Gas Laws

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Introduction

A few laws relating to the temperature, pressure, and volume of a gas make up the gas laws. These laws determine the behaviour of gases and are governed by certain interrelated properties. The parameters that are linked by the gas laws are as follows.

  • The volume occupied by a gas.

  • The pressure exerted by a gas on the walls of the container.

  • The absolute temperature of the gas.

  • The number of moles present in the gas or the amount of gaseous substance.


What are Gas Laws?

Towards the end of the 18th century, several scientists developed some gas laws. Each gas law is recognized by the name of the respective scientists who postulated it. Thus, today we recognize five important gas laws that are as follows. 

  1. Boyle’s Law gives a relationship between the pressure and the volume of a gas.

  2. Charles’s Law gives a relationship between the volume occupied by a gas and the absolute temperature of the gas.

  3. Gay-Lussac’s Law provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.

  4. Avogadro’s Law provides a relationship between the volume occupied by a gas and the amount of gaseous substance.

The Combined Gas Law which is also known as the ideal gas law, can be obtained by combining the above four laws individually given by four different scientists. Although the combination of these laws describes the behaviour of an ideal gas, they approximate the behaviour of real gases very closely.

All gases behave similarly under standard conditions. As the physical parameters change, the variations in their behaviour are noticed. These physical parameters include temperature, pressure, and volume of gases. A change in these parameters induces behavioural changes in gases. Hence, the gas laws describe these behavioral changes of gases.

Now let us have a look at the gas laws and understand its various applications.


Boyle’s Law

As stated above, Boyle’s Law explains the relationship between the pressure of a gas and the volume of the gas, at a constant temperature. So, it actually explains that the volume of a gas is inversely proportional to the pressure of a gas at a constant temperature.

It can be further given in an equation as follows. 

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.

K1 is constant.

Thus, Boyle’s law can be formulated as follows, to calculate the pressure or volume of a given gas, at a constant temperature.

P1V1 = P2V2


Charle’s Law

As per the Charle’s law,  the volume of a gas is directly proportional to its temperature (in Kelvin) in a closed system. Thus this law explains the relationship between the temperature and volume of the gas.

Charle’s law can be expressed by the following formula.

V ∝ T

Where, V = volume of gas,

T = temperature of the gas in Kelvin,

This equation can also be given as,

V1 / T1 = V2 / T2

Furthermore, V1 / T1 = V2 / T2 

⇒ V/T = constant= K2

So, V= K2T.

Thus, the value of K2 depends on the pressure of the gas, its amount, and also on the unit of volume.


Gay-Lussac’s Law

Gay-Lussac’s gas law gives the relationship between the temperature and the pressure of a gas, at constant volume. This means that at a constant volume, the pressure of the gas is directly proportional to its temperature.

For instance, when you heat a given volume of gas, the molecules in it gain energy and move faster. On cooling down, the change in temperature and pressure can be calculated by using the Gay-Lussac’s law.

This is mathematically expressed as follows. 

P ∝ T

Or,

P / T = k1

Or,

P1 / T1 = P2 / T2

where P is the pressure of the gas.

T is the temperature of the gas in expressed in Kelvin.


Avogadro’s Law

Avogadro’s gas law explains that at the same temperature and pressure, an equal number of molecules are present in equal volumes of gases. This law holds good for all gases. 

Avogadro’s law can be mathematically expressed as, 

V / n = constant

Or,

V1 / n1 = V2 / n2

where the ideal gas volume is V

n in the above equation represents the number of gas molecules.


Combined Gas Law or Ideal Gas Law

The general gas law or combined gas law is the law obtained by combining the above-mentioned gas laws. So, this gives the summations of Avogadro’s law, Charle’s law, and Boyle’s law. It aims at explaining the relationship between the volume and pressure for a fixed quantity of gas.

In general, it can be expressed as,

PV / T = K

When the same gas is compared in different cases, the law can be represented as,

P1V1 / T1 = P2V2 / T

So, the ideal gas law gives the relationship between four different parameters.

Mathematically,

PV=nRT

where,

V = volume of a given gas,

T = temperature of a given gas,

P = pressure of a given gas.

R = universal gas constant,

n = the number of moles.

An equivalent equation for this law is given below.

PV = kNT

Here, k is the Boltzman constant,

N is the number of gas molecules.

FAQ (Frequently Asked Questions)

1. The pressure exerted by a gas in container 1 is 3 kPa. When container 1 is emptied into a 10-liters container, the pressure exerted by the gas increases to 6 kPa. Find the volume of the container

Answer: 1. Let’s consider that the temperature and quantity of the gas remains constant

Given,

Initial pressure, P1 = 3 kPa

Final pressure, P2 = 6 kPa

Final volume, V2 = 10L

According to Boyle’s law, V1 = (P2V2)/P1

V1 = (6 kPa * 10 L)/3 kPa = 20 L

Therefore, the 20 L is the volume of container 1.


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

Answer:  P1T1 = P2T2

P2 = 626.3/303.15

P2 = 2.0659