How will each of the following affect the rate of the reaction: \(\operatorname{CO}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{NO}(g)\) if the rate law for the reaction is rate \(=k\left[\mathrm{NO}_{2}\right][\mathrm{CO}] ?\) (a) Increasing the pressure of \(\mathrm{NO}_{2}\) from 0.1 atm to \(0.3 \mathrm{atm}\) (b) Increasing the concentration of CO from \(0.02 M\) to \(0.06 M\)

The rate law is a mathematical expression that describes how the concentration of reactants influences the rate of a chemical reaction. In a rate law, the rate of a reaction is typically given by an equation where the rate is directly proportional to the product of the concentrations of the reactants, each raised to a power, which is known as the reaction order.

For the given reaction between carbon monoxide (CO) and nitrogen dioxide (NO₂), the rate law is provided as rate = k[NO₂][CO]. Here, 'k' is the rate constant, a unique value for each reaction that depends on the temperature and other physical conditions. The brackets around NO₂ and CO indicate the concentration of these reactants in molar units (M). This particular rate law suggests a first-order dependence on both NO₂ and CO, as there are no exponents written, implying that the powers are one.

When interpreting the rate law, it is crucial to understand that a change in the concentration of either reactant will lead to a proportional change in the reaction rate. This direct relationship is what allows chemists to predict how changes, like an increase in reactant concentration, will affect the reaction speed.

Chemical kinetics is the branch of chemistry that deals with the speed or rate at which a chemical reaction occurs and the factors that affect this rate. It’s a field that gives us an understanding of reaction mechanisms and how different variables such as temperature, pressure, reactant concentrations, and the presence of catalysts influence the rate of reaction.

In the context of the exercise, understanding chemical kinetics allows us to predict and explain how increasing the pressure of NO₂ or the concentration of CO will affect the rate of the reaction. The provided step-by-step solution shows a direct effect of these changes on the reaction rate, which follows the principles of chemical kinetics. In general, increasing the concentration of a reactant in a reaction with a rate law showing a first-order dependence on that reactant will increase the rate of the reaction proportionally. On the molecular level, higher concentrations mean more reactant molecules are available in a given volume, leading to an increased likelihood of collision and reaction, thus increasing the reaction rate.

Reactant concentration plays a pivotal role in the progression of a chemical reaction. In reaction rate chemistry, the concentration of a reactant is defined as the amount of that substance within a specific volume of solution. It is typically measured in molarity (M), which is moles per liter (mol/L).

The relation between reactant concentration and reaction rate is an inverse expression of the collision theory. According to this theory, reactions occur when reactant molecules collide with sufficient energy and an orientation that allows the formation of products. By increasing the reactant concentration, you increase the number of molecules in a given volume, which can lead to a higher frequency of effective collisions and thus an increased reaction rate.

This concept plays out in the exercise as well. By increasing the pressure of NO₂ (which is directly proportional to its concentration for a gas at constant temperature and volume), or the concentration of CO, the rate of the chemical reaction is expected to increase accordingly. Higher pressure and concentration mean more reactant molecules are present, resulting in a greater number of successful collisions per unit of time and thereby increasing the rate at which the reaction occurs.