The Gas Laws

Introduction: What Are the Gas Laws?

The gas laws are a group of laws that govern the behaviour of gases by providing relationships between the following:

• The volume occupied by the gas.
• The pressure exerted by a gas on the walls of its container.
• The absolute temperature of the gas.
• The amount of gaseous substance (or) the number of moles of gas.

The gas laws were developed towards the end of the 18^th century by numerous scientists (after whom the individual laws are named). The five gas laws are listed below:

• Boyle’s Law: It provides a relationship between the pressure and the volume of a gas.
• Charles’s Law: It provides a relationship between the volume occupied by a gas and the absolute temperature.
• Gay-Lussac’s Law: It provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
• Avogadro’s Law: It provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
• The Combined Gas Law (or the Ideal Gas Law): It can be obtained by combining the four laws listed above.

Under standard conditions, all gasses exhibit similar behaviour. The variations in their behaviours arise when the physical parameters associated with the gas, such as temperature, pressure, and volume, are altered. The gas laws basically describe the behaviour of gases and have been named after the scientists who discovered them.

We will look at all the gas laws below and also understand a few underlying topics.

• Boyle’s Law
• Charle’s Law
• Gay-Lussac Law
• Avogadro’s Law
• Combined Gas Law
• Combined Gas Law
• Ideal-gas
• Gas Law Table
• Gas Law Problems
• Applications of Gas Law

Boyle’s Law

Boyle’s law gives the relationship between the pressure of a gas and the volume of the gas at a constant temperature. Basically, the volume of a gas is inversely proportional to the pressure of a gas at a constant temperature.

Boyle’s law equation is written as:

V ∝ 1/P

Or

P ∝ 1/V

Or

PV = k₁

Where V is the volume of the gas, P is the pressure of the gas, and K₁ is the constant.  Boyle’s Law can be used to determine the current pressure or volume of gas and can also be represented as,

P₁V₁ = P₂V₂

Problems Related to Boyle’s Law

An 18.10mL sample of gas is at 3.500 atm. What will be the volume if the pressure becomes 2.500 atm, with a fixed amount of gas and temperature?

Solution:

By solving with the help of Boyle’s law equation

P₁V₁ = P₂V₂

V₂ = P₁V₁ / P₂

V₂ = (18.10 * 3.500 atm)/2.500 atm

V₂ = 25.34 mL

Also Read: Behaviour of Gases

Charle’s Law

Charle’s law states that at constant pressure, the volume of a gas is directly proportional to the temperature (in Kelvin) in a closed system. Basically, this law describes the relationship between the temperature and volume of the gas.

Mathematically, Charle’s law can be expressed as,

V ∝ T

Where, V = volume of gas, T = temperature of the gas in Kelvin. Another form of this equation can be written as,

V₁ / T₁ = V₂ / T₂

Problems Related to Charle’s Law

A sample of carbon dioxide in a pump has a volume of 21.5 mL, and it is at 50.0 °C. When the amount of gas and pressure remain constant, find the new volume of carbon dioxide in the pump if the temperature is increased to 75.0 °C.

Solution:

V₂ = V₁T₂/T₁

V₂ = 7,485.225/ 323.15

V₂ = 23.16 mL

Gay-Lussac Law

Gay-Lussac law gives the relationship between temperature and pressure at constant volume. The law states that at a constant volume, the pressure of the gas is directly proportional to the temperature of a given gas.

If you heat up a gas, the molecules will be given more energy; they move faster. If you cool down the molecules, they slow down, and the pressure decreases. The change in temperature and pressure can be calculated using the Gay-Lussac law, and it is mathematically represented as,

P ∝ T

Or

P / T = k₁

or

P₁ / T₁ = P₂ / T₂

Where, P is the pressure of the gas, and T is the temperature of the gas in Kelvin.

Problems Related to Gay-Lussac Law

Determine the pressure change when a constant volume of gas at 2.00 atm is heated from 30.0 °C to 40.0 °C.

Solution:

P₁ = 2.00 atm
P₂ =?
T₁ = (30 + 273) = 303 K
T₂ = (40 + 273) = 313 K

According to the Gay-Lussac law,
P ∝ T
P/T = constant
P₁/T₁ = P₂/T₂
P₂ =( P₁ T₂ ) / T₁
= (2 x 313) / 303
=2.06 atm

Avogadro’s Law

Avogadro’s law states that if the gas is an ideal gas, the same number of molecules exists in the system. The law also states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. This statement can be mathematically expressed as,

V / n = constant

Or

V₁ / n₁ = V₂ / n₂

Where V is the volume of an ideal gas and n represents the number of gas molecules.

