For the reaction `2NO_(2) to 2NO + O_(2)` which of the following is false?

Options

A. The decrease in `[NO_(2)]` and the increase in [NO] proceed at the same rate
B. The rate of formation of NO is twice the rate of formation of `O_(2)`
C. The average rates of increase in the concentration of NO and `O_(2)` are expressed as `(d[NO])/dt "and" (d[O_(2)])/dt`
D. `(d[NO])/dt = (2d[O_(2)])/dt`

Explanation

To determine which statement is false regarding the reaction \(2NO_2 \rightarrow 2NO + O_2\), we will analyze each statement based on the principles of chemical kinetics.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The balanced chemical equation is:
\[ 2NO_2 \rightarrow 2NO + O_2 \]
This indicates that 2 moles of nitrogen dioxide (NO2) decompose to form 2 moles of nitric oxide (NO) and 1 mole of oxygen (O2).

2. **Rate of Reaction**:
The rate of a reaction can be expressed in terms of the change in concentration of reactants and products over time. For the given reaction:
\[ \text{Rate} = -\frac{1}{2} \frac{d[NO_2]}{dt} = \frac{1}{2} \frac{d[NO]}{dt} = \frac{1}{1} \frac{d[O_2]}{dt} \]

3. **Analyzing the Statements**:
- **Statement A**: "Decrease in NO2 and the increase in NO proceed at the same rate."
- This statement is true because the rate of decrease of NO2 is equal to the rate of increase of NO, adjusted for stoichiometry.

- **Statement B**: "The rate of formation of NO is twice the rate of formation of O2."
- This statement is also true. From the stoichiometry of the reaction, for every 2 moles of NO produced, 1 mole of O2 is produced. Therefore, the rate of formation of NO is indeed twice that of O2.

- **Statement C**: "The average rate of increase in the concentration of NO and O2 are expressed as..."
- This statement needs careful consideration. The average rate of increase in concentration of NO is given by:
\[ \text{Rate of increase of } NO = \frac{1}{2} \frac{d[NO]}{dt} \]
and for O2:
\[ \text{Rate of increase of } O_2 = \frac{d[O_2]}{dt} \]
The average rate of increase of NO should include the factor of \( \frac{1}{2} \) because of its stoichiometry in the balanced equation. Hence, if this factor is missing in the statement, it is false.

4. **Conclusion**:
Based on the analysis, the false statement is **Statement C**, which incorrectly expresses the average rate of increase in concentration of NO without including the stoichiometric coefficient.

### Final Answer:
The false statement is **Statement C**.