The ideal gas law, given by ( PV = nRT ), is based on several key assumptions about the behavior of gases. These assumptions simplify the complex nature of real gases and make the law applicable under ideal conditions. The assumptions are as follows:

1. Large Number of Molecules:
   • The gas consists of a large number of molecules that are in constant, random motion. This assumption ensures statistical averages can be applied.
2. Point Particles:
   • The molecules of the gas are considered point particles, meaning they have negligible volume compared to the volume of the container. Essentially, the size of the gas molecules is much smaller than the distance between them.
3. No Intermolecular Forces:
   • There are no attractive or repulsive forces between the molecules except during elastic collisions. This means the potential energy of interaction between molecules is zero.
4. Elastic Collisions:
   • All collisions between gas molecules, and between molecules and the walls of the container, are perfectly elastic. This implies that there is no loss of kinetic energy in the collisions: Total kinetic energy before collision = Total kinetic energy after collision
5. Newton’s Laws of Motion:
   • The molecules obey Newton’s laws of motion, which means their behavior can be described using classical mechanics. This includes the conservation of momentum and energy.
6. Random Motion:
   • The molecules are in random motion and the distribution of their velocities follows the Maxwell-Boltzmann distribution.

These assumptions collectively define an “ideal” gas, which is a useful model for understanding the behaviour of real gases under many conditions, particularly at low pressures and high temperatures where real gases tend to show behaviours closer to ideal gases.

The development of this law is rooted in the contributions of several scientists over centuries:

1. Boyle’s Law (1662):

• Robert Boyle, an Irish physicist and chemist, discovered that the pressure (P) of a gas is inversely proportional to its volume (V) at constant temperature. This relationship is known as Boyle’s Law:
  PV = constant

1. Charles’s Law (1787):

• Jacques Charles, a French scientist, found that the volume (V) of a gas is directly proportional to its temperature (T) when pressure is held constant. This relationship is termed Charles’s Law:
  

1. Gay-Lussac’s Law (1809):

• Joseph Louis Gay-Lussac, a French chemist and physicist, established that the pressure (P) of a gas is directly proportional to its temperature (T) at a constant volume. This is known as Gay-Lussac’s Law:
  

1. Avogadro’s Hypothesis (1811):

• Amedeo Avogadro, an Italian scientist, proposed that equal volumes of all gases, at the same temperature and pressure, contain an equal number of molecules. This led to the concept of the mole and Avogadro’s number.

1. Development of the Combined Gas Law:

• The relationships described by Boyle, Charles, and Gay-Lussac were integrated into the combined gas law, which relates pressure, volume, and temperature without changing the amount of gas:
  

1. Ideal Gas Law (1834):

• Émile Clapeyron, a French engineer and physicist, combined Boyle’s, Charles’s, and Avogadro’s laws into a single equation of state for an ideal gas. He introduced the ideal gas law in the form:
  PV = nRT
• Here, (R) is the ideal gas constant, (n) is the number of moles of gas, (P) is the pressure, (V) is the volume, and (T) is the temperature in Kelvins.

The ideal gas law encapsulates the behaviour of gases under a variety of conditions and forms the basis for more advanced gas theories and real gas behaviour corrections.

What Is An Ideal Gas?

An ideal gas is a theoretical gas that perfectly follows these conditions:

1. The gas comprises a large number of molecules that move randomly.
2. All molecules are point particles (they occupy no space).
3. The molecules do not interact except during collisions.
4. All collisions between gas particles are perfectly elastic (see our conservation of momentum calculator for more).
5. The particles obey Newton’s laws of motion.

Ideal gas law equation

The properties of an ideal gas are summarised by the equation:

where:

• (p) — Pressure of the gas, measured in Pa;
• (V) — Volume of the gas, measured in m³;
• (n) — Amount of substance, measured in moles;
• (R) — Ideal gas constant;
• (T) — Temperature of the gas, measured in kelvins.

