the reaction below is at 323 k.
$\text{n}_2(\text{g}) + 3\text{h}_2(\text{g}) \
ightleftharpoons 2\text{nh}_3(\text{g})$
concentration: 0.0409 m, 0.0409 m, 0.0409 m
$\delta g^\circ = -33.0\text{ kj}$
calculate $\delta g$ at the current conditions.
$\delta g = \delta g^\circ + rt \ln q$
$\delta g = ?\text{ kj}$
include either a + or - sign and the magnitude in your answer.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Reaction Quotient", "Standard Gibbs Free Energy Change" ], "new_concepts": [ "Gibbs Free Energy under Non-Standard Conditions" ], "current_concepts": [ "Reaction Quotient", "Standard Gibbs Free Energy Change", "Gibbs Free Energy under Non-Standard Conditions" ] } ## Calculate the reaction quotient Using the *Reaction Quotient* knowledge point $$ \begin{aligned} Q &= \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} \ Q &= \frac{(0.0409)^2}{(0.0409)(0.0409)^3} \ Q &= \frac{1}{(0.0409)^2} \ Q &\approx 597.77 \end{aligned} $$ ## Calculate the non-standard Gibbs free energy change Using the *Standard Gibbs Free Energy Change* knowledge point $$ \begin{aligned} \Delta G &= \Delta G^\circ + RT \ln Q \ \Delta G^\circ &= -33.0\text{ kJ} = -33000\text{ J} \ R &= 8.314\text{ J}/(\text{mol}\cdot\text{K}) \ T &= 323\text{ K} \ RT \ln Q &= 8.314 \times 323 \times \ln(597.77) \ RT \ln Q &\approx 2685.42 \times 6.3932 \approx 17168.4\text{ J} \approx 17.2\text{ kJ} \ \Delta G &= -33.0\text{ kJ} + 17.2\text{ kJ} = -15.8\text{ kJ} \end{aligned} $$ The reaction below is at 323 K. $$\text{N}_2(\text{g}) + 3\text{H}_2(\text{g}) ightleftharpoons 2\text{NH}_3(\text{g})$$ [Concentration]: $0.0409\text{ M}$ for $\text{N}_2$, $0.0409\text{ M}$ for $\text{H}_2$, and $0.0409\text{ M}$ for $\text{NH}_3$. $$\Delta G^\circ = -33.0\text{ kJ}$$ Calculate $\Delta G$ at the current conditions. $$\Delta G = \Delta G^\circ + RT \ln Q$$ $\Delta G =$ $-15.8$ $\text{kJ}$ Include either a + or - sign AND the magnitude in your answer. { "subject": "Natural Science", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Natural Science", "Chemistry", "Chemical Thermodynamics" ] }

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Calculate the reaction quotient

Calculate the non-standard Gibbs free energy change

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