Which of the following will react at the highest rate ?

Options

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

Explanation

To determine which of the given options will react at the highest rate, we need to analyze the concentrations of the reactants in each case. The rate of a reaction is directly related to the concentration of the reactants, as described by the rate law, which states that the rate is proportional to the concentration of the reactants raised to the power of their respective coefficients in the balanced equation (the order of the reaction).

### Step-by-Step Solution:

1. **Identify the Concentration of Reactants:**
- For each option, calculate the concentration of the reactants A and B using the formula:
\[ \text{Concentration} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]

2. **Calculate Concentration for Each Option:**
- **Option 1:**
- Moles of A = 1, Volume = 1 L
- Concentration of A = \( \frac{1 \text{ mol}}{1 \text{ L}} = 1 \text{ M} \)
- Moles of B = 1, Volume = 1 L
- Concentration of B = \( \frac{1 \text{ mol}}{1 \text{ L}} = 1 \text{ M} \)

- **Option 2:**
- Moles of A = 2, Volume = 2 L
- Concentration of A = \( \frac{2 \text{ mol}}{2 \text{ L}} = 1 \text{ M} \)
- Moles of B = 2, Volume = 2 L
- Concentration of B = \( \frac{2 \text{ mol}}{2 \text{ L}} = 1 \text{ M} \)

- **Option 3:**
- Moles of A = 3, Volume = 3 L
- Concentration of A = \( \frac{3 \text{ mol}}{3 \text{ L}} = 1 \text{ M} \)
- Moles of B = 3, Volume = 3 L
- Concentration of B = \( \frac{3 \text{ mol}}{3 \text{ L}} = 1 \text{ M} \)

3. **Compare Concentrations:**
- From the calculations, we see that in all three options, the concentrations of both A and B are 1 M.

4. **Determine the Rate of Reaction:**
- Since the concentrations of the reactants are the same in all options, the rate of reaction will also be the same for all three options.

5. **Conclusion:**
- Therefore, all options will react at the same rate, and the correct answer is that they all react at the same rate.

### Final Answer:
All options will react at the same rate.