When a mixture of methane and bromine vapor is exposed to light, the following reaction occurs slowly: \(\mathrm{CH}_{4}(g)+\mathrm{Br}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{Br}(g)+\mathrm{HBr}(g)\) When a mixture of methane and bromine vapor is exposed to light, the following reaction occurs slowly:

Balancing chemical equations is an essential skill in chemistry, akin to solving a puzzle with molecular pieces. It's about ensuring that the number of atoms for each element is the same on both sides of the equation—this reflects the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction. To balance an equation, one must adjust the coefficients, which are the numbers in front of the compounds in a chemical equation.

For example, in the bromination of methane, the equation is balanced as shown in the step-by-step solution: one molecule of methane (CH_{4}) reacts with one molecule of bromine (Br_{2}) to form one molecule each of bromomethane (CH_{3}Br) and hydrogen bromide (HBr). A methodical approach to balancing equations starts with listing the number of atoms of each element before and after the reaction, then adjusting coefficients to match the numbers on each side.

Remember, coefficients should be the smallest set of whole numbers possible, and balancing equations does not involve changing the subscripts (the small numbers after elements that indicate the number of atoms) within the chemical formulas.

Photochemical reactions are fascinating chemical processes initiated by light. In these reactions, photons (light particles) provide the energy needed to break chemical bonds, leading to a series of chemical changes. A classic example is the reaction that happens when a mixture of methane and bromine vapor is exposed to light, as described in the original exercise. The light, typically ultraviolet, catalyzes the halogenation of methane, initiating the reaction.

The significance lies in the energy transferred from photons to reactant molecules, which perturbs the stable electronic configuration and causes homolytic cleavage where bonds split evenly. This generates free radicals, highly reactive atoms or molecules that have unpaired electrons. These radicals then participate in further steps, propagating the reaction to create new compounds. It's vital to understand that photochemical reactions can be quite selective and often proceed differently than thermal reactions, where heat is the driving force.

Furthermore, photochemical reactions underpin many natural processes, including photosynthesis and the formation of vitamin D in skin. They are also harnessed in various applications such as synthesis of complex organic compounds, photopolymerization, and environmental processes like the breakdown of pollutants.

The bromination of methane is an illustrative example of a photochemical reaction where methane, a simple alkane, reacts with bromine to form bromomethane and hydrogen bromide. This specific reaction showcases a type of substitution reaction known as halogenation. The bromine molecule is split into two bromine atoms by the energy from light, creating bromine radicals. A radical is an atom or group of atoms that has at least one unpaired electron and is, therefore, extremely reactive.

In step 1, a bromine radical abstracts a hydrogen atom from methane, generating HBr and a methyl radical. Then, the methyl radical reacts with another bromine molecule to form bromomethane. This leads to a chain reaction mechanism that can continue until the reactants are consumed or the reaction is terminated by radical recombination.

Controlling this process is essential in industrial chemistry to create specific brominated products. The reactivity of methane and other alkanes with halogens is a fundamental aspect of organic chemistry, often used to introduce functional groups into hydrocarbons, which can then be further transformed into more complex organic compounds.