Among the following for spontaneity of chemical reaction there should be

Options

A. Decrease in entropy and increase in free energy
B. Decrease in entropy and free energy both
C. Increase in entropy and decrease in free energy
D. Increase in entropy and free energy both

Answer

To determine the spontaneity of a chemical reaction, we can use the Gibbs free energy equation:

\[ \Delta G = \Delta H - T \Delta S \]

Where:
- \(\Delta G\) = change in Gibbs free energy
- \(\Delta H\) = change in enthalpy
- \(T\) = temperature in Kelvin
- \(\Delta S\) = change in entropy

For a reaction to be spontaneous, the condition that must be satisfied is:

\[ \Delta G < 0 \]

Now, let’s analyze the options given in the question:

1. **Decrease in entropy**: If entropy decreases, \(\Delta S\) is negative. This means that the term \(T \Delta S\) will also be negative (since T is always positive). Therefore, \(\Delta G\) could potentially be positive or negative depending on the value of \(\Delta H\). This option does not guarantee spontaneity.

2. **Decrease in entropy and free energy both**: If both entropy and free energy decrease, it means that \(\Delta S\) is negative and \(\Delta G\) is also increasing (becoming less negative or more positive). This will not lead to spontaneity, as \(\Delta G\) will not be less than zero. This option is incorrect.

3. **Increase in entropy**: If entropy increases, \(\Delta S\) is positive. This means that \(T \Delta S\) will be positive. If \(\Delta H\) is also negative (exothermic reaction), then \(\Delta G\) will be negative, leading to spontaneity. Thus, this option supports spontaneity.

4. **Increase in free energy**: If free energy increases, \(\Delta G\) becomes more positive, which means it is non-spontaneous. This option is incorrect.

Based on the analysis, the correct condition for spontaneity is:

**Increase in entropy and decrease in free energy.**

### Summary of Steps:
1. Write down the Gibbs free energy equation.
2. Identify the condition for spontaneity (\(\Delta G < 0\)).
3. Analyze each option based on the effects of \(\Delta H\) and \(\Delta S\) on \(\Delta G\).
4. Conclude that the correct option is the one that leads to an increase in entropy.