Bubble point

Last updated March 16, 2019

In thermodynamics, the bubble point is the temperature (at a given pressure) where the first bubble of vapor is formed when heating a liquid consisting of two or more components.^[1]^[2] Given that vapor will probably have a different composition than the liquid, the bubble point (along with the dew point) at different compositions are useful data when designing distillation systems.^[3]

Thermodynamics is the branch of physics that has to do with heat and temperature and their relation to energy and work. The behavior of these quantities is governed by the four laws of thermodynamics, irrespective of the composition or specific properties of the material or system in question. The laws of thermodynamics are explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, chemical engineering and mechanical engineering.

Temperature is a physical quantity expressing hot and cold. It is measured with a thermometer calibrated in one or more temperature scales. The most commonly used scales are the Celsius scale, Fahrenheit scale, and Kelvin scale. The kelvin is the unit of temperature in the International System of Units (SI), in which temperature is one of the seven fundamental base quantities. The Kelvin scale is widely used in science and technology.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

Calculating the bubble point

At the bubble point, the following relationship holds:

\sum _{i=1}^{N_{c}}y_{i}=\sum _{i=1}^{N_{c}}K_{i}x_{i}=1

where

K_{i}\equiv {\frac {y_{ie}}{x_{ie}}}

.

K is the distribution coefficient or K factor, defined as the ratio of mole fraction in the vapor phase ${\big (}y_{ie}{\big )}$ to the mole fraction in the liquid phase ${\big (}x_{ie}{\big )}$ at equilibrium.
When Raoult's law and Dalton's law hold for the mixture, the K factor is defined as the ratio of the vapor pressure to the total pressure of the system:^[1]

Raoult's law ( law) is a law of thermodynamics established by French chemist François-Marie Raoult in 1887. It states that the partial vapor pressure of each component of an ideal mixture of liquids is equal to the vapour pressure of the pure component multiplied by its mole fraction in the mixture. In consequence, the relative lowering of vapour pressure of a dilute solution of nonvolatile solute is equal to the mole fraction of solute in the solution.

In chemistry and physics, Dalton's law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This empirical law was observed by John Dalton in 1801 and published in 1802. and is related to the ideal gas laws.

K_{i}={\frac {P'_{i}}{P}}

Given either of $x_{i}$ or $y_{i}$ and either the temperature or pressure of a two-component system, calculations can be performed to determine the unknown information.^[4]

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In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium. It is that temperature and pressure at which the sublimation curve, fusion curve and the vaporisation curve meet. For example, the triple point of mercury occurs at a temperature of −38.83440 °C and a pressure of 0.2 mPa.

Vapor pressure or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid. A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure. As the temperature of a liquid increases, the kinetic energy of its molecules also increases. As the kinetic energy of the molecules increases, the number of molecules transitioning into a vapor also increases, thereby increasing the vapor pressure.

In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.

Flash evaporation is the partial vapor that occurs when a saturated liquid stream undergoes a reduction in pressure by passing through a throttling valve or other throttling device. This process is one of the simplest unit operations. If the throttling valve or device is located at the entry into a pressure vessel so that the flash evaporation occurs within the vessel, then the vessel is often referred to as a flash drum.

In chemistry, colligative properties are properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present. The number ratio can be related to the various units for concentration of solutions. The assumption that solution properties are independent of nature of solute particles is only exact for ideal solutions, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by assuming that the solution is ideal.

In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas.

Critical point (thermodynamics) Temperature and pressure point where phase boundaries disappear

In thermodynamics, a critical point is the end point of a phase equilibrium curve. The most prominent example is the liquid-vapor critical point, the end point of the pressure-temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a critical temperatureT_c and a critical pressurep_c, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.