Problems Related to Avogadro’s Law

At constant temperature and pressure, 6.00 L of a gas is known to contain 0.975 mol. If the amount of gas is increased to 1.90 mol, what new volume will result?

Solution:

V₁ = 6.00 L
V₂ = ?
n₁ = 0.975
n₂ = 1.90 mol

According to Avogadro’s law
V ∝ n
V/n = constant
V₁ / n₁ = V₂ / n₂
V₂ = V₁n₂/n₁
V₂ = (6 x 1.90)/ 0.975 = 11.69 L

Combined Gas Law

The combined gas law, also known as a general gas equation, is obtained by combining three gas laws which include Charle’s law, Boyle’s Law and Gay-Lussac law. The law shows the relationship between temperature, volume and pressure for a fixed quantity of gas.

The general equation of combined gas law is given as,

PV / T = k

If we want to compare the same gas in different cases, the law can be represented as,

P₁V₁ / T₁ = P₂V₂ / T₂ 

Also Read: Kinetic Theory of Gas 

Ideal Gas Law

Much like the combined gas law, the ideal gas law is also an amalgamation of four different gas laws. Here, Avogadro’s law is added, and the combined gas law is converted into the ideal gas law. This law relates four different variables, which are pressure, volume, number of moles or molecules and temperature. Basically, the ideal gas law gives the relationship between these four different variables.

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Boyle’s Law – Video Lesson

Ideal Gas Equation

Mathematically Ideal gas law is expressed as,

PV = nRT

Where,

V = volume of gas

T = temperature of the gas

P = pressure of the gas

R = universal gas constant

And n denotes the number of moles

We can also use the equivalent equation given below.

PV = kNT

Where, k = Boltzmann constant and N = number of gas molecules.

Ideal Gas

Ideal gases are also known as perfect gas. It establishes a relationship among the four different gas variables such as pressure (P), Volume (V), Temperature (T) and amount of gas (n).

Ideal Gas Properties and Characteristics

• The motion of ideal gas in a straight line is constant and random.
• The gas occupies a very small space because the particle in the gas is minimal.
• There is no force present between the particle of the gas. Particles only collide elastically with the walls of the container and with each other.
• The average kinetic energy of the gas particle is directly proportional to the absolute temperature.
• The gases are made up of many of the same particles (atoms or molecules), which are perfectly hard spheres and also very small.
• The actual volume of the gas molecule is considered negligible as compared to the space between them, and because of this reason, they are considered as the point masses.

Gas Law Formula Table

The following table consists of all the formulas of Gas Law:

Problems Related to Gas Law

(1) A sealed jar whose volume is exactly 1 L, which contains 1 mole of air at a temperature of 20 degrees Celcius, assuming that the air behaves as an ideal gas. So, what is the pressure inside the jar in Pa?

Solution:

By solving with the help of the ideal gas equation,

PV = nRT

(1) By rearranging the equation, we can get,

P = nRT/V

(2) Write down all the values which are known in the SI unit.

n= 1

R= 8.314J/K/mol

T= 20degree celcius=(20+273.15)K=293.15K

V=1L=0.001m³

(3) Put all the values in the equation

P= nRT/V

P=(1*8.314*293.15)/0.001

P= 2,437,249

P=2.437*10^6 Pa

The pressure is almost 24atm.

Application of Gas-law

During summer, when the temperature is high, and pressure is also high, a tire is at risk of bursting because it is inflated with air. Or when you start climbing a mountain, you feel problems related to inhaling. Why does it happen?

When the physical condition changes with changes in the environment, the behaviour of gases particle also deviates from their normal behaviour. These changes in gas behaviour can be studied by studying various laws known as gas laws.

Gas laws have been around for quite some time now, and they significantly assist scientists in finding amounts, pressure, volume, and temperature related to matters of gas.

Besides, the gas law, along with modern forms, are used in many practical applications that concern gas. For example, respiratory gas measurements of tidal volume and vital capacity etc., are done at ambient temperature while these exchanges actually take place in the body at 37 degrees Celsius. The law is used often in thermodynamics as well as in fluid dynamics. Also, it can be used in weather forecast systems.

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