Name: predicting vapor pressure with temperature
Uploaded: 2020-09-24T15:06:49.000Z
Duration: 2 min 35 s
Channel: JoVE

K12 Standards

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NC K-12 Science Standard Course of Study

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Chemistry

Energy

PS.Chm.7.1

Clausius-Clapeyron Equation

Recall that the vapor pressure of a liquid increases with a rise in temperature. However, this dependence is not linear.
To illustrate, the vapor pressure of water at 50 &#176;C is 0.122 atm, while at 100 &#176;C, it is 1 atm. Vapor pressure curves sharply upward with increasing temperature, resulting in an exponential curve.
In comparison, when the natural log of vapor pressure is plotted against reciprocal temperature, a straight line is obtained, and its equation is called the Clausius&#8211;Clapeyron equation.
Here, R is the ideal gas constant; c, a constant characteristic of the liquid, is the y-intercept; and the slope of the line is equal to the negative of the molar heat of vaporization over the gas constant.
The equation allows the calculation of the molar heat of vaporization from the experimental measurements of equilibrium vapor pressures and temperatures.
For example, suppose the natural log of ethanol vapor pressure plotted as a function of reciprocal temperature gives a straight line with the slope of negative 4638 kelvins.
The equation for the slope of the line, along with the value of R, gives the molar heat of vaporization of ethanol as 38&#8201;560 joules per mole.
If the molar heat o

clausius-clapeyron equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance&#8217;s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
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where &#916;Hvap is the enthalpy of vaporization for the liquid, R is the gas constant, and A is a constant whose value depends on the chemical identity of the substance. Temperature (T) must be in kelvin in this equation. However, since the relationship between vapor pressure and temperature is not linear, the equation is often rearranged into logarithmic form to yield the linear equation:
<img alt="Chemical structure of caffeine molecule; diagram illustrating its molecular composition." src="/files/ftp_upload/11348/11348_Equation_2.png" style="text-align: center; height: 75px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram with force vectors and conditions &#931;Fx=0, &#931;Fy=0; mechanical balance illustration." />
For any liquid, if the enthalpy of vaporization and vapor pressure at a particular temperature is known, the Clausius-Clapeyron equation allows to determine the liquid&#8217;s vapor pressure at a different temperature. To do this, the linear equation may be expressed in a two-point format. If at temperature T1, the vapor pressure is P1, and at temperature T2, the vapor pressure is P2, the corresponding linear equations are:
<img alt="Chemical formula of capsaicin, diagram illustrating its molecular structure." src="/files/ftp_upload/11348/11348_Equation_3.png" style="text-align: center; height: 75px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equations &#931;Fx=0 diagram; forces, vectors, equilibrium analysis, engineering mechanics." />
Since the constant, A, is the same, these two equations may be rearranged to isolate ln A and then set them equal to one another:
<img alt="Enzyme-substrate complex diagram, illustrating catalytic process and binding interactions." src="/files/ftp_upload/11348/11348_Equation_4.png" style="text-align: center; height: 75px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram, &#931;Fx=0, MA=0, showing forces and moments in a balanced beam system." />
which can be combined into:
<img alt="HPLC chromatography diagram explaining ethanol analysis process with equipment setup details." src="/files/ftp_upload/11348/11348_Equation_5.png" style="text-align: center; height: 75px;" data-altupdatedat="1754904545000" data-alt="Pascal's Triangle diagram illustrating binomial coefficients and combinatorial equations." />
This text is adapted from<a href="https://openstax.org/books/chemistry-2e/pages/10-3-phase-transitions"> Openstax, Chemistry 2e, Section 10.3: Phase Transitions</a>.

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor ...

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Liquids, Solids, and Intermolecular Forces

KEY TERMS AND CONCEPTS

predicting vapor pressure with temperature

Predicting vapor pressure with temperature is a key use of the Clausius-Clapeyron equation. It describes how the equilibrium between a liquid and its vapor changes as temperature changes. When temperature rises, the vapor pressure of the liquid also rises.

The equation gives a quantitative link between vapor pressure, P, and temperature, T. It shows the rate at which vapor pressure increases for each unit increase in temperature. In this relationship, ΔHvap is the enthalpy of vaporization, R is the gas constant, and A is a constant that depends on the substance’s chemical identity. Temperature must be written in kelvin.

Because the relationship between vapor pressure and temperature is not linear, the equation is often rewritten in logarithmic form. This form makes the equation linear, which is easier to use in calculations. If the enthalpy of vaporization and the vapor pressure at one temperature are known, the equation can be used to find the vapor pressure at a different temperature.

The equation can also be written in a two-point form. In this format, T1 has vapor pressure P1, and T2 has vapor pressure P2. The two linear equations are rearranged to isolate ln A, set the expressions equal, and combine them into a single working equation.

Predicting Vapor Pressure with Temperature

predicting-vapor-pressure-with-temperature

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Predicting vapor pressure with temperature is a key use of the Clausius-Clapeyron equation. It describes how the equilibrium between a liquid and its vapor changes as temperature changes. When temperature rises, the vapor pressure of the liquid also rises. The equation gives a quantitative link between vapor pressure, P, and temperature, T. It shows the rate at which vapor pressure increases for each unit increase in temperature. In this relationship, ΔHvap is the enthalpy of vaporization, R...

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key terms and concepts

Learn how the Clausius-Clapeyron equation links vapor pressure and temperature, why kelvin is required, and how the two-point form predicts a liquid’s vapor pressure.

Predicting Vapor Pressure with Temperature | JoVE K12

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PS.Chm.7.3

Understand the relationship among pressure, temperature, volume, and phase.

Predicting Vapor Pressure with Temperature

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