8g of CH$_4$ occupies 11.2 at S.T.P. What volume would 22g of CH$_3$CH$_2$CH$_3$ occupy under the same condition?

1. Analyze the Question

We are given the mass and volume of Methane ($CH_4$) at Standard Temperature and Pressure (S.T.P.). We need to find the volume that a specific mass of Propane ($CH_3CH_2CH_3$) would occupy under the same conditions.

2. Explain the Concept

At S.T.P., the molar volume of any ideal gas is constant: 1 mole of any gas occupies 22.4 dm³. To solve this, we use the relationship:

Once we find the number of moles of the gas, we multiply by the molar volume (22.4 dm³/mol) to find the total volume.

3. Show the Solution

Step 1: Calculate the moles of Propane ($C_3H_8$)

• Chemical formula for Propane: $CH_3CH_2CH_3$ is $C_3H_8$.
• Molar mass of $C_3H_8 = (3 \times 12) + (8 \times 1) = 36 + 8 = 44 \text{ g/mol}$.
• Given mass of Propane = $22 \text{ g}$.
• $\text{Moles of Propane} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{22}{44} = 0.5 \text{ moles}$.

Step 2: Calculate the volume of Propane

• Since 1 mole of any gas occupies 22.4 dm³ at S.T.P.:
• $\text{Volume} = \text{Moles} \times 22.4 \text{ dm}^3/\text{mol}$
• $\text{Volume} = 0.5 \times 22.4 = 11.2 \text{ dm}^3$.

(Note: The information about $CH_4$ provided in the question is actually a distractor or a confirmation of the S.T.P. conditions, as 8g of $CH_4$ is 0.5 moles, which also occupies 11.2 dm³).

4. Identify the Answer

Comparing our result to the given options, the correct volume is 11.2 dm³.

5. Tip

Always remember the "Magic Number" 22.4! At S.T.P., if you know the number of moles of a gas, you simply multiply by 22.4 to get the volume in dm³. Don't get distracted by extra data—focus on the molar mass of the substance you are actually asked to calculate.