The compressibility factor (Z), also known as the compression factor or the gas deviation factor, is a correction factor which describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure. It is a useful thermodynamic property for modifying the ideal gas law to account for the real gas behaviour. In general, deviation from ideal behaviour becomes more significant the closer a gas is to a phase change, the lower the temperature or the larger the pressure. Compressibility factor values are usually obtained by calculation from equations of state (EOS), such as the virial equation which take compound-specific empirical constants as input. For a gas that is a mixture of two or more pure gases, the gas composition must be known before compressibility can be calculated.
Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts that plot $as a function of pressure at constant temperature.$

The acentric factor $is a conceptual number introduced by Kenneth Pitzer in 1955, proven to be very useful in the description of matter. It has become a standard for the phase characterization of single & pure components. The other state description parameters are molecular weight, critical temperature, critical pressure, and critical volume. The acentric factor is said to be a measure of the non-sphericity (centricity) of molecules. As it increases, the vapor curve is "pulled" down, resulting in higher boiling points.$

In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy or pressure and volume. In fact, all thermodynamic potentials are expressed in terms of conjugate pairs. The product of two quantities that are conjugate has units of energy or sometimes power.

The McCabe–Thiele method is considered to be the simplest and perhaps most instructive method for the analysis of binary distillation. It uses the fact that the composition at each theoretical tray is completely determined by the mole fraction of one of the two components and is based on the assumption of constant molar overflow which requires that:

In thermodynamics and chemical engineering, the vapor–liquid equilibrium (VLE) describes the distribution of a chemical species between the vapor phase and a liquid phase.

$Vapor quality mass fraction in a saturated mixture that is vapor$

In thermodynamics, vapour quality is the mass fraction in a saturated mixture that is vapour; in other words, saturated vapour has a "quality" of 100%, and saturated liquid has a "quality" of 0%. Vapour quality is an intensive property which can be used in conjunction with other independent intensive properties to specify the thermodynamic state of the working fluid of a thermodynamic system. It has no meaning for substances which are not saturated mixtures . Vapor quality is an important quantity during the adiabatic expansion step in various thermodynamic cycles. Working fluids can be classified by using the appearance of droplets in the vapour suring the expansion step.

Relative volatility is a measure comparing the vapor pressures of the components in a liquid mixture of chemicals. This quantity is widely used in designing large industrial distillation processes. In effect, it indicates the ease or difficulty of using distillation to separate the more volatile components from the less volatile components in a mixture. By convention, relative volatility is usually denoted as $.$

The non-random two-liquid model is an activity coefficient model that correlates the activity coefficients $of a compound with its mole fractions in the liquid phase concerned. It is frequently applied in the field of chemical engineering to calculate phase equilibria. The concept of NRTL is based on the hypothesis of Wilson that the local concentration around a molecule is different from the bulk concentration. This difference is due to a difference between the interaction energy of the central molecule with the molecules of its own kind and that with the molecules of the other kind . The energy difference also introduces a non-randomness at the local molecular level. The NRTL model belongs to the so-called local-composition models. Other models of this type are the Wilson model, the UNIQUAC model, and the group contribution model UNIFAC. These local-composition models are not thermodynamically consistent for a one-fluid model for a real mixture due to the assumption that the local composition around molecule i is independent of the local composition around molecule j. This assumption is not true, as was shown by Flemr in 1976. However, they are consistent if a hypothetical two-liquid model is used.$

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.

A saturation dome is a graphical representation of the combination of vapor and gas that is used in thermodynamics. It can be used to find either the pressure or the specific volume as long as one already has at least one of these properties.

VTPR is an estimation method for the calculation of phase equilibria of mixtures of chemical components. The original goal for the development of this method was to enable the estimation of properties of mixtures which contain supercritical components. These class of substances couldn't be predicted with established models like UNIFAC.

References

1 2 McCabe, Warren L.; Smith, Julian C.; Harriot, Peter (2005), Unit Operations of Chemical Engineering (seventh ed.), New York: McGraw-Hill, pp. 737–738, ISBN 0-07-284823-5
↑ Smith, J. M.; Van Ness, H. C.; Abbott, M. M. (2005), Introduction to Chemical Engineering Thermodynamics (seventh ed.), New York: McGraw-Hill, p. 342, ISBN 0-07-310445-0
↑ Perry, R.H.; Green, D.W., eds. (1997). Perry's Chemical Engineers' Handbook (7th ed.). McGraw-hill. ISBN 0-07-049841-5.
↑ Smith, J. M.; Van Ness, H. C.; Abbott, M. M. (2005), Introduction to Chemical Engineering Thermodynamics (seventh ed.), New York: McGraw-Hill, p. 351, ISBN 0-07-310445-0

Bubble point

Contents

Calculating the bubble point

Related Research Articles

References

See also