### 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.

Equal volumes of gas contain equal numbers of molecules.

### 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 $P_{1}=P_{2}$ $\dfrac {V_{1}}{T_{1}}=\dfrac {V_{2}}{T_{2}}$ $T_{2} =\dfrac {V_{2}T_{1}}{V_{1}} =\dfrac {2V_1 \times 300}{V_{1}} =300 \times 2=600\ K =327^{\circ}$

### Solved Example:

#### 69-2-02

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

### Solved Example:

#### 69-2-03

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

### Solved Example:

#### 69-2-05

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

### Solved Example:

#### 69-2-06

Which of the following statements about gases is false?

### 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:

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