Following are the values of `E_(a) and Delta H` for three reactions carried out at the same temperature :
`I: E_(a) =20 kJ mol^(-1), Delta H =-60 kJ mol^(-1)`
`II: E_(a) =10 kJ mol^(-1), Delta H =-20 kJ mol^(-1)`
`III: E_(a) =40 kJ mol^(-1), Delta H=+15 kJ mol^(-1)`
If all the three reaction have same frequency factor then fastest and slowest reactions are :

Options

A. `{:("Fastest","Slowest"),("I","II"):}`
B. `{:("Fastest","Slowest"),("II","III"):}`
C. `{:("Fastest","Slowest"),("I","III"):}`
D. can't be predicted.

Answer

To determine the fastest and slowest reactions among the three given reactions based on their activation energies (E_a), we can follow these steps:

### Step 1: Understand the relationship between activation energy and reaction rate
The rate of a chemical reaction is influenced by its activation energy. According to the Arrhenius equation, a lower activation energy leads to a higher rate constant (k) and thus a faster reaction. Conversely, a higher activation energy results in a lower rate constant and a slower reaction.

### Step 2: List the activation energies for each reaction
We have the following activation energies for the three reactions:
- Reaction I: E_a = 20 kJ/mol
- Reaction II: E_a = 10 kJ/mol
- Reaction III: E_a = 40 kJ/mol

### Step 3: Compare the activation energies
Now, we compare the activation energies to determine which reaction is the fastest and which is the slowest:
- Reaction I: 20 kJ/mol
- Reaction II: 10 kJ/mol (lowest activation energy)
- Reaction III: 40 kJ/mol (highest activation energy)

### Step 4: Identify the fastest and slowest reactions
From the comparison:
- The fastest reaction is Reaction II (E_a = 10 kJ/mol) because it has the lowest activation energy.
- The slowest reaction is Reaction III (E_a = 40 kJ/mol) because it has the highest activation energy.

### Conclusion
Thus, the fastest reaction is Reaction II and the slowest reaction is Reaction III.

### Summary
- Fastest reaction: Reaction II (E_a = 10 kJ/mol)
- Slowest reaction: Reaction III (E_a = 40 kJ/mol)

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