Which of the following is the correct expression for the rate of disappearance of NO(g) in the reaction 2 NO(g) + O_2(g) → 2 NO_2(g)?

• A. -rac{1}{2} rac{d[NO_2]}{dt}
• B. -rac{d[NO_2]}{dt}
• C. -rac{1}{2} rac{d[NO]}{dt}
• D. -rac{d[O_2]}{dt}

Answer: (C)

Verified step by step guidance

1. Identify the balanced chemical equation: \$2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g)$.
2. Recall that the rate of disappearance of a reactant is related to the change in concentration over time, expressed as \(-\frac{d[\text{Reactant}]}{dt}\).
3. Use the stoichiometric coefficients to relate the rates of disappearance or appearance of each species. For NO, the coefficient is 2, so the rate of disappearance of NO is related to the rate of appearance of NO\(_2\) by the ratio of their coefficients.
4. Write the general rate expression relating NO and NO\(_2\): \(-\frac{1}{2} \frac{d[\text{NO}]}{dt} = \frac{1}{2} \frac{d[\text{NO}_2]}{dt}\), noting the negative sign for disappearance and positive for appearance.
5. From this, express the rate of disappearance of NO in terms of the rate of change of NO\(_2\) or O\(_2\) concentrations, ensuring the stoichiometric factors are correctly applied.