Question

question 14

what volume container (in liters) would be required to hold 5.25 kg of sulfur dioxide gas under a pressure of 50.00 psi at 25.0 °c?

Explanation:

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<reasoning>

Convert mass of sulfur dioxide to moles

Using the Molar Mass Calculation knowledge point
\[

$$\begin{aligned} &\text{Molar mass of } \text{SO}_2 = 32.06 + 2 \times 15.999 = 64.06\text{ g/mol}\\ &m = 5.25\text{ kg} = 5250\text{ g}\\ &n = \frac{5250\text{ g}}{64.06\text{ g/mol}} \approx 81.954\text{ mol} \end{aligned}$$

\]

Convert pressure to atmospheres

Using the Pressure Unit Conversion knowledge point
\[

$$\begin{aligned} &1\text{ atm} = 14.696\text{ psi}\\ &P = \frac{50.00\text{ psi}}{14.696\text{ psi/atm}} \approx 3.4023\text{ atm} \end{aligned}$$

\]

Convert temperature to Kelvin

Using the Gas Laws knowledge point
\[

$$\begin{aligned} &T = 25.0^\circ\text{C} + 273.15 = 298.15\text{ K} \end{aligned}$$

\]

Calculate the volume using the Ideal Gas Law

Using the Gas Laws knowledge point
\[

$$\begin{aligned} &V = \frac{nRT}{P}\\ &R = 0.082057\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K})\\ &V = \frac{81.954\text{ mol} \times 0.082057\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}) \times 298.15\text{ K}}{3.4023\text{ atm}} \approx 589.3\text{ L} \end{aligned}$$

\]

Apply significant figures

Using the Significant Figures knowledge point
\[

$$\begin{aligned} &\text{Given values: } 5.25\text{ kg (3 sig figs), } 50.00\text{ psi (4 sig figs), } 25.0^\circ\text{C (3 sig figs)}\\ &\text{Final volume rounded to 3 significant figures: } 589\text{ L} \end{aligned}$$

\]
</reasoning>

<answer>
What volume container (in liters) would be required to hold 5.25 kg of sulfur dioxide gas under a pressure of 50.00 psi at 25.0 °C? <blank>589</blank>
</answer>

<post_analysis>
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"Natural Science",
"Chemistry",
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]
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Answer:

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<reasoning>

Convert mass of sulfur dioxide to moles

Using the Molar Mass Calculation knowledge point
\[

$$\begin{aligned} &\text{Molar mass of } \text{SO}_2 = 32.06 + 2 \times 15.999 = 64.06\text{ g/mol}\\ &m = 5.25\text{ kg} = 5250\text{ g}\\ &n = \frac{5250\text{ g}}{64.06\text{ g/mol}} \approx 81.954\text{ mol} \end{aligned}$$

\]

Convert pressure to atmospheres

Using the Pressure Unit Conversion knowledge point
\[

$$\begin{aligned} &1\text{ atm} = 14.696\text{ psi}\\ &P = \frac{50.00\text{ psi}}{14.696\text{ psi/atm}} \approx 3.4023\text{ atm} \end{aligned}$$

\]

Convert temperature to Kelvin

Using the Gas Laws knowledge point
\[

$$\begin{aligned} &T = 25.0^\circ\text{C} + 273.15 = 298.15\text{ K} \end{aligned}$$

\]

Calculate the volume using the Ideal Gas Law

Using the Gas Laws knowledge point
\[

$$\begin{aligned} &V = \frac{nRT}{P}\\ &R = 0.082057\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K})\\ &V = \frac{81.954\text{ mol} \times 0.082057\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}) \times 298.15\text{ K}}{3.4023\text{ atm}} \approx 589.3\text{ L} \end{aligned}$$

\]

Apply significant figures

Using the Significant Figures knowledge point
\[

$$\begin{aligned} &\text{Given values: } 5.25\text{ kg (3 sig figs), } 50.00\text{ psi (4 sig figs), } 25.0^\circ\text{C (3 sig figs)}\\ &\text{Final volume rounded to 3 significant figures: } 589\text{ L} \end{aligned}$$

\]
</reasoning>

<answer>
What volume container (in liters) would be required to hold 5.25 kg of sulfur dioxide gas under a pressure of 50.00 psi at 25.0 °C? <blank>589</blank>
</answer>

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