What volume (in litres) will $128.0\text{ g}$ of sulfur dioxide gas ($\text{SO}_2$) occupy at STP?

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01-11-2026
Chemistry

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What volume (in litres) will $128.0\text{ g}$ of sulfur dioxide gas ($\text{SO}_2$) occupy at STP?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T20:52:10-05:00

Calculate the number of moles of $SO_2$ using the given mass and molar mass: $n = \frac{128.0}{64.064} \approx 1.9980 \, \text{mol}$.
Determine the volume at STP by multiplying the number of moles by the molar volume: $V = 1.9980 \times 22.414 \approx 44.78 \, \text{L}$.
The volume occupied by the gas is $\boxed{44.78 \, \text{L}}$.

Explanation

Calculating the Moles of Sulfur Dioxide Gas

To find the volume that 128.0 g of sulfur dioxide gas ($SO_2$) occupies at STP, we first need to determine the amount of substance in moles. The mass of the gas is given as $128.0 \, \text{g}$ and the molar mass is given as $64.064 \, \text{g/mol}$. The number of moles ($n$) is calculated using the formula:
\[n = \frac{m}{M}\]
Substituting the given values:
\[n = \frac{128.0 \, \text{g}}{64.064 \, \text{g/mol}} \approx 1.9980 \, \text{mol}\]

Calculating the Volume at STP

At standard temperature and pressure (STP), the molar volume of an ideal gas is defined as approximately $22.414 \, \text{L/mol}$. We can now calculate the volume ($V$) of the gas by multiplying the number of moles by this molar volume:
\[V = n \times V_m\]
\[V = 1.9980 \, \text{mol} \times 22.414 \, \text{L/mol}\]
Performing the multiplication, we get:
\[V \approx 44.783 \, \text{L}\]
Rounding to a reasonable number of significant figures based on the input data, we obtain the final volume.

Conclusion

Based on the calculations, the volume occupied by 128.0 g of $SO_2$ gas at STP is approximately 44.78 Litres.
\[\boxed{44.78 \, \text{L}}\]

Examples

Understanding the relationship between mass, moles, and volume is essential in fields like chemistry and chemical engineering. For example, when industrial engineers design storage tanks for gases like sulfur dioxide, they must calculate how much space the gas will occupy at specific pressures and temperatures to ensure safety and efficiency. Using the molar volume at STP allows chemists to quickly convert between the mass of a substance and the space it occupies, which is crucial for controlling reactions and handling materials in laboratory and industrial settings.