Question

(a) Use enthalpies of formation given in Appendix $C$ to calculate $\mathrm{\Delta }H$ for the reaction $B{r}_2(g)⟶2$ Br $(g),$ and use this value to estimate the bond enthalpy $D(\mathrm{Br}-\mathrm{Br}).$ (b) How large is the difference between the value calculated in part (a) and the value given in Table 5.4 ?

Short answer

(a) The given reaction is: $B{r}_2(g)⟶2Br(g)$. To calculate $\mathrm{\Delta }H$ for the reaction, we use the formula: $$\mathrm{\Delta }H=2\mathrm{\Delta }{H}_f(Br(g))-\mathrm{\Delta }{H}_f(B{r}_2(g))$$. Then, estimate the bond enthalpy $D(Br-Br)\approx \mathrm{\Delta }H$. (b) To find the difference between the calculated value and the one in Table 5.4, use: $$Difference=|D(Br-Br{)}_{calculated}-D(Br-Br{)}_{Table5.4}|$$.

Step-by-step solution

Identify the given reaction and relevant enthalpies of formation

The given reaction is: $$B{r}_2(g)⟶2Br(g)$$ We are given the enthalpies of formation for $B{r}_2(g)$ and $Br(g)$ in Appendix C. We will use these values to calculate the enthalpy change for the given reaction.

Calculate the enthalpy change for the reaction

To calculate the enthalpy change $\mathrm{\Delta }H$, we can use the formula: $$\mathrm{\Delta }H=\sum \mathrm{\Delta }{H}_f(\text{products})-\sum \mathrm{\Delta }{H}_f(\text{reactants})$$ We'll plug in the enthalpies of formation values from Appendix C for $B{r}_2(g)$ and $Br(g)$: $$\mathrm{\Delta }H=2\mathrm{\Delta }{H}_f(Br(g))-\mathrm{\Delta }{H}_f(B{r}_2(g))$$

Estimate the bond enthalpy

Since the reaction involves breaking one Br-Br bond on the reactant side, the enthalpy change is approximately equal to the bond enthalpy: $$D(Br-Br)\approx \mathrm{\Delta }H$$

Compare the calculated value with the one given in Table 5.4

Once we have calculated the bond enthalpy of Br-Br, we can compare the result with the value provided in Table 5.4. The difference between these two values can be calculated as follows: $$Difference=|D(Br-Br{)}_{calculated}-D(Br-Br{)}_{Table5.4}|$$ This will give us the difference between the calculated value and the one found in the table.

Key concepts

Chemical Thermodynamics

At the heart of chemistry lies the study of energy changes in chemical reactions, which is the essence of chemical thermodynamics. This branch of thermodynamics deals with the heat and work aspects of chemical processes and how they are governed by the laws of thermodynamics.

In a chemical reaction, substances transform into new products, and along with this transformation, there's a transfer or transformation of energy. The energy change associated with a chemical reaction relates to the enthalpy of the reactants and products, a concept known as enthalpy change. It provides insight into whether a reaction will release heat and be exothermic, or absorb heat and be endothermic.

Understanding enthalpy changes is critical for predicting reaction spontaneity, energy efficiency of processes, and even in designing storage materials for energy. For instance, when considering the reaction of bromine, knowing the enthalpy allows chemists to predict if the reaction requires energy input or if it will release energy into the surroundings.

Enthalpy Change Calculation

Enthalpy change, denoted as $\mathrm{\Delta }H$, is a measure of the total heat content change in a chemical reaction at constant pressure. Calculating this change involves enthalpies of formation, which represent the heat absorbed or released when one mole of a compound is formed from its elements in their standard states.

The equation $\mathrm{\Delta }H=\sum \mathrm{\Delta }{H}_f(\text{products})-\sum \mathrm{\Delta }{H}_f(\text{reactants})$ demonstrates the principle of conservation of energy; the total enthalpy change in a reaction is the difference between the enthalpies of the products and the reactants. For simplification in homework exercises, like the bromine reaction given in the question, this formula is a straightforward tool for students to handle enthalpy change calculations efficiently.

It's important to note that accurate enthalpy calculations are not just academic exercises but also have practical applications in fields like materials science, engineering, and environmental science where energy management is crucial.

Bond Enthalpy

Bond enthalpy, also known as bond dissociation energy, is a vital concept when discussing chemical bonds and their strengths. It is the energy required to break one mole of a bond in a chemical compound at a constant temperature and pressure.

The bond enthalpy gives a measure of how strong a chemical bond is. For a diatomic molecule like $B{r}_2$, the bond enthalpy of the $Br-Br$ bond can be approximated from the enthalpy change of the reaction, as seen in homework problems. In chemical thermodynamics, understanding bond enthalpies helps in characterizing chemical reactions, whether they require energy to proceed or release energy upon proceeding.

When calculating bond enthalpies, one must consider that they are average values taken from multiple similar compounds due to variations in bond energies in different molecular environments. Bond enthalpy calculations serve not just to reinforce theoretical understanding but also to help predict reaction pathways and potentials in chemical synthesis and kinetic studies.