$\Delta G ext{ for a spontaneous process at constant pressure and temperature is :}$

Q: $\Delta G \text{ for a spontaneous process at constant pressure and temperature is :}$

$\Delta G \text{ for a spontaneous process at constant pressure and temperature is :}$

Question

$\Delta G 	ext{ for a spontaneous process at constant pressure and temperature is :}$

Accepted Answer

For a spontaneous process at constant pressure and temperature, the change in Gibbs free energy, denoted as $\Delta G$, is a crucial factor in determining the spontaneity of the process. Let's explore why Option 2, $\Delta G < 0$, is the correct answer and why the other options are incorrect.

### Explanation for Option 2: $\Delta G < 0$

1. **Definition of Spontaneity**: A process is considered spontaneous if it can occur without any external intervention. In thermodynamics, the spontaneity of a process at constant pressure and temperature is determined by the Gibbs free energy change, $\Delta G$.

2. **Gibbs Free Energy**: The Gibbs free energy is a thermodynamic potential that measures the maximum reversible work that may be performed by a thermodynamic system at constant temperature and pressure. The formula for Gibbs free energy change is:
   $$
   \Delta G = \Delta H - T\Delta S
   $$
   where $\Delta H$ is the change in enthalpy, $T$ is the temperature, and $\Delta S$ is the change in entropy.

3. **Condition for Spontaneity**: For a process to be spontaneous, the Gibbs free energy change must be negative ($\Delta G < 0$). This indicates that the process can proceed without external energy input, releasing free energy that can be harnessed to do work.

### Explanation for Why Other Options are Incorrect

1. **Option 1: $\Delta G = 0$**
   - A $\Delta G$ of zero indicates a system in equilibrium, not a spontaneous process. At equilibrium, there is no net change occurring in the system, and the process is neither spontaneous nor non-spontaneous.

2. **Option 3: $\Delta G > 0$**
   - A positive $\Delta G$ signifies a non-spontaneous process. This means that the process requires an input of energy to proceed, which is contrary to the definition of spontaneity.

3. **Option 4: $\Delta G = 1$**
   - This option is incorrect because it implies a specific numerical value for $\Delta G$ without context. The spontaneity of a process is not determined by a specific value like 1 but rather by the sign of $\Delta G$. A positive value, such as 1, would indicate a non-spontaneous process.

In conclusion, for a process to be spontaneous at constant pressure and temperature, the Gibbs free energy change must be negative ($\Delta G < 0$), which is why Option 2 is the correct answer.