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?

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?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Molar Mass Calculation", "Pressure Unit Conversion", "Gas Laws" ], "new_concepts": [ "Ideal Gas Law Calculations" ], "current_concepts": [ "Molar Mass Calculation", "Pressure Unit Conversion", "Gas Laws", "Ideal Gas Law Calculations" ] } ## 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 $$ \begin{aligned} &\text{Given values: } 5.25\text{ kg (3 sig figs), } 50.00\text{ psi (4 sig figs), } 25.0^\circ\text{C (3 sig figs)}\ &\text{Final volume rounded to 3 significant figures: } 589\text{ L} \end{aligned} $$ 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? 589 { "subject": "Natural Science", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Natural Science", "Chemistry", "Ideal Gas Law Calculations" ] }

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Question

Explanation:

Convert mass of sulfur dioxide to moles

Convert pressure to atmospheres

Convert temperature to Kelvin

Calculate the volume using the Ideal Gas Law

Apply significant figures

Answer: