The term `-dx//dt` in the rate expresison refers to the

Options

A. The concentration of the reactants
B. Increase in the concentration of the reactants
C. The instantaneous rate of the reaction
D. The average rate of the reaction

Answer

To solve the question regarding the term \(-\frac{dx}{dt}\) in the rate expression, we can break it down step by step:

### Step-by-Step Solution:

1. **Understanding the Variables**:
- In the expression \(-\frac{dx}{dt}\), \(x\) typically represents the concentration of a reactant in a chemical reaction.
- The term \(dx\) signifies a change in concentration, while \(dt\) signifies a change in time.

2. **Interpreting the Derivative**:
- The expression \(-\frac{dx}{dt}\) indicates the rate of change of concentration with respect to time.
- The negative sign indicates that as the reaction proceeds, the concentration of the reactant decreases.

3. **Defining Rate of Reaction**:
- The rate of a reaction is defined as the change in concentration of a reactant or product per unit time.
- Therefore, \(-\frac{dx}{dt}\) represents the rate at which the concentration of the reactant is decreasing over an infinitesimally small interval of time.

4. **Instantaneous Rate vs. Average Rate**:
- The term \(-\frac{dx}{dt}\) specifically refers to the instantaneous rate of reaction, which is the rate at a specific moment in time.
- In contrast, the average rate of reaction is calculated over a finite time interval and is represented as \(-\frac{\Delta x}{\Delta t}\), where \(\Delta\) denotes a finite change.

5. **Conclusion**:
- Thus, the term \(-\frac{dx}{dt}\) in the rate expression refers to the instantaneous rate of the reaction.

### Final Answer:
The term \(-\frac{dx}{dt}\) in the rate expression refers to the **instantaneous rate of the reaction**.

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