Ideal gas constant

The gas constant (R) is also known as the molar or universal constant. It appears in many fundamental equations, such as the ideal gas law. The value of this constant is:

R = 8.31446261815324 J/(mol·K)

The gas constant is often defined as the product of Boltzmann’s constant (k), Which can be worked out using our online calculator here. and Avogadro’s number (N_A):

Ideal Gas Law Calculator

To use the calculator, select the variable you wish to find from the “Select Variable to Calculate” dropdown menu. Once selected, leave the corresponding cell blank e.g. if pressure is selected leave the pressure field blank. Then proceed to enter the other 3 variable and the answer will reveal itself in the calculated value cell.

When Can I Use The Ideal Gas Law?

The ideal gas law applies to gases at low densities, where intermolecular forces are negligible. Under these conditions, any gas can be approximately modelled by the equation ( PV = nRT ), which relates pressure, temperature, and volume.

Industrial Applications of The Ideal Gas Law

The ideal gas law, is essential in various industries for predicting gas behavior under different conditions. Key applications include:

Chemical Industry

• Reactions and Processes: Calculating gas volumes and pressures in chemical production and reactor design.

Petrochemical and Oil Industry

• Gas Recovery and Processing: Designing compressors and pipelines for natural gas and hydrocarbons.

Pharmaceuticals

• Synthesis and Quality Control: Managing gas conditions during drug synthesis and ensuring quality control.

Food and Beverage Industry

• Packaging and Preservation: Determining the pressure and volume of gases for packaging and carbonation processes.

Environmental Engineering

• Air Pollution Control: Designing emission control systems and predicting pollutant behavior.

Aerospace and Aviation

• Aircraft and Spacecraft Design: Managing gas mixtures and pressures in cabins and analyzing jet engine performance.

HVAC (Heating, Ventilation, and Air Conditioning)

• System Design and Optimization: Ensuring proper airflow and optimizing energy efficiency.

Metallurgy and Material Science

• Gas Metal Reactions: Controlling gas-metal reactions in processes like carburizing.

Manufacturing and Mechanical Engineering

• Pneumatics and Control Systems: Designing pneumatic systems for automation and manufacturing.

These applications demonstrate the ideal gas law’s versatility in efficiently designing, optimising, and controlling gas-involved systems across various industries.

What Is The Formula of The Ideal Gas Law?

The ideal gas law formula is:

where:

• (p) — Pressure of the gas, measured in Pa;
• (V) — Volume of the gas, measured in m³;
• (n) — Amount of substance, measured in moles;
• (R) — Ideal gas constant;
• (T) — Temperature of the gas, measured in kelvins.

Ensure to use consistent units! The common value for R (8.314 J/(mol·K)), refers to pressure measured in pascals.

What Are The Three Thermodynamic Laws Related To The Ideal Gas Law?

The ideal gas law involves four parameters, but three are directly related to thermodynamics: pressure, temperature, and volume. By determining each one, we identify three laws:

1. Determining temperature finds the isothermal transformation. This is known also as Boyle’s law: PV = k.
2. Determining volume finds the isochoric transformation. This is known also as Charles’s law: .
3. Determining pressure finds the isobaric transformation. This is known also as Gay-Lussac’s law: .

How Do I Calculate The Temperature Of A Gas Given Volume, Moles, And Pressure?

To calculate the temperature:

1. Calculate the results of pressure multiplied by the volume using the units pascals and cubic meters.
2. Calculate the results of the number of moles multiplied by the gas constant. When using pascals and cubic meters, the constant is R = 8.3145 J/(mol·K).
3. Divide the result of step 1 by the result of step 2 to find the temperature in kelvin: .

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 Comprehensive Guide to the Ideal Gas Law | History, Breakdown, and Interactive Calculator appeared first on Engineeringness.

