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From Wikipedia

Vapor-liquid equilibrium

Vapor-liquid equilibrium (sometimes abbreviated as VLE) is a condition where a liquid and its vapor (gas phase) are in equilibrium with each other, a condition or state where the rate of evaporation (liquid changing to vapor) equals the rate of condensation (vapor changing to liquid) on a molecular level such that there is no net (overall) vapor-liquid interconversion. Although in theory equilibrium takes forever to reach, such an equilibrium is practically reached in a relatively closed location if a liquid and its vapor are allowed to stand in contact with each other long enough with no interference or only gradual interference from the outside.

VLE data introduction

The concentration of a vapor in contact with its liquid, especially at equilibrium, is often in terms of vapor pressure, which could be a partial pressure (part of the total gas pressure) if any other gas(es) are present with the vapor. The equilibrium vapor pressure of a liquid is usually very dependent on temperature. At vapor-liquid equilibrium, a liquid with individual components (compounds) in certain concentrations will have an equilibrium vapor in which the concentrations or partial pressures of the vapor components will have certain set values depending on all of the liquid component concentrations and the temperature. This fact is true in reverse also; if a vapor with components at certain concentrations or partial pressures is in vapor-liquid equilibrium with its liquid, then the component concentrations in the liquid will be set dependent on the vapor concentrations, again also depending on the temperature. The equilibrium concentration of each component in the liquid phase is often different from its concentration (or vapor pressure) in the vapor phase, but there is a correlation. Such VLE concentration data is often known or can be determined experimentally for vapor-liquid mixtures with various components. In certain cases such VLE data can be determined or approximated with the help of certain theories such as Raoult's Law, Dalton's Law, and/or Henry's Law.

Such VLE information is useful in designing columns for distillation, especially fractional distillation, which is a particular specialty of chemical engineers. Distillation is a process used to separate or partially separate components in a mixture by boiling (vaporization) followed by condensation. Distillation takes advantage of differences in concentrations of components in the liquid and vapor phases.

In mixtures containing two or more components where their concentrations are compared in the vapor and liquid phases, concentrations of each component are often expressed as mole fractions. A mole fraction is number of moles of a given component in an amount of mixture in a phase (either vapor or liquid phase) divided by the total number of moles of all components in that amount of mixture in that phase.

Binary mixtures are those having two components. Three-component mixtures could be called ternary mixtures. There can be VLE data for mixtures with even more components, but such data becomes copious and is often hard to show graphically. VLE data is often shown at a certain overall pressure, such as 1 atm or whatever pressure a process of interest is conducted at. When at a certain temperature, the total of partial pressures of all the components becomes equal to the overall pressure of the system such that vapors generated from the liquid displace any air or other gas which maintained the overall pressure, the mixture is said to boil and the corresponding temperature is the boiling point (This assumes excess pressure is relieved by letting out gases to maintain a desired total pressure). A boiling point at an overall pressure of 1 atm is called the normal boiling point.

Thermodynamic description of vapor-liquid equilibrium

The field of thermodynamics describes when vapor-liquid equilibrium is possible, and its properties. Much of the analysis depends on whether the vapor and liquid consist of a single component, or if they are mixtures.

Pure (single-component) systems

If the liquid and vapor are pure, in that they consist of only one molecular component and no impurities, then the equilibrium state between the two phases is described by the following equations:

P^{liq} = P^{vap}\,;
T^{liq} = T^{vap}\,; and
\tilde{G}^{liq} = \tilde{G}^{vap}

where P^{liq}\, and P^{vap}\, are the pressures within the liquid and vapor, T^{liq}\, and T^{vap}\, are the temperatures within the liquid and vapor, and \tilde{G}^{liq} and \tilde{G}^{vap} are the molar Gibbs free energies (units of energy per amount of substance) within the liquid and vapor, respectively. In other words, the temperature, pressure and molar Gibbs free energy are the same between the two phases when they are at equilibrium.

An equivalent, more common way to express the vapor-liquid equilibrium condition in a pure system is by using the concept of fugacity. Under this view, equilibrium is described by the following equation:

f^{\,liq}(T_s,P_s) = f^{\,vap}(T_s,P_s)

where f^{\,liq}(T_s,P_s) and f^{\,vap}(T_s,P_s) are the fugacities of the liquid and vapor, respectively, at the system temperature T_s\, and pressure P_s\,. Using fugacity is often more convenient for calculation, given that the fugacity of the liquid is, to a good approximation, pressure-independent, and it is often convenient to use the quantity \phi=f/P\,, the dimensionless fugacity coefficient, which is 1

Latent heat

Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature, meaning a phase transition such as the melting of ice or the boiling of water. The term was introduced around 1750 by Joseph Black as derived from the Latin latere, to lie hidden.

In meteorology, latent heat flux is the flux of heat from the Earth's surface to the atmosphere that is associated with evaporation or transpiration of water at the surface and subsequent condensation of water vapor in the troposphere. It is an important component of Earth's surface energy budget. Latent heat flux is commonly measured with the Bowen ratio technique, or by eddy covariance.


Two of the more common forms of latent heat (or enthalpies or energies) encountered are latent heat of fusion (melting) and latent heat of vaporization (boiling). These names describe the direction of energy flow when changing from one phase to the next: from solid to liquid, and to gas.

