5. calculate the partial pressure of each gas and the total pressure for each of the following gas mixtures:
a. $0.200\text{ mol n}_2$ and $2.33\text{ g of o}_2$ in a $500.0\text{ ml}$ vessel at $25^\circ\text{c}$
b. $0.0150\text{ mol h}_2$, $4.22\text{ mg of he}$, and $0.030\text{ mol nh}_3$ at $50^\circ\text{c}$ in a $1.00\text{ l}$ vessel

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{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Molar Mass Calculation", "Ideal Gas Law Calculations", "Significant Figures" ], "new_concepts": [ "Daltons Law of Partial Pressures" ], "current_concepts": [ "Molar Mass Calculation", "Ideal Gas Law Calculations", "Daltons Law of Partial Pressures", "Significant Figures" ] } ## Convert given quantities to moles Using the *Molar Mass Calculation* and *Significant Figures* knowledge points $$ \begin{aligned} &\text{For part a:}\ &n_{\text{N}_2} = 0.200\text{ mol}\ &n_{\text{O}_2} = \frac{2.33\text{ g}}{32.00\text{ g/mol}} \approx 0.07281\text{ mol}\ &\text{For part b:}\ &n_{\text{H}_2} = 0.0150\text{ mol}\ &n_{\text{He}} = \frac{4.22 \times 10^{-3}\text{ g}}{4.003\text{ g/mol}} \approx 0.001054\text{ mol}\ &n_{\text{NH}_3} = 0.030\text{ mol} \end{aligned} $$ ## Convert temperature and volume to standard units Using the *Ideal Gas Law Calculations* knowledge point $$ \begin{aligned} &\text{For part a:}\ &T = 25^\circ\text{C} + 273.15 = 298.15\text{ K}\ &V = 500.0\text{ mL} = 0.5000\text{ L}\ &\text{For part b:}\ &T = 50^\circ\text{C} + 273.15 = 323.15\text{ K}\ &V = 1.00\text{ L} \end{aligned} $$ ## Calculate partial and total pressures for part a Using the *Ideal Gas Law Calculations* and *Significant Figures* knowledge points $$ \begin{aligned} &P_{\text{N}_2} = \frac{n_{\text{N}_2}RT}{V} = \frac{(0.200\text{ mol})(0.08206\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}))(298.15\text{ K})}{0.5000\text{ L}} \approx 9.79\text{ atm}\ &P_{\text{O}_2} = \frac{n_{\text{O}_2}RT}{V} = \frac{(0.07281\text{ mol})(0.08206\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}))(298.15\text{ K})}{0.5000\text{ L}} \approx 3.56\text{ atm}\ &P_{\text{total}} = P_{\text{N}_2} + P_{\text{O}_2} = 9.79\text{ atm} + 3.56\text{ atm} = 13.35\text{ atm} \end{aligned} $$ ## Calculate partial and total pressures for part b Using the *Ideal Gas Law Calculations* and *Significant Figures* knowledge points $$ \begin{aligned} &P_{\text{H}_2} = \frac{n_{\text{H}_2}RT}{V} = \frac{(0.0150\text{ mol})(0.08206\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}))(323.15\text{ K})}{1.00\text{ L}} \approx 0.398\text{ atm}\ &P_{\text{He}} = \frac{n_{\text{He}}RT}{V} = \frac{(0.001054\text{ mol})(0.08206\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}))(323.15\text{ K})}{1.00\text{ L}} \approx 0.0280\text{ atm}\ &P_{\text{NH}_3} = \frac{n_{\text{NH}_3}RT}{V} = \frac{(0.030\text{ mol})(0.08206\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}))(323.15\text{ K})}{1.00\text{ L}} \approx 0.80\text{ atm}\ &P_{\text{total}} = P_{\text{H}_2} + P_{\text{He}} + P_{\text{NH}_3} = 0.398\text{ atm} + 0.0280\text{ atm} + 0.80\text{ atm} \approx 1.23\text{ atm} \end{aligned} $$ ## Question a * $P_{\text{N}_2} = 9.79\text{ atm}$ * $P_{\text{O}_2} = 3.56\text{ atm}$ * $P_{\text{total}} = 13.35\text{ atm}$ ## Question b * $P_{\text{H}_2} = 0.398\text{ atm}$ * $P_{\text{He}} = 0.0280\text{ atm}$ * $P_{\text{NH}_3} = 0.80\text{ atm}$ * $P_{\text{total}} = 1.23\text{ atm}$ { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Chemistry", "Daltons Law of Partial Pressures" ] }

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Explanation:

Convert given quantities to moles

Convert temperature and volume to standard units

Calculate partial and total pressures for part a

Calculate partial and total pressures for part b

Answer:

Question a

Question b