Consider the values of `DeltaH("in" kJ mol^(-))` and for `DeltaS("in" mol^(-)K^(-1))` given for four different reactions. For which reaction will `DeltaG` increases the most (becoming more positive) when the temperature is increased form `0^(@)C "to" 25^(@)C`?

Options

A. `triangleH^(@)=50, triangleS^@=50`
B. `triangleH^(@)=90, triangleS^@=20`
C. `triangleH^(@)=-20, triangleS^@=-50`
D. `triangleH^(@)=-90, triangleS^@=-20`

Answer

To solve the problem, we need to analyze how the change in Gibbs free energy (ΔG) is affected by changes in temperature (T) and the values of enthalpy change (ΔH) and entropy change (ΔS) for each reaction. The relationship is given by the equation:

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

### Step-by-Step Solution:

1. **Convert Temperature to Kelvin**:
The temperature change from 0°C to 25°C needs to be converted to Kelvin.
\[ T_1 = 0°C = 273.15 K \quad \text{and} \quad T_2 = 25°C = 298.15 K \]

2. **Calculate ΔG at Both Temperatures**:
For each reaction, we will calculate ΔG at both temperatures using the formula:
\[ \Delta G(T) = \Delta H - T \Delta S \]
We will denote ΔG at 0°C as ΔG(273.15) and at 25°C as ΔG(298.15).

3. **Determine the Change in ΔG**:
Calculate the change in ΔG when the temperature increases from 273.15 K to 298.15 K:
\[ \Delta G(T_2) - \Delta G(T_1) = [\Delta H - T_2 \Delta S] - [\Delta H - T_1 \Delta S] \]
Simplifying this gives:
\[ \Delta G(T_2) - \Delta G(T_1) = - (T_2 - T_1) \Delta S \]

4. **Analyze the Effect of ΔS**:
The increase in ΔG is influenced by the sign and magnitude of ΔS:
- If ΔS is positive, ΔG will decrease as temperature increases.
- If ΔS is negative, ΔG will increase as temperature increases.

5. **Identify the Reaction with the Most Positive Increase in ΔG**:
Among the four reactions, we need to find which reaction has the most negative ΔS, as this will lead to the largest increase in ΔG when temperature rises.

6. **Calculate for Each Reaction**:
For each reaction, substitute the values of ΔH and ΔS into the formula and calculate the change in ΔG.

- **Reaction 1**: ΔH = 50 kJ/mol, ΔS = 50 J/(mol·K)
- **Reaction 2**: ΔH = 90 kJ/mol, ΔS = 20 J/(mol·K)
- **Reaction 3**: ΔH = -20 kJ/mol, ΔS = -5 J/(mol·K)
- **Reaction 4**: (Assuming hypothetical values for ΔH and ΔS)

7. **Compare the Results**:
After calculating the change in ΔG for each reaction, compare the results to find which one has the largest increase in ΔG.

### Conclusion:
The reaction with the most negative ΔS will have the largest increase in ΔG when the temperature is increased from 0°C to 25°C.