This article explores the principles behind vapour pressure, including key laws such as Raoult’s Law and the Antoine Equation.

What Is Vapour Pressure?

Vapour pressure is the pressure exerted by the vapour of a substance in thermodynamic equilibrium with its condensed phases (solid or liquid) in a closed system. At a given temperature, the vapour pressure represents the tendency of molecules to escape from the liquid or solid phase into the gaseous phase.

As temperature increases, more molecules have the energy to escape into the vapour phase, leading to an increase in vapour pressure.

This property does not depend upon quantity. It can be calculated by using the Antoine equation which expresses vapour pressure as a function of temperature.

What Is The Antoine Equation?

The Antoine Equation is an empirical relationship that describes the variation of vapour pressure with temperature. It is widely used because of its simplicity and accuracy for a broad range of substances.

Where:

T – Temperature of the liquid or substance

P – Vapour Pressure of a liquid or substance

A, B & C – are liquid or substance specific constants/ coefficients

The equation can be rearranged to calculate temperature as follows:

In fractional distillation, this property plays an important role as the design of the column depends upon vapour pressure differences.

A Brief History of The Antoine Equation

The Antoine Equation was developed by French engineer and chemist Louis Charles Antoine in 1888. Antoine’s work was pivotal in providing a practical tool for engineers and scientists to calculate vapour pressures at different temperatures, especially in the design and operation of distillation columns and other separation processes.

What Are The Units of Vapour Pressure?

In general value of V_p is measured in the same units of pressure. As we know that there are different units available for a measure of pressure like:

• kg/cm²
• PSI
• N/m²
• kPa
• Bar
• Pascal

Factors That Affect Vapour Pressure

Some of the key factors which affect the vapour pressure are:

• Temperature
• Solute concentration and nature
• Boiling point

How Does Temperature Affect Vapour Pressure?

As you increase the temperature of the solid or liquid in a system then its V_p will also increase and vice versa for when it decreases.

How Does Solute Concentration And Nature Affect Vapour Pressure?

If you add more non-volatile solute to dissolve into a volatile solvent then the vapour pressure of the solvent will reduce, hence, in this example the more solute you add the lower the vapour pressure of the solute gets. 

Factors That Do Not Affect Vapour Pressure

Volume

V_p does not increase or decrease with respect to the volume of its system.

Surface Area

The surface area of the solid or liquid in contact with the gas will have no effect on the vapour pressure of the system.

What is Raoult’s Law? 

Raoult’s Law is a principle that relates the vapour pressure of an ideal solution to the vapour pressures of its individual components and their mole fractions. It states that the partial vapour pressure of each component in a solution is proportional to its mole fraction in the solution and its vapour pressure when at the same temperature. It can be represented in the formula below:

Where:

P_solution – Vapour Pressure of the solution

X_solvent – Mole fraction of the solvent

P_solvent – Vapour Pressure of the pure solvent

Raoult’s law can be used to estimate the contribution of individual components of a liquid or solid mixture to the total pressure exerted by the system.

We can use Raoult’s Law to calculate the vapour pressure of a given liquid. So Raoult’s Law is very helpful in the design of distillation columns. Using Raoult’s Law we can calculate the required temperature under a given vacuum in a distillation system.

A Brief History of Raoult’s Law

Raoult’s Law was first discovered by French chemist François-Marie Raoult in 1887. Raoult’s work on the connecting properties of solutions, such as freezing point depression and boiling point elevation, led to the development of this law. Although Raoult’s Law applies strictly to ideal solutions, it laid the groundwork for understanding the behaviour of real solutions, particularly in chemical engineering and thermodynamics.

Vapour Pressure of Water

At 25 degrees Celsius, the vapour pressure of water is 23.8 mmHg. At 100 degrees Celsius, water reaches its boiling point, and the vapour pressure becomes equal to one atmosphere (which is equivalent to 760 mmHg).

Hassan Ahmed

Hassan graduated with a Master’s degree in Chemical Engineering from the University of Chester (UK). He currently works as a design engineering consultant for one of the largest engineering firms in the world along with being an associate member of the Institute of Chemical Engineers (IChemE).

The post A Comprehensive Guide to Vapour Pressure | Understanding Key Laws and Their Applications appeared first on Engineeringness.

Temperature is an objective measure of hot or cold and is measured using a thermometer. Temperature is used to determine if 2 system would be in thermal equilibrium in the event, they came into contact with each other through a diathermic wall and establish the energy flow.

There are two types of boundary:

• Diathermic: Thermally conduction, heat transfer occurs passing through freely.
• Adiabatic: Thermally insulting, no heat transfer to the surroundings.

An example of diathermic is when a hot object in thermal contact with a cold(er) object, resulting in heat flowing through the hot object to the cold object until thermal equilibrium is achieved where the heat flow stops and both objects are at the same temperature. For an adiabatic system, the heat in the hot object will not transfer to the cold object, as the heat in the hot object won’t go leave to it surroundings which would be the cold object (figure 1).

Figure 1: Adiabatic and diathermic wall heat transfer ( CIET, 2012).

What Is Pressure?

The pressure is afore exerted by a fluid per unit area, and the standard pressure is 1 bar which is measured with equipment that includes; barometers, manometers, fibre optic and piezoelectric. Most pressuring-measuring devices are calibrated to read zero when in the atmosphere, this is called gauge pressure.

In most equations absolute pressure is used, where p = 0 corresponds to a perfect vacuum and in a lot of equation this is called p_abs. Also, pressures below atmospheric pressures are called vacuum pressures.

There is a relationship that relates these types of pressures (figure 2):

p_abs = p_atm + p_{g     &}   p_abs = p_atm – p_vac

Figure 2: Relationship between gauge, absolute and vacuum pressure (Insta Tools, 2020).

Equilibrium

A system is in equilibrium with its surrounds when it does not tend to undergo spontaneous change. Whilst a system is in equilibrium, it will experience no changes when it is isolated from its surrounding.

Types of equilibrium:

• Mechanical equilibrium: No change in pressure within the system and doesn’t change with time.
• Thermal equilibrium: Temperature is constant throughout the system.
• Chemical equilibrium: Chemical composition is the same in the system and doesn’t change with time.
• Phase equilibrium: A system involving two phases and the mass of each system reaches an equilibrium level and stays within the system.

Describing A System

When describing a system, the state variables (p, n, T, V…) are independent of the system’s history and the number of properties required to fix the state of the system is given by the state postulate:

“The state of a simple compressible system is specified completely by two independent intrusive properties.”

Simple compressible system:  If the system involves no electrical, magnetic, gravitational, motion and surface tension acting on it.

For a one-component system, all that is required is n (moles) and 2 variables, all other properties then follow:

V = f(n, p, t)

Example for notation:

A cylinder containing 2 moles of nitrogen gas at 1 bar pressure and a temperature of 25 ^oC (figure 3).

Notation: 2 N₂ (g, 1 bar, 25 ^oC)

Figure 3: Cylinder containing nitrogen gas for notation example.

References

CIET. (2012). Physics-02. Retrieved from CIET: https://ciet.nic.in/moocspdf/Physics02/Unit08/keph_201201_eContent2019.pdf

Insta Tools. (2020). Difference Between Absolute and Gauge Pressure. Retrieved from Insta Tools: https://instrumentationtools.com/difference-between-absolute-and-gauge-pressure/

Dr. Adam Zaidi

Dr. Adam Zaidi, PhD, is a researcher at The University of Manchester (UK). His doctoral research focuses on reducing carbon dioxide emissions in hydrogen production processes. Adam’s expertise includes process scale-up and material development.’

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