# Ideal Gas Law

Last Updated : 24 Apr, 2023

The ideal gas law also called the general gas equation, is an equation that provides the relation among the various parameters of the gas i.e. they provide the relation among pressure(P), temperature(T), and Volume(V) of the gas. It is a combination of Charles’s law, Boyle’s Law, Avogadro’s law, and Gay-Lussac’s law. This law was first stated by the French physicist Benoit Paul Émile Clapeyron in 1834.

Let’s learn about Ideal Gas Law and its derivation and others in detail.

## What is Ideal Gas?

An ideal gas is a gas that exists only in theory but practically it does not exist. It consists of particles where only elastic collision occurs. An ideal gas is also called a perfect gas. Ideal gas does not exist in the environment but some gases behave as perfect gases which include  Nitrogen, Oxygen, Hydrogen, and Carbon Dioxide, and others behave ideally under the specific condition of temperature and pressure.

## Ideal Gas Laws

Ideal gas laws are the combination of the observational work of Boyle in the seventeenth century and Charles in the eighteenth century.

Boyle’s law: The gas pressure is inversely proportional to the gas volume for a given amount of gas kept at a fixed temperature i.e. at constant temperature the relation between the pressure and volume of a quantity of gas can be written as,

P ∝ 1 / V

PV = Constant

where
P is the pressure
V is the volume

Charles’ law: The gas volume is directly proportional to the gas temperature for a given fixed amount of gas kept at a constant pressure i.e. at constant temperature the relation between the volume and temperature of a quantity of gas can be written as,

V ∝  T

V / T = Constant

where
T is the Temperature
V is the volume

## Ideal Gas Law Units

For Ideal Gas Law various units are,

PV = nRT

where,

• P is the pressure which is measured in pascals(Pa) or atm
• V is the volume which is measured in m3 or Liters(l)
• T is the temperature which is measured in Kelvin(K)

### Universal Gas Constant (R)

R is a universal gas constant and it is denoted by R.

• In the SI system, the value of the Universal Gas Constant is 8.314 kJ/mole.K
• In the CGS system, the value of the Universal Gas Constant is 0.082 L.atm/K.mol

## Ideal Gas Equation

These two laws apply to low-density gases and can be grouped into a single relationship. It’s worth noting that,

PV = Constant…(1)

V/T = Constant…(2)

From eq(1) and (2)

PV/T = constant

It can be stated in a more general form that applies to any quantity of any low-density gas, not simply a specific quantity of that gas. This relationship describes the ideal gas law and knows as the ideal gas equation

It can be expressed as,

PV / T = nR

PV = nRT

where,
n is the number of moles in the sample of gas
R is the universal gas constant

Note: The universal gas constant (R) has a value of 8.314 kJ/mole in the SI system.

It can also be stated in a more general form that applies to any quantity of any low-density gas, not simply a specific quantity of that gas.

## Derivation of the Ideal Gas Equation

Let P is the pressure exerted by the gas, V is the volume f the gas, and T be the Temperature.

According to Boyle’s Law,

P ∝ 1/V

V ∝ 1/P……(1)

According to Charles’ Law,

V ∝  T……..(2)

When P and T are both constant, the volume of a gas is proportional to the number of moles of gas. i.e.

V ∝  n …….(3)

Compare equations (1), (2), and (3) as

V ∝  nT/P

PV = nRT

where
R is the Universal gas constant and it is value of 8.314 J/molK

## Absolute Temperature

Thermodynamic temperature is another name for absolute temperature. The value of absolute temperature equals zero Kelvin or -273 °C. The thermodynamic energy of a system is lowest at this temperature. The velocity of the gas particles stops at an absolute zero temperature. This signifies that the particles of the gas really aren’t moving. At absolute zero, the volume of the gas is zero.

For more, Temperature Scales

## Relationship between Pressure and Temperature

The temperature has a direct relationship with pressure and volume i.e.

PV ∝ T

This relationship enables a gas that will be utilized to determine the temperature in a Gas thermometer with a constant volume.

Therefore, at constant volume, the relationship can be written as,

P ∝ T

Here, the temperature is read in terms of pressure with a constant-volume gas thermometer.

A straight line emerges from a plot of pressure against temperature.

Observations on real gases differ from the values anticipated by the ideal gas law at low temperatures. However, the relationship is linear over a wide temperature range, and it appears that if the gas remained a gas, the pressure would drop to zero with decreasing temperature. Extrapolating the straight line to the axis yields the absolute minimum temperature for an ideal gas. Absolute zero is defined as a temperature of – 273.15 degrees Celsius. The Kelvin temperature scale, often known as the absolute scale of temperature, is founded on absolute zero.

