Problem 69 - Chemistry The Central Science

Question

For each of the following compounds, write a balanced thermochemical equation depicting the formation of one mole of the compound from its elements in their standard states and use Appendix \(\mathrm{C}\) to obtain the value of \(\Delta H_{f}^{\circ}\) : (a) \(\mathrm{NO}_{2}(g)\) (b) \(\mathrm{SO}_{3}(g),(\mathrm{c}) \mathrm{NaBr}(s)\) (d) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s)\)

Step-by-Step Solution

Answer

The balanced thermochemical equations and standard enthalpies of formation for the given compounds are: a) \(N_{2}(g) + O_{2}(g) \rightarrow 2NO_{2}(g)\), \(\Delta H_{f}^{\circ}(\mathrm{NO}_{2}(g)) = 33.18 \thinspace \mathrm{kJ/mol}\) b) \(S(s) + \dfrac{3}{2}O_{2}(g) \rightarrow SO_{3}(g)\), \(\Delta H_{f}^{\circ}(\mathrm{SO}_{3}(g)) = -395.7 \thinspace \mathrm{kJ/mol}\) c) \(Na(s) + \dfrac{1}{2}Br_{2}(l) \rightarrow NaBr(s)\), \(\Delta H_{f}^{\circ}(\mathrm{NaBr}(s)) = -361.0\thinspace \mathrm{kJ/mol}\) d) \(Pb(s) + 2N_{2}(g) + 6O_{2}(g) \rightarrow Pb(NO_{3})_{2}(s)\), \(\Delta H_{f}^{\circ}(\mathrm{Pb}(NO_{3})_{2}(s)) = -590.3\thinspace \mathrm{kJ/mol}\)

Step 1: a) Balanced thermochemical equation for NO2(g) formation

We need to form 1 mole of nitrogen dioxide (NO2) from its elements, nitrogen (N2) and oxygen (O2). Both nitrogen and oxygen are in their gaseous state and diatomic form in their standard state. The balanced thermochemical equation for this process is: \(N_{2}(g) + O_{2}(g) \rightarrow 2NO_{2}(g)\) Now we can look up the standard enthalpy of formation for NO2(g).

Step 2: a) Standard enthalpy of formation for NO2(g)

Consulting Appendix C or other reference sources, we find that the standard enthalpy of formation for NO2(g) is: \(\Delta H_{f}^{\circ}(\mathrm{NO}_{2}(g)) = 33.18 \thinspace \mathrm{kJ/mol}\)

Step 3: b) Balanced thermochemical equation for SO3(g) formation

We will form 1 mole of sulfur trioxide (SO3) from its elements, sulfur (S) and oxygen (O2). Sulfur is a solid and oxygen is a diatomic gas in their standard state. The balanced thermochemical equation for this process is: \(S(s) + \dfrac{3}{2}O_{2}(g) \rightarrow SO_{3}(g)\) Now we can look up the standard enthalpy of formation for SO3(g).

Step 4: b) Standard enthalpy of formation for SO3(g)

Consulting Appendix C or other reference sources, we find that the standard enthalpy of formation for SO3(g) is: \(\Delta H_{f}^{\circ}(\mathrm{SO}_{3}(g)) = -395.7 \thinspace \mathrm{kJ/mol}\)

Step 5: c) Balanced thermochemical equation for NaBr(s) formation

Now, we need to form 1 mole of sodium bromide (NaBr) from its elements, sodium (Na) and bromine (Br2). Sodium is a solid and bromine is a diatomic liquid in their standard states. The balanced thermochemical equation for this process is: \(Na(s) + \dfrac{1}{2}Br_{2}(l) \rightarrow NaBr(s)\) Now we can look up the standard enthalpy of formation for NaBr(s).

Step 6: c) Standard enthalpy of formation for NaBr(s)

Consulting Appendix C or other reference sources, we find that the standard enthalpy of formation for NaBr(s) is: \(\Delta H_{f}^{\circ}(\mathrm{NaBr}(s)) = -361.0\thinspace \mathrm{kJ/mol}\)

Step 7: d) Balanced thermochemical equation for Pb(NO3)2(s) formation

Finally, we need to form 1 mole of lead nitrate [Pb(NO3)2] from its elements, lead (Pb), nitrogen (N2), and oxygen (O2). Lead is a solid, nitrogen is a diatomic gas, and oxygen is a diatomic gas in their standard states. The balanced thermochemical equation for this process is: \(Pb(s) + 2N_{2}(g) + 6O_{2}(g) \rightarrow Pb(NO_{3})_{2}(s)\) Now we can look up the standard enthalpy of formation for Pb(NO3)2(s).

Step 8: d) Standard enthalpy of formation for Pb(NO3)2(s)

Consulting Appendix C or other reference sources, we find that the standard enthalpy of formation for Pb(NO3)2(s) is: \(\Delta H_{f}^{\circ}(\mathrm{Pb}(NO_{3})_{2}(s)) = -590.3\thinspace \mathrm{kJ/mol}\)

Key Concepts

Standard Enthalpy of Formation

Understanding the standard enthalpy of formation, or the enthalpy change associated with forming one mole of a compound from itselements in their standard states.

Chemical Compound Formation

The formation of a chemical compound is a reaction where elements combine to form a compound.

Balanced Chemical Reactions

The importance lies in the conservation of mass and energy, necessitating that the number of atoms for each element remain constant before and after the reaction.