Question 15.6: Reaction Mechanisms I The balanced equation for the reaction...
Reaction Mechanisms I
The balanced equation for the reaction of gaseous nitrogen dioxide and fluorine is
2 NO_{2} (g) + F_{2} (g) → 2 NO_{2} F(g)
The experimentally determined rate law is
Rate = k [NO_{2}][F_{2}]
A suggested mechanism for this reaction is
NO_{2} + F_{2} \xrightarrow[]{k_{1}} NO_{2} F + F Slow
F + NO_{2} \xrightarrow[]{k_{2}} NO_{2} F Fast
Is this an acceptable mechanism? That is, does it satisfy the two requirements?
The first requirement for an acceptable mechanism is that the sum of the steps give the balanced equation:
NO_{2} + F_{2} → NO_{2} F + F
\underline{ F + NO_{2} → NO_{2} F }
2 NO_{2} + F_{2} + \cancel{F} → 2 NO_{2} F + \cancel{F}
Overall reaction: 2 NO_{2} + F_{2} → 2 NO_{2} F
The first requirement is met.
The second requirement is that the mechanism must agree with the experimentally determined rate law. Since the proposed mechanism states that the first step is rate determining, the overall reaction rate must be that of the first step. The first step is bimolecular, so the rate law is
Rate = k_{1} [NO_{2}][F_{2}]
This has the same form as the experimentally determined rate law. The proposed mechanism is acceptable because it satisfies both requirements. (Note that we have not proved it is the correct mechanism.)