Consider the reaction of both reactants the rate of the reaction increases by a factor of 8. However, if only the concentration of `"CI"_2` is doubled, the rate is increased by a factor of 2. The order of this reaction with respect to NO is:

Options

A. 3
B. 0
C. 1
D. 2

Explanation

To determine the order of the reaction with respect to NO, we can analyze the information provided in the question step by step.

### Step 1: Understand the Rate Law
The rate of a reaction can be expressed by the rate law:
\[ \text{Rate} = k[\text{Cl}_2]^x[\text{NO}]^y \]
where \( k \) is the rate constant, \( x \) is the order of the reaction with respect to Cl2, and \( y \) is the order of the reaction with respect to NO.

### Step 2: Analyze the Given Information
1. When both reactants are present, the rate increases by a factor of 8.
2. When the concentration of Cl2 is doubled, the rate increases by a factor of 2.

### Step 3: Set Up the Equations
From the second piece of information (doubling Cl2):
- If we double the concentration of Cl2, the new rate becomes:
\[ \text{Rate}_{\text{new}} = k[2\text{Cl}_2]^x[\text{NO}]^y \]
This can be simplified to:
\[ \text{Rate}_{\text{new}} = k(2^x[\text{Cl}_2]^x)[\text{NO}]^y = 2^x \cdot \text{Rate}_{\text{original}} \]
Given that this increases the rate by a factor of 2:
\[ 2^x = 2 \]
This implies:
\[ x = 1 \]

### Step 4: Use the First Condition
Now, using the first condition (both reactants increasing the rate by a factor of 8):
- The new rate when both reactants are considered is:
\[ \text{Rate}_{\text{new}} = k[\text{Cl}_2]^x[\text{NO}]^y \]
This can be expressed as:
\[ \text{Rate}_{\text{new}} = k[\text{Cl}_2]^1[\text{NO}]^y = 8 \cdot \text{Rate}_{\text{original}} \]
Substituting \( x = 1 \):
\[ k[\text{Cl}_2]^1[\text{NO}]^y = 8 \cdot k[\text{Cl}_2]^1[\text{NO}]^y \]
This simplifies to:
\[ [\text{NO}]^y = 8 \]
This implies:
\[ y = 3 \] (since \( 2^3 = 8 \))

### Step 5: Conclusion
Thus, the order of the reaction with respect to NO is:
\[ \text{Order with respect to NO} = y = 3 \]

### Final Answer
The order of the reaction with respect to NO is **3**.

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