For the reaction 2NO + O2 → 2NO2, the experimentally determined rate law is rate = k[NO]^2[O2]. What is the overall reaction order, what is the order with respect to O2, and what are the units of the rate constant k?

• A. Overall order: 2; O2 order: 1; Units of k: M^{-1} s^{-1}
• B. Overall order: 3; O2 order: 2; Units of k: M^{-2} s^{-1}
• C. Overall order: 3; O2 order: 1; Units of k: M^{-2} s^{-1}
• D. Overall order: 2; O2 order: 2; Units of k: M^{-1} s^{-1}

Answer: (C)

Verified step by step guidance

1. Identify the rate law given: \(\text{rate} = k[\text{NO}]^{2}[\text{O}_2]\).
2. Determine the order with respect to each reactant by looking at the exponents in the rate law: the order with respect to NO is 2, and the order with respect to O2 is 1.
3. Calculate the overall reaction order by summing the individual orders: overall order = 2 (from NO) + 1 (from O2) = 3.
4. Recall that the units of the rate constant \(k\) depend on the overall reaction order and the rate units. The general formula for the units of \(k\) is \(\text{units of rate} \div (\text{units of concentration})^{\text{overall order}}\).
5. Since rate is typically expressed in molarity per second (\(\mathrm{M\,s^{-1}}\)) and concentration in molarity (\(\mathrm{M}\)), substitute these into the formula: units of \(k = \mathrm{M\,s^{-1}} \div \mathrm{M}^{3} = \mathrm{M}^{-2} \mathrm{s^{-1}}\).