Ideal Gas Laws

  • Explain and apply Boyle’s, Charles’, and Avogadro’s gas Laws to observations of gas behavior.

  • Apply gas laws to stoichiometric problems

  • Define the conditions of STP.

Charles’ Law:

For a fixed mass of gas at constant pressure, the volume is directly proportional to the kelvin temperature. \[\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}\]

Boyle’s Law:

For a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure. \[p_1 V_1 = p_2 V_2\]

General Gas Equation:

\[PV = nRT\]

Van Der Waals Equation:

The van der Waals equation corrects for the volume of, and attractive forces between, gas molecules:

\[(P + \dfrac{a}{\bar{v}^2})(\bar{v}- b) = \bar{R}T\]

There are two corrective factors in van der Waals equation. The first, \(\dfrac{a}{\bar{v}^2}\) , alters the pressure in the ideal gas equation. It accounts for the intermolecular attractive forces between gas molecules.
The factor b accounts for the volume occupied by the gas molecules. Since b corresponds to the total volume per mole occupied by gas molecules, it closely corresponds to the volume per mole of the liquid state, whose molecules are closely layered. b is generally much smaller in magnitude than a. The values of a and b generally increase with the size and complexity of the molecule.

Avogadro’s Hypothesis:

Equal volumes of gas contain equal numbers of molecules.

Solved Examples

Solved Example:

69-2-01

A perfect gas at 27$^\circ$C is heated at constant pressure till its volume is double. The final temperature is: (Based on CIL MT Mech 2020)

Solution:
\[T_{1}=27^{\circ}C=27+273=300\ K\] \[V_{2}=2V_{1}\] \[\dfrac {P_{1}V_{1}}{T_{1}}=\dfrac {P_{2}V_{2}}{T_{2}}\] Given \[P_{1}=P_{2}\] \[\dfrac {V_{1}}{T_{1}}=\dfrac {V_{2}}{T_{2}}\] \[T_{2} =\dfrac {V_{2}T_{1}}{V_{1}} =\dfrac {2V_1 \times 300}{V_{1}} =300 \times 2=600\ K =327^{\circ}\]

Correct Answer: B

Solved Example:

69-2-02

The statement that molecular weights of all gases occupy the same volume is known as:

Correct Answer: A

Solved Example:

69-2-03

Of the following, _________ is a valid statement of Charles' law.

Correct Answer: A

Solved Example:

69-2-04

According to Avogadro's Hypothesis:

Correct Answer: A

Solved Example:

69-2-05

Of the following, which is a correct statement of Boyle's law?

Correct Answer: A

Solved Example:

69-2-06

Which of the following statements about gases is false?

Correct Answer: D

Solved Example:

69-2-07

The value of the product of molecular weight and the gas characteristic constant for all the gases in S.I. units is:

Correct Answer: B

Solved Example:

69-2-08

Molecular volume of any perfect gas at 600 $\times$ $10^3$ N/m$^2$ and 27$^\circ$C will be:

Correct Answer: A