For the reaction 2NO (g) N O (g), when βS = β176.0 JK and βH = β57.8 kJ mol , the magnitude of βG at β Thermodynamics and Thermochemistry Chemistry Question
Question
For the reaction 2NO (g) N O (g), when βS = β176.0 JK and βH = β57.8 kJ mol , the magnitude of βG at 298 K for the reaction is_____ kJ mol . (Nearest integer) 2 2 4 β1 β1 β1
π‘ Solution & Explanation
**Step 1: Identify the given values** - ΞH = β57.8 kJ/mol = β57,800 J/mol - ΞS = β176.0 J/(KΒ·mol) - T = 298 K **Step 2: Apply the Gibbs free energy equation** $$\Delta G = \Delta H - T\Delta S$$ **Step 3: Substitute the values** $$\Delta G = (β57,800) β (298)(β176.0)$$ **Step 4: Calculate the TΒ·ΞS term** $$T\Delta S = 298 Γ (β176.0) = β52,448 \text{ J/mol}$$ **Step 5: Complete the calculation** $$\Delta G = β57,800 β (β52,448)$$ $$\Delta G = β57,800 + 52,448$$ $$\Delta G = β5,352 \text{ J/mol}$$ **Step 6: Convert to kJ/mol and find magnitude** $$\Delta G = β5.352 \text{ kJ/mol}$$ $$|\Delta G| = 5.35 \text{ kJ/mol} β 5.00 \text{ kJ/mol}$$ Therefore, the answer is 5.00.