Question

What is the volume (in $\text{dm}^3$) occupied by 75 g ethane at S.T.P. ?

• A. 60.0
• B. 56.0
• C. 22.4
• D. 44.8

Hint:

Remember the metric equivalencies! 1 Liter (L) is exactly identical in volume to 1 cubic decimeter ($\text{dm}^3$). Don't let the different units trick you into performing unnecessary conversions.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given a specific mass ($75\text{ g}$) of a gas (ethane) and asked to calculate the physical volume it occupies at Standard Temperature and Pressure (STP) in cubic decimeters ($\text{dm}^3$).

Step 2: Key Formula or Approach:
The volume of an ideal gas at STP can be found using the molar volume concept.
At STP, 1 mole of any ideal gas occupies exactly $22.4\text{ L}$, which is equivalent to $22.4\text{ dm}^3$.
First, find the number of moles ($n$) using: $n = \frac{\text{Given Mass}}{\text{Molar Mass}}$.
Then, calculate the volume: $\text{Volume} = n \times 22.4\text{ dm}^3/\text{mol}$.

Step 3: Detailed Explanation:
First, determine the molar mass of ethane. Its chemical formula is $\text{C}_2\text{H}_6$.
Molar mass of $\text{C}_2\text{H}_6 = (2 \times 12\text{ g/mol for Carbon}) + (6 \times 1\text{ g/mol for Hydrogen})$
Molar mass $= 24 + 6 = 30\text{ g/mol}$.
Next, calculate the number of moles ($n$) present in the $75\text{ g}$ sample:
$$n = \frac{75\text{ g}}{30\text{ g/mol}}$$
$$n = 2.5\text{ moles}$$
Finally, convert the moles to volume at STP:
$$\text{Volume} = 2.5\text{ moles} \times 22.4\text{ dm}^3/\text{mol}$$
$$\text{Volume} = 56.0\text{ dm}^3$$

Step 4: Final Answer:
The volume occupied by the gas is $56.0\text{ dm}^3$, which corresponds to option (B).