The reaction NO + O3 giving NO2 + O2 is first order in each reactant with k = 2.20 x 10^7 L/mol/s. What is the rate when [NO] = 3.3 x 10^-6 M and [O3] = 5.9 x 10^-7 M?
A8.6 x 10^-5 mol/L/s
B4.3 x 10^-5 mol/L/s
C7.3 x 10^1 mol/L/s
D4.3 x 10^-6 mol/L/s
Answer & Solution
Correct answer: B. 4.3 x 10^-5 mol/L/s
1. First order in each reactant gives the rate law rate = k[NO][O3].
2. Substitute everything: 2.20 x 10^7 L/mol/s x 3.3 x 10^-6 mol/L x 5.9 x 10^-7 mol/L.
3. Multiply the mantissas: 2.20 x 3.3 x 5.9 = 42.8.
4. Add the exponents: 7 + (-6) + (-7) = -6, so the raw product is 42.8 x 10^-6.
5. In standard form that is 4.3 x 10^-5 mol per litre per second.
6. Units check: L/mol/s times two factors of mol/L leaves mol/L/s.
7. The value 7.3 x 10^1 stops after multiplying by [NO] and never brings in the ozone concentration.
8. The value 8.6 x 10^-5 doubles the answer, and 4.3 x 10^-6 is a one decade exponent slip.
_Source: OpenStax Chemistry (CC BY 4.0), Ch 12 "Kinetics", section 12.3 Rate Laws_
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