Which of the following will react at the highest rate ?

Options

A. `1 mol` of `A` and `1 mol B` in a `1-L` vessel
B. `2 mol` of `A` and `2 mol B` in a `2-L` vessel
C. `3 mol` of `A` and `3 mol B` in a `3-L` vessel
D. All would react at the same rate

Explanation

To determine which of the given cases will react at the highest rate, we need to analyze the concentration of the reactants in each case. The rate of a reaction is often directly proportional to the concentration of the reactants. Concentration can be calculated using the formula:

\[ \text{Concentration (Molarity)} = \frac{\text{Number of moles}}{\text{Volume (in liters)}} \]

Let's break down the cases provided:

### Step 1: Calculate the concentration for each case

1. **Case 1**:
- Moles of A = 1 mole
- Moles of B = 1 mole
- Volume = 1 liter
- Concentration of A = \( \frac{1 \text{ mole}}{1 \text{ L}} = 1 \text{ M} \)
- Concentration of B = \( \frac{1 \text{ mole}}{1 \text{ L}} = 1 \text{ M} \)

2. **Case 2**:
- Moles of A = 2 moles
- Moles of B = 2 moles
- Volume = 2 liters
- Concentration of A = \( \frac{2 \text{ moles}}{2 \text{ L}} = 1 \text{ M} \)
- Concentration of B = \( \frac{2 \text{ moles}}{2 \text{ L}} = 1 \text{ M} \)

3. **Case 3**:
- Moles of A = 3 moles
- Moles of B = 3 moles
- Volume = 3 liters
- Concentration of A = \( \frac{3 \text{ moles}}{3 \text{ L}} = 1 \text{ M} \)
- Concentration of B = \( \frac{3 \text{ moles}}{3 \text{ L}} = 1 \text{ M} \)

### Step 2: Compare the concentrations

From the calculations above, we can see that:

- In **Case 1**, the concentration of A and B is 1 M.
- In **Case 2**, the concentration of A and B is also 1 M.
- In **Case 3**, the concentration of A and B remains 1 M.

### Step 3: Conclusion

Since the concentration of the reactants is the same in all three cases (1 M), the rate of reaction will also be the same. Therefore, all cases will react at the same rate.

### Final Answer

All cases will react at the same rate.

---