Calculate ΔG° (in kJ/mol) for each of the following reactions from the equilibrium constant at the temperature given.
(a)
N2(g) + 2 O2(g) equilibrium reaction arrow 2 NO2(g) T = 840.°C K = 3.3 ✕ 10−10
ΔG°	=

The standard Gibbs free energy change (\(\Delta G^\circ\)) for a reaction can be calculated using the following formula:

\[
\Delta G^\circ = -RT \ln K
\]

where:
- \( R \) is the gas constant, which is \( 8.314 \, \text{J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} \),
- \( T \) is the temperature in Kelvin (\( K \)),
- \( K \) is the equilibrium constant.

### Step 1: Convert Temperature to Kelvin
Given \( T = 840^\circ C \):
\[
T = 840 + 273.15 = 1113.15 \, K
\]

### Step 2: Substitute the Values
- \( R = 8.314 \, \text{J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} \),
- \( T = 1113.15 \, K \),
- \( K = 3.3 \times 10^{-10} \).

### Step 3: Calculate \(\Delta G^\circ\)
\[
\Delta G^\circ = - (8.314) (1113.15) \ln (3.3 \times 10^{-10})
\]

Now let's compute this numerically:

\[
\ln (3.3 \times 10^{-10}) \approx -21.83
\]

\[
\Delta G^\circ \approx - (8.314) (1113.15) (-21.83) \approx 202277.4 \, \text{J/mol} = 202.3 \, \text{kJ/mol}
\]

### Final Answer:
\[
\Delta G^\circ \approx 202.3 \, \text{kJ/mol}
\]

Would you like further details or have any questions? Here are some related questions to explore:

1. How does a change in temperature affect the value of \( \Delta G^\circ \)?
2. What happens to \( \Delta G^\circ \) if \( K \) is increased?
3. What is the physical significance of a positive or negative \( \Delta G^\circ \)?
4. How does \( \Delta G^\circ \) relate to the spontaneity of a reaction?
5. What other thermodynamic parameters can be used to describe chemical reactions?

**Tip:** Always ensure the temperature is in Kelvin when using thermodynamic equations like \(\Delta G^\circ = -RT \ln K\).

Calculate ΔG° (in kJ/mol) for each of the following reactions from the equilibrium constant at the temperature given. (a) N2(g) + 2 O2(g) equilibrium reaction arrow 2 NO2(g) T = 840°C, K = 3.3 × 10^−10

Learn to calculate the standard Gibbs free energy change (ΔG°) for a reaction using the equilibrium constant and temperature. This example uses the reaction N2(g) + 2 O2(g) → 2 NO2(g) at T = 840°C and K = 3.3 × 10^−10. Explore key thermodynamic concepts such as Gibbs free energy, logarithmic functions, and their impact on reaction spontaneity.

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