Question

What is the mass of 33.6 dm$^3$ of methane gas at S.T.P.?

• A. $4.8 \times 10^{-2}$ kg
• B. $3.3 \times 10^{-2}$ kg
• C. $1.6 \times 10^{-2}$ kg
• D. $2.4 \times 10^{-2}$ kg

Hint:

Notice that the given volume ($33.6\text{ dm}^3$) is exactly $1.5$ times the standard volume of $22.4\text{ dm}^3$. Therefore, you have exactly $1.5$ moles of gas. Multiply $1.5$ by the molar mass of methane ($16\text{ g}$) to instantly arrive at $24\text{ g}$ or $2.4 \times 10^{-2}\text{ kg}$.

Answer 1

The Correct Option is D

Step 1: Identify the route.
We are given a gas volume at STP and asked for its mass, so we go volume -> moles -> mass.
Step 2: Use the molar volume.
At STP one mole of any gas occupies $22.4$ dm$^3$.
Step 3: Find the moles.
$n = \dfrac{33.6}{22.4} = 1.5$ mol of methane.
Step 4: Get the molar mass of methane.
$\text{CH}_4$ has mass $12 + 4(1) = 16$ g mol$^{-1}$.
Step 5: Compute mass in grams.
Mass $= n \times M = 1.5 \times 16 = 24$ g.
Step 6: Convert to kilograms.
$24$ g $= 0.024$ kg $= 2.4 \times 10^{-2}$ kg, which is option (4).
\[ \boxed{\text{Mass} = 2.4 \times 10^{-2} \text{ kg}} \]