An ideal gas is a gas composed of randomly moving point particles that interact only through elastic collisions. Ideal gas is a theoretical concept. The ideal gas concept is beneficial because it follows the ideal gas law. Here we discuss Ideal Gas Law Formula and its applications.

**Ideal Gas Law Formula**

**What is an Ideal Gas Law?**

The concept of anÂ Ideal gasÂ is an approximation that helps us to predict the behavior of real gases. The term ideal gas refers to a theoretical gas composed of molecules, which follow a few rules they are:

- Ideal gas molecules do not attract or repel each other.
- The ideal gas molecules interact by elastic collision.
- These molecules themselves take up no volume.
- Ideal gas molecules are moving point particles that have no volume of themselves.

**Ideal Gas Law**

The Ideal Gas Law created to show the relationship between pressure, volume, number of moles of gas and temperature. It shows the equation of a hypothetical or theoretical ideal gas. Pressure and volume have an inverse relationship with each other but have a direct relationship with Temperature.

The equation for the Ideal Gas Law is:

**P** Ã—**Â V = n** Ã—**Â R** Ã—**Â T**

P | Pressure (atm) |

V | Volume (L) |

n | Number of moles (mol) |

R | The Ideal Gas Constant (0.08206 L-atm/mol-K) |

T | Temperature (Kelvin) |

**Derivation of Ideal Gas Law**

Ideal Gas Law is a combination of three simple gas laws. They are Avogadro’s Law, Boyleâ€™s Law and Charles’s Law.

Now we derive the Ideal Gas Law.

i) Avogadro’s Law: It states that the volume of a gas is directly proportional to the number of moles.

\(V \propto n ————— (1) \)

ii) Boyle’s Law: It states that the pressure of a gas is inversely proportional to its volume.

\(V \propto \frac{1}{P} ————— (2) \)

iii) Charles’s Law: It states that the volume of a gas is directly proportional to its Kelvin temperature.

\(V \propto T —————– (3) \)

For Ideal Gas Law we combine all the 3 equations, we get

\(V \propto \frac{ n Ã— T }{P}\)

To covert the proportionality to equality we use universal gas constant R. We get,

\(V = \frac{ n Ã— R Ã—T }{P} \)

Ideal Gas Law is given as

P Ã— V = n Ã—R Ã—T

**Solved Examples**

**Q 1. **Calculate the volume 5.00 moles of gas will occupy at 30Â°Celsius and 765 mm Hg. (R= 8.314 J/mol K)

**Answer:**Â The number of moles isÂ nÂ = 5.00moles, temperature isÂ TÂ = 30Â°CÂ and pressure isÂ PÂ = 765Â mmHg, R= 8.314 J/mol K

First, we convert Temperature to Kelvin and Pressure to Atmospheres for the ideal gas equation.

TÂ = 30 + 273 = 303 K

PÂ = \(\frac{765}{760}\) = 1.006 atm

Ideal Gas Law Equation =>Â \(P \times V = n \times R \times T \)

\(1.006 \times (V) = 3.00 \times (0.08314) \times (303) \)

VÂ = 75.123 L

The volume of the gas would be 75.123 Litres

**Q 2:** How many moles of â€˜Heâ€™ are contained in a 5- litre canister at 100 KPa and 25Â Â° C. Take R= 8.314 J/mol K

**Answer:** Using the Ideal gas equation, n = \(\frac{P \times V}{R \times T} \)

Therefore, on substituting the values

T = 25 + 273 = 298

we get,

= \(100 \times 5/ 8.314 \times 298 = \frac{500}{2477.572}\) = 0.2018 moles

Hence,Â 0.2018 moles of â€˜Heâ€™ are contained in a 5-litre canister at 100 KPa and 25Â Â° C

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