Step 1: Understanding the Concept:
The rate of a chemical reaction can be expressed in terms of the rate of disappearance of any reactant or the rate of formation of any product, divided by their respective stoichiometric coefficients from the balanced chemical equation.
Step 2: Key Formula or Approach:
For a general reaction \(aA + bB \longrightarrow cC + dD\), the overall rate of reaction is given by:
\[ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt} \]
Step 3: Detailed Explanation:
The given balanced chemical equation is:
\[ \text{NO}_{2(\text{g})} + \text{CO}_{(\text{g})} \longrightarrow \text{NO}_{(\text{g})} + \text{CO}_{2(\text{g})} \]
Based on the stoichiometry of the reaction, 1 mole of \(\text{CO}\) reacts to produce 1 mole of \(\text{NO}\).
Therefore, the rate expression is:
\[ -\frac{d[\text{CO}]}{dt} = +\frac{d[\text{NO}]}{dt} \]
Here, \(+\frac{d[\text{NO}]}{dt}\) represents the rate of formation of \(\text{NO}\), which is given as \(\text{Y mol dm}^{-3}\text{ s}^{-1}\).
\(-\frac{d[\text{CO}]}{dt}\) represents the rate of disappearance of \(\text{CO}\).
Since they are equal, the rate of disappearance of \(\text{CO}\) is also \(\text{Y mol dm}^{-3}\text{ s}^{-1}\).
Step 4: Final Answer:
The correct option is (A).