Bromine monofluoride (BrF) disproportionates to bromine gas and bromine trifluoride or pentafluoride. Use the following to find \(\Delta H_{\mathrm{rxn}}^{0}\) for the decomposition of BrF to its elements: $$\begin{aligned}3 \mathrm{BrF}(g) & \longrightarrow \mathrm{Br}_{2}(g)+\mathrm{BrF}_{3}(l) & & \Delta H_{\mathrm{rn}}=-125.3 \mathrm{~kJ} \\\5 \mathrm{BrF}(g) & \longrightarrow 2 \mathrm{Br}_{2}(g)+\mathrm{BrF}_{5}(l) & & \Delta H_{\mathrm{rn}}=-166.1 \mathrm{~kJ} \\\\\mathrm{BrF}_{3}(I)+\mathrm{F}_{2}(g) & \longrightarrow \mathrm{BrF}_{5}(l) & & \Delta H_{\mathrm{rn}}=-158.0 \mathrm{~kJ}\end{aligned}$$

A disproportionation reaction is a type of redox reaction where a single substance is simultaneously oxidized and reduced, forming two different products. In this exercise, Bromine monofluoride (BrF) undergoes disproportionation to form bromine gas (Br₂) and bromine trifluoride (BrF₃) or pentafluoride (BrF₅). This is evident in the balanced reactions provided:

• 3 BrF(g) → Br₂(g) + BrF₃(l)
• 5 BrF(g) → 2 Br₂(g) + BrF₅(l)

Understanding the concept of disproportionation is crucial because it helps in balancing redox reactions and calculating the associated energy changes. By noting how BrF is both oxidized and reduced, we can further comprehend the enthalpy calculations required in these reactions.

Enthalpy (◌H) is a measure of the total heat content in a system. It is crucial for predicting the feasibility and direction of chemical reactions, especially those involving heat exchange. In our specific problem, we are interested in finding ◌H of the given reactions for the decomposition of BrF. This involves manipulating the equations to derive the target reaction. Start by considering the given reactions and recognizing that we need to find enthalpy change (ΔH) for BrF decomposing into its elements: BrF(g) → 1/2 Br₂(g) + 1/2 F₂(g).The process involves reversing and scaling reactions to match the target decomposition equation. For example, dividing and reversing the given reactions, adding their enthalpy changes properly, and finally arriving at the required enthalpy change (ΔH). It is essential to keep track of the sign and magnitude of ΔH when reactions are reversed or scaled.

Chemical reactions involve the transformation of reactants into products. This process is governed by conservation laws like mass and energy balance. In the context of our exercise, we deal with multiple reactions involving BrF decomposing into various products. Understanding how to balance these reactions and combining them to derive new reactions is key to solving problems involving chemical synthesis.

• Identify the target reaction: BrF(g) → 1/2 Br₂(g) + 1/2 F₂(g).
• Manipulate the provided equations using algebraic methods—reverse and scale reactions if necessary.
• Combine these equations to eliminate intermediate products and get the desired outcome.By performing these steps, students can solve enthalpy-related problems efficiently and understand the underlying principles governing chemical reactions. Mastery of these concepts enables deeper insights into reaction mechanisms and energy changes during chemical transformations.