For the reaction, `2NOrarrN_(2)+O_(2)`, the expression `-(1)/(2)(d[NO])/(dt)` represents:

Options

A. the rat of formation of NO
B. the average rate of the reaction
C. the instantaneous rate of the reaction
D. all of the above

Answer

To solve the question regarding the expression `-(1)/(2)(d[NO])/(dt)` for the reaction `2NO ⇌ N2 + O2`, we can follow these steps:

### Step 1: Understand the Reaction
The reaction involves the decomposition of nitrogen monoxide (NO) into nitrogen (N2) and oxygen (O2). The stoichiometry of the reaction indicates that 2 moles of NO produce 1 mole of N2 and 1 mole of O2.

### Step 2: Define the Rate of Reaction
In chemical kinetics, the rate of a reaction can be expressed in terms of the change in concentration of reactants and products over time. For a general reaction:

\[ aA + bB \rightarrow cC + dD \]

The rate of reaction can be expressed as:

\[ \text{Rate} = -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = \frac{1}{c} \frac{d[C]}{dt} = \frac{1}{d} \frac{d[D]}{dt} \]

### Step 3: Apply to the Given Reaction
For the reaction `2NO ⇌ N2 + O2`, we can express the rate of reaction in terms of the concentration of NO:

\[ \text{Rate} = -\frac{1}{2} \frac{d[NO]}{dt} \]

Here, `[NO]` is the concentration of nitrogen monoxide.

### Step 4: Interpretation of the Expression
The expression `-(1)/(2)(d[NO])/(dt)` specifically represents the rate at which NO is being consumed in the reaction. Since NO is a reactant, its concentration decreases as the reaction proceeds. The negative sign indicates that the concentration of NO is decreasing over time.

### Step 5: Conclusion
Thus, the expression `-(1)/(2)(d[NO])/(dt)` represents the instantaneous rate of the reaction, which is the rate at a specific moment in time.

### Final Answer
The expression `-(1)/(2)(d[NO])/(dt)` represents the instantaneous rate of the reaction.

---