Free energy change is related to enthalpy and entropy changes as:

Options

A. `DeltaG = DeltaH - T DeltaS`
B. `DeltaG = T DeltaS - DeltaH`
C. `DeltaG^(@) = (DeltaH - DeltaS)/(T)`
D. `DeltaG = DeltaH + T DeltaS`

Answer

To relate free energy change (ΔG) to enthalpy (ΔH) and entropy (ΔS), we can use the Gibbs-Helmholtz equation. Here’s a step-by-step breakdown of how this relationship is derived:

### Step 1: Understand the Definitions
- **Enthalpy (ΔH)**: It is a measure of the total heat content of a system.
- **Entropy (ΔS)**: It is a measure of the disorder or randomness in a system.
- **Free Energy (ΔG)**: It is the energy available to do work in a thermodynamic process.

### Step 2: Start with the First Law of Thermodynamics
The first law of thermodynamics states that:
\[ q = \Delta U + W \]
where \( q \) is the heat added to the system, \( \Delta U \) is the change in internal energy, and \( W \) is the work done by the system.

### Step 3: Relate Enthalpy to Internal Energy
Enthalpy is defined as:
\[ H = U + PV \]
Thus, the change in enthalpy can be expressed as:
\[ \Delta H = \Delta U + P \Delta V \]

### Step 4: Substitute into the First Law
From the first law, we can express heat transfer as:
\[ q = \Delta U + P \Delta V + W_{non-expansion} \]
This means:
\[ q = \Delta H + W_{non-expansion} \]

### Step 5: Define Entropy Change
The change in entropy (ΔS) can be expressed as:
\[ \Delta S = \frac{q_{rev}}{T} \]
where \( q_{rev} \) is the reversible heat exchange and \( T \) is the absolute temperature.

### Step 6: Relate Heat Transfer to Entropy
For reversible processes, we can write:
\[ q = T \Delta S \]
Thus, substituting this into our previous equation gives:
\[ T \Delta S = \Delta H + W_{non-expansion} \]

### Step 7: Define Free Energy Change
The free energy change (ΔG) is defined as:
\[ \Delta G = \Delta H - T \Delta S \]
This equation shows how free energy change is related to enthalpy and entropy changes.

### Final Equation
Thus, the relationship between free energy change, enthalpy change, and entropy change is given by:
\[ \Delta G = \Delta H - T \Delta S \]

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