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To calculate the standard Gibbs free energy change (\( \Delta G^\circ \)) for the given reaction at equilibrium, we can use the following formula derived from thermodynamics:

\[
\Delta G^\circ = -RT \ln K_{\text{eq}}
\]

Where:
- \( R \) is the universal gas constant (\( 8.314 \, \text{J/mol·K} \))
- \( T \) is the temperature in Kelvin. At 25°C, this is \( 298.15 \, \text{K} \).
- \( K_{\text{eq}} \) is the equilibrium constant for the reaction, which can be calculated using the equilibrium concentrations of the reactants and products.

For the reaction \( A + B \rightleftharpoons C + D \), the equilibrium constant \( K_{\text{eq}} \) is expressed as:

\[
K_{\text{eq}} = \frac{[C][D]}{[A][B]}
\]

From the dataTo calculate the standard Gibbs free energy change (\( \Delta G^\circ \)) for the given reaction at equilibrium, we can use the following formula derived from thermodynamics:

\[
\Delta G^\circ = -RT \ln K_{\text{eq}}
\]

Where:
- \( R \) is the universal gas constant (\( 8.314 \, \text{J/mol·K} \))
- \( T \) is the temperature in Kelvin. At 25°C, this is \( 298.15 \, \text{K} \).
- \( K_{\text{eq}} \) is the equilibrium constant for the reaction, which can be calculated using the equilibrium concentrations of the reactants and products.

For the reaction \( A + B \rightleftharpoons C + D \), the equilibrium constant \( K_{\text{eq}} \) is expressed as:

\[
K_{\text{eq}} = \frac{[C][D]}{[A][B]}
\]

From the 
- \( [A] = 10 \, \mu M = 10 \times 10^{-6} \, M \)
- \( [B] = 15 \, \mu M = 15 \times 10^{-6} \, M \)
- \( [C] = 10 \, \mu M = 10 \times 10^{-6} \, M \)
- \( [D] = 10 \, \mu M = 10 \times 10^{-6} \, M \)

Let's first calculate \( K_{\text{eq}} \) and then find \( \Delta G^\circ \). I will now compute the results.The standard Gibbs free energy change (\( \Delta G^\circ \)) for the reaction is approximately \( 1005 \, \text{J/mol} \), which matches the closest answer of **1000 J/mol**.

Would you like further details or have any questions? Here are five related questions to expand on this topic:

1. How does the equilibrium constant (\( K_{\text{eq}} \)) influence the Gibbs free energy?
2. What is the significance of a positive or negative \( \Delta G^\circ \)?
3. How would a temperature change affect \( \Delta G^\circ \) for this reaction?
4. Why is the Gibbs free energy important in determining the spontaneity of a reaction?
5. How can you experimentally determine the equilibrium constant for a reaction?

**Tip**: Always remember to check if the reaction is at equilibrium before applying the formula for \( \Delta G^\circ \), as it assumes equilibrium conditions.

Consider the reaction A + B ↔ C + D. After reaching equilibrium at 25°C, the following concentrations of reactants and products were measured: [A] = 10 µM, [B] = 15 µM, [C] = 10 µM, [D] = 10 µM. Calculate ΔG° for this reaction.

Learn how to calculate the Gibbs free energy (ΔG°) for a reaction at equilibrium. The problem involves equilibrium concentrations of reactants and products, applying the thermodynamic formula ΔG° = -RT ln(K_eq). Suitable for Grades 10-12 chemistry students.

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