Part a consider the formation of nitryl fluoride: 2no2 (g) + f2 (g) ⇌2no2f (g) the reaction is first order in f2 and second order overall. what is the rate law?

The reaction is:

2 NO₂ (g) + F₂ (g) ⇆ 2 NO₂F (g)

The stoichiometric coefficients of the substances balance out each other to obey the Law of Definite Proportions. Now, you have to note that determining the reaction rate expression is specific to a certain type of reaction. So, this are determined empirically through doing experiments. Sometimes in chemical reaction engineering, to make things simple, you assume that the reaction is elementary. This means that the order of a reaction with respect to a certain substance follows their individual stoichiometric coefficients. Bu there is no need for that assumption. It is already stated that the rate order is 1 with respect to F₂ and 2 if we talk about the overall order. You can determine the overall order if you add all the exponents in the expression. For this reaction, the reaction rate can be written as

Reaction rate of disappearance of reactants = Reaction rate of formation of products.

Therefore, we can have two reaction rate expressions for this. But since the problem specifies F₂, we focus on the reactants side. The expression would be

-r = k[NO₂][F₂]

The negative sign before r signifies the rate of disappearance. If it were in terms of the product, that would have been positive. The term k denotes for the reaction rate constant. That is also empirical. Now, the exponents of the reactants represent their rate order. Since F₂ is specified that order is 1, the exponent is also 1. Because the overall rate order is 2, then that means that the exponent of NO₂ is also 1.