What is the AG of an ATP-coupled reaction where the endergonic component's AH=-30 kJ/mol, AS=-0.2 kJ/mol, and the reaction is taking place at 210K? Give your AG for the coupled reaction in kJ/mol. Hint: the AG of ATP hydrolysis is -30.5 kJ/mol. kJ/mol

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### Calculating the ΔG of an ATP-Coupled Reaction

**Question:**
What is the ΔG of an ATP-coupled reaction where the endergonic component's ΔH = -30 kJ/mol, ΔS = -0.2 kJ/mol, and the reaction is taking place at 210K? Give your ΔG for the coupled reaction in kJ/mol. Hint: the ΔG of ATP hydrolysis is -30.5 kJ/mol.

**Calculation Steps:**

1. **Determine ΔG for the endergonic reaction component:**
   Using the Gibbs Free Energy equation:
   \[
   ΔG = ΔH - TΔS
   \]
   Given:
   \[
   ΔH = -30 \text{kJ/mol}
   \]
   \[
   ΔS = -0.2 \text{kJ/mol·K}
   \]
   \[
   T = 210 \text{K}
   \]

   Substitute the values into the equation:
   \[
   ΔG = -30 \text{kJ/mol} - (210 \text{K} \times -0.2 \text{kJ/mol·K})
   \]
   \[
   ΔG = -30 \text{kJ/mol} + 42 \text{kJ/mol}
   \]
   \[
   ΔG = 12 \text{kJ/mol}
   \]

2. **Combine the ΔG values for the coupled reaction:**
   The overall ΔG for the coupled reaction is the sum of the ΔG values of the endergonic reaction and the ATP hydrolysis.

   Given:
   \[
   ΔG_{\text{ATP hydrolysis}} = -30.5 \text{kJ/mol}
   \]
   \[
   ΔG_{\text{coupled reaction}} = 12 \text{kJ/mol} + (-30.5 \text{kJ/mol})
   \]
   \[
   ΔG_{\text{coupled reaction}} = 12 \text{kJ/mol} - 30.5 \text{kJ/mol}
   \]
   \[
   ΔG_{\text{coupled reaction}} = -18.5 \text{kJ/mol}
   \]

**Answer:**
\[
\boxed{-18.5 \text{kJ/mol}}
\]
Transcribed Image Text:### Calculating the ΔG of an ATP-Coupled Reaction **Question:** What is the ΔG of an ATP-coupled reaction where the endergonic component's ΔH = -30 kJ/mol, ΔS = -0.2 kJ/mol, and the reaction is taking place at 210K? Give your ΔG for the coupled reaction in kJ/mol. Hint: the ΔG of ATP hydrolysis is -30.5 kJ/mol. **Calculation Steps:** 1. **Determine ΔG for the endergonic reaction component:** Using the Gibbs Free Energy equation: \[ ΔG = ΔH - TΔS \] Given: \[ ΔH = -30 \text{kJ/mol} \] \[ ΔS = -0.2 \text{kJ/mol·K} \] \[ T = 210 \text{K} \] Substitute the values into the equation: \[ ΔG = -30 \text{kJ/mol} - (210 \text{K} \times -0.2 \text{kJ/mol·K}) \] \[ ΔG = -30 \text{kJ/mol} + 42 \text{kJ/mol} \] \[ ΔG = 12 \text{kJ/mol} \] 2. **Combine the ΔG values for the coupled reaction:** The overall ΔG for the coupled reaction is the sum of the ΔG values of the endergonic reaction and the ATP hydrolysis. Given: \[ ΔG_{\text{ATP hydrolysis}} = -30.5 \text{kJ/mol} \] \[ ΔG_{\text{coupled reaction}} = 12 \text{kJ/mol} + (-30.5 \text{kJ/mol}) \] \[ ΔG_{\text{coupled reaction}} = 12 \text{kJ/mol} - 30.5 \text{kJ/mol} \] \[ ΔG_{\text{coupled reaction}} = -18.5 \text{kJ/mol} \] **Answer:** \[ \boxed{-18.5 \text{kJ/mol}} \]
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