con una temperatura $20^\circ\text{c} \
ightarrow {}^\circ\text{k}$

1.- calcular la masa del oxigeno tiene una velocidad $310\text{ m/s}$ y una $t^\circ\text{c}$ $12^\circ\text{c}$

2.- obtener la masa del nitrogeno si tiene una $t^\circ\text{c}$ de $13^\circ\text{c}$ y una velocidad de $145\text{ m/s}$

Question

con una temperatura $20^\circ\text{c} \
ightarrow {}^\circ\text{k}$

1.- calcular la masa del oxigeno tiene una velocidad $310\text{ m/s}$ y una $t^\circ\text{c}$ $12^\circ\text{c}$

2.- obtener la masa del nitrogeno si tiene una $t^\circ\text{c}$ de $13^\circ\text{c}$ y una velocidad de $145\text{ m/s}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Ideal Gas Law", "Root Mean Square Speed", "Gas Temperature Conversion" ], "current_concepts": [ "Ideal Gas Law", "Root Mean Square Speed", "Gas Temperature Conversion" ] } ## Convert temperatures to Kelvin $$ \begin{aligned} T_1 &= 12^\circ\text{C} + 273.15 = 285.15\text{ K} \ T_2 &= 13^\circ\text{C} + 273.15 = 286.15\text{ K} \end{aligned} $$ ## Calculate the mass of an Oxygen molecule $$ \begin{aligned} v_{\text{rms}} &= \sqrt{\frac{3 k_B T}{m}} \implies m = \frac{3 k_B T}{v^2} \ k_B &= 1.3806 \times 10^{-23}\text{ J/K} \ m_{\text{O}_2} &= \frac{3 \times (1.3806 \times 10^{-23}\text{ J/K}) \times 285.15\text{ K}}{(310\text{ m/s})^2} \ m_{\text{O}_2} &\approx 1.228 \times 10^{-25}\text{ kg} \end{aligned} $$ ## Calculate the mass of a Nitrogen molecule $$ \begin{aligned} m_{\text{N}_2} &= \frac{3 \times (1.3806 \times 10^{-23}\text{ J/K}) \times 286.15\text{ K}}{(145\text{ m/s})^2} \ m_{\text{N}_2} &\approx 5.634 \times 10^{-25}\text{ kg} \end{aligned} $$ ## Question 1 $m_{\text{O}_2} \approx 1.23 \times 10^{-25}\text{ kg}$ ## Question 2 $m_{\text{N}_2} \approx 5.63 \times 10^{-25}\text{ kg}$ { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Kinetic Theory of Gases" ] }

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Question

Explanation:

Convert temperatures to Kelvin

Calculate the mass of an Oxygen molecule

Calculate the mass of a Nitrogen molecule

Answer:

Question 1

Question 2