Determine the standard free energy change for the reaction below.

\[ 2 \text{CO(g)} + 2 \text{NO(g)} \rightarrow \text{N}_2\text{(g)} + 2 \text{CO}_2\text{(g)} \]

Given:

$\Delta G^\circ_f (\text{CO(g)}) = -137.2 \, \text{kJ/mol} $

$\Delta G^\circ_f (\text{CO}_2\text{(g)}) = -394.4 \, \text{kJ/mol} $

$\Delta G^\circ_f (\text{NO(g)}) = 97.6 \, \text{kJ/mol} $

The standard free energy change (ΔG°) for the given reaction is -319.2 kJ/mol. To determine the standard free energy change (ΔG°) for the reaction:

2 CO(g) + 2 NO(g) → N₂(g) + 2 CO₂(g)

we can use the standard free energy of formation (ΔG°f) values for the given compounds. The standard free energy change (ΔG°) can be calculated using the equation:

ΔG° = ΣΔG°f(products) - ΣΔG°f(reactants)

Given ΔG°f values:

ΔG°f(CO(g)) = -137.2 kJ/mol

ΔG°f(CO2(g)) = -394.4 kJ/mol

ΔG°f(NO(g)) = 97.6 kJ/mol

Using these values, we can calculate ΔG° for the reaction:

ΔG° = (2 * ΔG°f(CO2(g)) + ΔG°f(N2(g))) - (2 * ΔG°f(CO(g)) + 2 * ΔG°f(NO(g)))

ΔG° = (2 * (-394.4 kJ/mol) + 0 kJ/mol) - (2 * (-137.2 kJ/mol) + 2 * 97.6 kJ/mol)

ΔG° = (-788.8 kJ/mol) - (-274.4 kJ/mol + 195.2 kJ/mol)

ΔG° = -788.8 kJ/mol + 469.6 kJ/mol

ΔG° = -319.2 kJ/mol

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