Intermediate is created and destroyed, and therefore does not appear on the net equation, which is \(\displaystyle 2O_{3} \rightarrow 3O_{2}\). Thus, the intermediate is \(\displaystyle O\). Note that when asked for an intermediate, the coefficient in front of it is not used, rather we are looking for the species that is a product of one reaction and a reactant in a subsequent step.

The reactant \(\displaystyle B\) is not included in the rate law expression, and therefore altering its concentration does not affect the rate of the reaction. Catalysts always increase the rate of reactions by lowering its activation energy. Increasing temperature (average kinetic energy of the molecules) increases the frequency of collisions, and increases the proportion of collisions that have enough energy to overcome the activation energy and undergo a chemical reaction. Increasing the concentration of \(\displaystyle A\) will increase the rate of the reaction as indicated by the rate law.

For this question, we're asked to identify something that will always increase the rate of a reaction. Notice that the question specifically states "always."

Let's go through each answer choice and see how it affects the reaction rate.

When the concentration of reactants is increased, this may increase the reaction rate, but not always. For example, if a reaction is zero-order with respect to its reactants, then changing the reactant concentration will have no effect on the rate.

Just like with reactants, decreasing the concentration of products may or may not change the reaction rate. If the reaction rate is zero-order with respect to the products, then a change in their concentration will have no effect on the reaction rate.

A change in temperature is the only thing that is guaranteed to change the reaction rate. This is because changing the temperature will directly change the rate constant of the reaction. Increasing the temperature will increase the rate constant, and hence the reaction rate.

The rate-determining step in a reaction mechanism is a kinetic bottleneck, in that it prevents the overall reaction from proceeding; thus, it is what determines how quickly the overall reaction can proceed.

Product concentration would not affect a forward reaction rate, since that is what is being formed. Catalysts specifically speed up reaction rates, as does temperature. Medium can also affect reaction rate because some molecules are more likely to react with each other in certain environments. 

The transition state is the energy barrier in a reaction—energy is needed to reach this state. Once it is acheived, however, it can either revert back to reactants or dissociate into products without any added energy. 

First order reactions have the rate equation \(\displaystyle Rate = k[A]\). As the molarity of A decreases, the rate slows.

The half-life equation is \(\displaystyle t_{\frac{1}{2}}=\frac{ln(2)}{k}\). The half-life is constant with respect to time and concentration, depending only on the rate constant.

Lastly, the overall reaction can have any number of reactants. A reaction is first order because its rate-limiting step has only one reactant.

Only statement II is true.

According to Le Chatelier's principle, an increase in the concentration of reactants will cause the reaction to shift to the right in order to re-establish equilibrium. Thus, immediately after reactant A is added, the forward reaction will increase and the net rate of formation of the products will be positive. 

The integrated rate law shown is for a reaction rate law with a first-order dependence on reactact A. If such a rate law accurately describes the kinetics of the reaction, then ln[A] will vary linearly with respect to time. 

Since reactant molecules collide and interact to break old bond and form new ones, any factors affecting collision and interactions will affect the reaction rate. Thus, increasing temperature will increase both the frequency of collisions and the average kinetic energy of the molecules. Enzymes bring molecules close to each other and orient them in a way that facilitates reactions.