Always include the ∆ngRT correction term in bomb calorimetry problems when calcu lating thermodynamic equilibrium parameters
The thermodynamic relationship is given by:
\( \Delta G = \Delta H - T\Delta S \)
At equilibrium, \( \Delta G = 0 \), so:
\( T\Delta S = \Delta H - \Delta n_gRT \)
The reaction gives:
\( \Delta n_g = \text{moles of gaseous products} - \text{moles of gaseous reactants} \)
From the reaction:
\( \Delta n_g = 2 - \frac{7}{2} = -\frac{3}{2} \)
\( T\Delta S = -1406 + \left(-\frac{3}{2} \cdot 0.0083 \cdot 300 \right) \)
\( T\Delta S = -1406 + (-3.735) \)
\( T\Delta S \approx -1409.735 \, \text{kJ} \)
\( T\Delta S \approx -1411 \, \text{kJ} \)
The minimum value of \( T\Delta S \) needed to reach equilibrium is: \( 1411 \, \text{kJ}. \)