A learner investigates the relationship between the pressure and volume of an enclosed DIATOMIC gas at 25 °C. He records the volume of the gas for different pressures in the table below. Write down the name of the gas law being investigated.

According to Boyle's Law, $P = k \left(\frac{1}{V}\right)$, where $k$ is a constant. Using the first two data points from the table (40 kPa, 0.02 cm$^{-3}$) and (80 kPa, 0.04 cm$^{-3}$):

The constant $k$ is $2000 \text{ kPa} \cdot \text{cm}^3$.

1.5.1 Use the conditions at a pressure of 100 kPa and calculate the molar mass of the enclosed gas.
Given:
Mass of gas ($m$) = $2.49 \times 10^{-2}$ g
Pressure ($P$) = 100 kPa
Volume ($V$) = 22 cm$^3$ (from table at 100 kPa)
Temperature ($T$) = 25 °C
Ideal gas constant ($R$) = $8.314 \text{ J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$

1.5.2 Write down the molecular formula of the enclosed gas.
The calculated molar mass is approximately $28.05 \text{ g/mol}$. The problem states the gas is diatomic.
Comparing this to common diatomic gases:

• Nitrogen (N$_2$) has a molar mass of $2 \times 14.01 \text{ g/mol} = 28.02 \text{ g/mol}$. The molecular formula of the enclosed gas is $\boxed{\text{N}_2}$.

1.6 The sketch graph below shows the relationship between volume and temperature for an ideal gas.
This graph illustrates Charles's Law. It shows that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature (in Kelvin). The linear relationship passing through the origin is characteristic of this law.