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 options will react at the highest rate, we need to analyze the concentration of each reactant in the options provided. The rate of a reaction is generally proportional to the concentration of the reactants.

### Step-by-Step Solution:

1. **Understand the Rate of Reaction**:
The rate of a reaction is defined as the change in concentration of reactants or products over time. Mathematically, it can be expressed as:
\[ \text{Rate} = \frac{d[\text{Reactant}]}{dt} \]

2. **Identify Concentration**:
Concentration is defined as the number of moles of a substance divided by the volume it occupies:
\[ \text{Concentration} = \frac{\text{moles}}{\text{volume}} \]

3. **Calculate Concentration for Each Option**:
- **Option A**: If there is 1 mole in 1 L, then:
\[ \text{Concentration of A} = \frac{1 \text{ mole}}{1 \text{ L}} = 1 \text{ M} \]
- **Option B**: If there are 2 moles in 2 L, then:
\[ \text{Concentration of B} = \frac{2 \text{ moles}}{2 \text{ L}} = 1 \text{ M} \]
- **Option C**: If there are 3 moles in 3 L, then:
\[ \text{Concentration of C} = \frac{3 \text{ moles}}{3 \text{ L}} = 1 \text{ M} \]

4. **Compare Concentrations**:
From the calculations, we see that:
- Concentration of A = 1 M
- Concentration of B = 1 M
- Concentration of C = 1 M

5. **Conclusion**:
Since all options have the same concentration of 1 M, they will all react at the same rate. Therefore, the correct answer is that all options will react at the same rate.

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

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