An ideal gas (or perfect gas) conforms to the idealised relationship between temperature, volume and pressure called the ideal gas law. The ideal gas law contains both Boyles’ law and Charles’ law as special cases and states that for a specified quantity of gas of volume, V and pressure, P it is proportional to the absolute temperature (equation 1), with k being a constant. This is called the equation of and is enough to describe the gross behaviour.

PV = kT

Equation 1: Ideal gas state equation for a specified quantity of gas.

(1.1)

For any gas, another form of state equation can be used, according to Avogadro’s number, if the constant specifying the quantity of gas is expressed in terms of the number of molecules of gas. This is done by using the mass unit the gram mole (molecular weight expressed in grams), and the equation of state of n gram-moles of a perfect gas changes (equation 2), with R being the universal gas constant, with a value of 8.314 joules per gram-mole-kelvin (Gregersen, 2020).

PV = nRT

Equation 2:  Equation of state of an ideal gas for any gas.

(1.2)

Kinetic Theory Assumptions About Ideal Gases

An ideal gas or a perfect gas and obeys the ideal gas law (equation 2) it is a good describer for the behaviour of the many gases under many condition types, although there no such thing as an ideal gas in the real world, real gases will be discussed in greater detail in another post.

The ideal gas law can be derived from the kinetic theory of gases and relies on the key assumptions:

• No (or entirely negligible) intermolecular forces between the gas molecules/atoms,
• Molecules/atoms are points and do not occupy any volume.

Other Assumptions are:

• Molecules behave as rigged spheres,
• Molecules/atoms move randomly in straight lines,
• Pressure is caused by collisions between molecules/atoms and the walls of the container,
• Temperature is proportional to the average kinetic energy of the molecules/atoms,
• Molecules/atoms are equally sized.

Summary of Gas Laws:

• Boyles’ law – Isothermal expansion/compression

An ideal gas obeys Boyles’ law at all pressure and for a fixed amount of gas, the pressure and volume at constant temperature are related by:

PV = constant or P₁V ₁ = P₂V ₂

• Charles’ law – Isobaric compression/expansion

Charles’ law identifies absolute zero and for a fixed amount of gas, the volume and temperature of a fixed amount of gas at constant pressure are related by, with k being the constant (figure 1):

V = k x T

This law shows that increasing the temperature will increase the kinetic energy of the gas molecules, resulting in the gas occupying a greater volume at the same pressure.

Figure 1:  Volume Temperature Graph for Gases (Priyamstudycentre, 2020).

• Gay-Lussac law – for a fixed amount of gas, the pressure and volume are directly proportional to the gas’s absolute temperature, with k being a constant.

When the temperature is in kelvin:

P = k x T_k

When the temperature is in degrees Celsius:

P = k x (T_k + 273.15)

• Avogadro’s’ principle – Equal volumes of gases at the same temperature and pressure contain the same number of molecules, with k being a constant and n is the number of moles

V = k x n

Mixtures of Gases (Daltons Law)

When there is a mixture of gases, the partial pressure, P_i, of a gas is the mole fraction, x_i, multiplied by the total pressure (equation 3).

P_i = x_iP

Equation 3: Partial pressure equation.

(1.3)

The mole fraction of a gas within the mixture is a fraction of the total number of moles in the mixture (equation 4).

x_i = n_i/n

Equation 4: mole fraction equation.

(1.4)

Daltons’ law can be used to find out the total pressure of a system or one partial pressure if the total pressure and the rest of the partial pressures are given. This is because Daltons’ law states that the total pressure of a perfect gas is the sum of the partial pressures of the gases (equation 5).

P = P_i + P_j + ….

Equation 5: Daltons’ law.

(1.5)

References

Gregersen, E. (2020). Gas laws. Retrieved from Encyclopedia Britannica: https://www.britannica.com/science/gas-laws

Priyamstudycentre. (2020). Gases. Retrieved from Priyamstudycentre: https://www.priyamstudycentre.com/2019/02/physical-properties-gases.html

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.’

The post A Breakdown | What Is An Ideal Gas? appeared first on Engineeringness.