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.