The image given below shows the relationship between the Pressure and Temperature of an Ideal Gas.

On the Kelvin temperature scale, – 273.15 °C is taken as the zero point, that is 0 K. In both the Kelvin and Celsius temperature systems, the unit size is the same. So, the relation between them can be expressed as

T = t + 273.15

where
t is the temperature in °C

## Solved Examples on Ideal Gas Law

Example 1: What is the volume occupied by 2.34 grams of carbon dioxide gas at STP?

Solution:

Given,

Weight (m) of the carbon dioxide = 2.34 grams

At STP

Temperature = 273.0 K
Pressure = 1.00 atm.

R = 0.08206 L atm mol¯11

Number of mole n is,

n = m / M

where,
n is the number of moles,
m is the weight
M is the molar mass of the substance.

Molar Mass of carbon dioxide = 44.0 g mol¯1

n = 2.34 g / 44.0 g mol¯1
= 0.0532 mol

According to the ideal gas equation,

PV = nRT

V = nRT / P

Substituting all the values,

V = [0.0532) (0.08206) (273.0)] / 1.00

= 1.19 L

Example 2: A sample of argon gas at STP occupies 56.2 litres. Determine the number of moles of argon and the mass of argon in the sample.

Solution:

Given,

Volume (V) of the Argon = 56.2 liters

At STP,
Temperature = 273.0 K.
Pressure = 1.00 atm.

Molar mass of Argon gas = 39.948 g/mol

According to Ideal Gas equation,

PV = nRT

n = PV / RT…(1)

Substituting all the values in the above equation,

n = [(1.00 atm) (56.2 L) ] / [ (0.08206 L atm mol¯1 K¯1) (273.0 K)]

= 2.50866 mol

Number of mole n,

n = m/M

m = nM…(2)

Substituting all the values in the above equation,

m = (2.50866 mol)×(39.948 g/mol)

= 100 g

Example 3: At what temperature will 0.654 moles of neon gas occupy 12.30 litres at 1.95 atmospheres?

Solution:

Given,

Volume (V) of Neon Gas = 12.30 litres

Pressure = 1.95 atm

Number of Moles = 0.654 moles

According to Ideal Gas Equation,

PV = nRT

T = PV / nR

Substituting all values in above equation,

T = [(1.95 atm) ×(12.30 L)] / [(0.654 mol)×(0.08206 L atm mol¯1 1)]

= 447 K

Example 4: 5.600 g of solid CO2 is put in an empty sealed 4.00 L container at a temperature of 300 K. When all the solid CO2 becomes gas, what will be the pressure in the container?

Solution:

Given,

Weight (m) of carbon dioxide = 5.600 g

Volume (V) of the carbon dioxide = 4.00 L

Temperature = 300 K

Molar Mass of carbon dioxide = 44.0 g mol¯1

Number of Mole n,

n = m/M…(1)

Substituting all the values in the above equation,

n = (5.600 g) / (44.009 g/mol)

= 0.1272467 mol

According to the Ideal Gas Equation,

PV = nRT

P = nRT/V…(2)

Substituting all the values in the above equation,

P = (0.1272467 mol)× (0.08206 L atm mol¯1 1)× (300 K)/ (4.00 L)

= 0.7831 atm

## FAQs on Ideal Gas Laws

### Q1: What is the Ideal Gas Law?

The Ideal Gas Law is a law which provides the relation among various parameters of the gas such as pressure, temperature, and volume of the gas. According to Ideal Gas Law,

PV = nRT

### Q2: What is Ideal Gas examples?

There is no such gas which behaves as a perfect noble gas, but we can take some gases which almost behave as Ideal Gas which are, Nitrogen, Oxygen, Hydrogen, Carbon Dioxide, and others.

### Q3: Who derived the Ideal Gas Law?

Ideal Gas law was first derived by the French physicist Benoît Paul Émile Clapeyron.

### Q4: Why is Ideal Gas law inaccurate?

Ideal Gas Law is inaccurate because it only works on ideal gas under perfect motion and it fails at a higher pressure and lower temperature.

### Q5: How is Ideal Gas law used in everyday life?

The ideal gas law is used in everyday life in various scenarios such as,

• Airbags in the car expand on the basis of the Ideal Gas Law.
• The coolant gas added in Refrigerators, and AC cools using the principal of Ideal Gas Law
• The ventilation provided in the high-rise buildings uses the Ideal gas law.

### Q6: What is the Ideal Gas Equation?

Ideal gas equation is,

PV = nRT

where,
P is Pressure of the Gas
V is Volume of the Gas
T is Temperature of the Gas
n is the number of moles of the gas
R is Universal Gas Constant

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