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Ideal Gas Law Formula

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 an Ideal gas 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:

  1. Ideal gas molecules do not attract or repel each other.
  2. The ideal gas molecules interact by elastic collision.
  3. These molecules themselves take up no volume.
  4. 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 × V = n × R × 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, Boyle’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
\(V \propto \frac{ n × T }{P}\)

To covert the proportionality to equality we use universal gas constant R. We get,
\(V = \frac{ n × R ×T }{P} \)

Ideal Gas Law is given as
P × V = n ×R ×T

Solved Examples

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

Answer: The number of moles is n = 5.00moles, temperature is T = 30°C and pressure is P = 765 mmHg, R= 8.314 J/mol K

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

T = 30 + 273 = 303 K

P = \(\frac{765}{760}\) = 1.006 atm

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

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

V = 75.123 L

The volume of the gas would be 75.123 Litres

Q 2: How many moles of ‘He’ are contained in a 5- litre canister at 100 KPa and 25 ° 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, 0.2018 moles of ‘He’ are contained in a 5-litre canister at 100 KPa and 25 ° C

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