's first law.  When we dissolve a gas in a liquid, the amount of gas dissolved is proportional to the partial  pressure of the gas above the liquid, that's Henry's law.  More information about the topic will be found in the book and in the lecture.  Thanks for watching.
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