1. Gas Laws

Introduction

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 18th 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.

 

 

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

 

 

 

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

 

 

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

 

 

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

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.