In both cases, the change is endothermic, meaning that the system absorbs energy on going from solid to liquid to gas. The change is exothermic (the process releases energy) for the opposite direction. For example, in the atmosphere, when a molecule of water evaporates from the surface of any body of water, energy is transported by the water molecule into a lower temperature air parcel that contains less water vapor than its surroundings. Because energy is needed to overcome the molecular forces of attraction between water particles, the process of transition from a parcel of water to a parcel of vapor requires the input of energy causing a drop in temperature in its surroundings. If the water vapor condenses back to a liquid or solid phase onto a surface, the latent energy absorbed during evaporation is released as sensible heat onto the surface. The large value of the enthalpy of condensation of water vapor is the reason that steam is a far more effective heating medium than boiling water, and is more hazardous.

The terms sensible heat and latent heat are not special forms of energy, instead they characterize the same form of energy, heat, in terms of their effect on a material or a thermodynamic system. Heat is thermal energy in the process of transfer between a system and its surroundings or between two systems with a different temperature.

Both sensible and latent heats are observed in many processes while transporting energy in nature. Latent heat is associated with the phase changes of atmospheric water vapor, mostly vaporization and condensation, whereas sensible heat is energy transferred that affects the temperature of the atmosphere.


The term latent heat was introduced around 1750 by Joseph Black, and is derived from the Latin latere, meaning to lie hidden. In 1847, James Prescott Joule characterized latent energy as the energy of interaction in a given configuration of particles, i.e. a form of potential energy, and the sensible heat as an energy that was indicated by the thermometer, relating the latter to thermal energy.

Specific latent heat

A specific latent heat (L) expresses the amount of energy in form of heat (Q) required to completely effect a phase change of a unit of mass (m), usually , of a substance as an intensive property:

L = \frac {Q}{m}

Intensive properties are material characteristics and are not dependent on the size or extend of the sample. Commonly quoted and tabulated in the literature are the specific latent heat of fusion and the specific latent heat of vaporization for many substances.

From this definition, the latent heat for a given mass of a substance is calculated by

Q = {m} {L}


Q is the amount of energy released or absorbed during the change of phase of the substance (in kJ or in BTU),
m is the mass of the substance (in kg or in lb), and
L is the specific latent heat for a particular substance (kJ-kgm−1 or in BTU-lbm−1), either Lf for fusion, or Lv for vaporization.

Table of latent heats

The following table shows the latent heats and change of phase temperatures of some common fluids and gases.

Latent heat for water

The latent heat of condensation of water in the temperature range from −40 °C to 40 °C is approximated by the following empirical cubic function:

L_{water}(T)=-0.0000614342 T^3+0.00158927 T^2-2.36418 T+2500.79

with a determination coefficient of R^2=0.999988, where T is in °C.

From Yahoo Answers

Question:At 50 Cellius, vapor pressure of pure methyl alcohol is 0.529 atm, pure elthyl alcohol is 0.292atm. Calculate vapor pressure of elthyl alcohol? At 50 Cellius, in a solution contaning 65.82g of methyl alcohol and 89.0g of elthyl alcohol. (molar weight of: methyl alcohol is 32.05g/mol, elthyl alcohol is 46.08g/mol)

Answers:? mol CH3OH = 65.82g * 1mol/32.05g = 2.054mol CH3OH ? mol C2H7OH = 89.0g * 1mol/46.08g = 1.93mol C2H7OH Raoult's Law : P(T) = P(A) + P(B) + ... P(A) = P(Standard)(A) * X(A) P(T) = 1.93/(1.93+2.054) * 0.292 + 2.054/(1.93+2.054) * 0.529 P(T) = 0.141atm + 0.273atm = 0.414atm

Question:I need a complete solution for this please! Thanks... here's the complete question: The standard enthalpy of formation of gaseous molecular bromine is 30.7 kJ/mol. Use this information to calculate the molar heat of vaporization of molecular bromine at 25 degree celsius. I need a complete solution for this please..

Answers:The equation is: Br (l) ---------> Br(g) We know that in the standard condition, Bromine is liquid. So the the standard enthalpy of formation for the liquid Bromine is zero . The enthalpy of the above equation can be calculated by the following formula: A= Delta sign X= The standard enthalpy of formation of gaseous Bromine Y= The standard enthalpy of formation of liquid Bromine AH = Enthalpy of the above equation ---------------------------- AH = X - Y ----> AH = 30.7 - 0 ------> AH= 30.7 KJ/mol

Question:A compound X contains element Q. Percent by weight of element Q is 64.8%. The Vapor Density of compound X at 27 C and 750 mm Hg is 3.53 g per liter. Calculate molecular weight of compound X.

Answers:There isn't enough information, you aren't given a second volume.

Question:These two questions really stumped me so I would really appreciate some help. 1. A student found that at 750 torr atmospheric pressure and .1 degree C, the corrected volume of the trapped air was 2.20mL. Under these conditions, how many moles of trapped air are present? 2. This student then heated the breaker of water and found that at 70 degree C the corrected volume of the bubble was 4.05mL. What should she report as the vapor pressure of water at this temperature?

Answers:for number 1, use the Ideal gas law PV = nRT Convert P to atm, V to L, and T to Kelvins. R = 0.082057 atm * L / mol * K and plug in and solve for n.

From Youtube

Enthalpy Changes for Chemical Reactions :General Chemistry lecture covering endothermic and exothermic reactions, Hess Law, bond energies, and standard enthalpies of formation for chemical substances. We also describe the method of calculating the enthalpy of combustion for materials.