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Chapter 16: Q16.6 CYL (page 895)

Calculate the standard entropy change for the following reaction:

\({\bf{Ca(OH}}{{\bf{)}}_{\bf{2}}}{\bf{(\;s)}} \to {\bf{CaO(s) + }}{{\bf{H}}_{\bf{2}}}{\bf{O(l)}}\)

Short Answer

Expert verified

The standard entropy change for above process is \(120.644\;{\rm{J}}/{\rm{Kmol}}\)

Step by step solution

01

Define enthalpy of the reaction

  • Enthalpy change is defined as the difference in enthalpies of all the product and the reactants each multiplied with their respective number of moles. It is represented as
  • The equation used to calculate enthalpy change is of a reaction is:
  • \(\Delta {H_{rxn}} = \sum {\left[ {n \times \Delta {H_{f({\rm{ product }})}}} \right]} - \sum {\left[ {n \times \Delta {H_{f({\rm{ reactant }})}}} \right]} \)
02

Determine the enthalpy of the reaction.

Reaction is:

\(\begin{array}{l}{\rm{Ca}}{({\rm{OH}})_2}(\;{\rm{S}}) \to {\rm{CaO}}({\rm{S}}) + {{\rm{H}}_2}{\rm{O - - - - - - - }}({\rm{l}})\\\Delta {S^\theta }\left( {{\rm{Ca}}{{({\rm{OH}})}_2}} \right) = 83.39\;{\rm{J}}/{\rm{molK}}\\\Delta {S^\theta }({\rm{CaO}}) = 38.2\;{\rm{J}}/{\rm{molK}}\\\Delta {S^\theta }\left( {{{\rm{H}}_2}{\rm{O}}} \right) = 69.91\;{\rm{J}}/{\rm{molK}}\end{array}\)

Calculate \(\Delta {s^\theta }\) of the reaction:

\(\Delta {S^\theta } = \Delta {S^\theta }(\)Product \() - \Delta {S^\theta }({\mathop{\rm Reactant}\nolimits} )\)

\(\Delta {S^\theta } = \left[ {\Delta {S^\theta }({\rm{CaO}}) + \Delta {S^\theta }\left( {{{\rm{H}}_2}{\rm{O}}} \right)} \right] - \left[ {\Delta {S^\theta }\left( {{\rm{Ca}}{{({\rm{OH}})}_2}} \right)} \right]\)

\(\Delta {S^\theta } = [38.2 + 69.91] - [83.39]\)

\(\Delta {S^\theta } = (108.11 - 83.39){\rm{J}}\mid {\rm{kmol}}\)

\(\Delta {s^\theta } = + 24.72\;{\rm{J}}/{\rm{kmo}}\quad \)(Answer)

Hence; the standard entropy changed is \( + 24.72\;{\rm{J}}/{\rm{kmol}}\)

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Most popular questions from this chapter

What happens to \({\bf{\Delta G}}_{{\bf{298}}}^{\bf{^\circ }}\) (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?

(a) \({\bf{S(s) + }}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{S}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

(b) \({\bf{2S}}{{\bf{O}}_{\bf{2}}}{\bf{(g) + }}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{S}}{{\bf{O}}_{\bf{3}}}{\bf{(g)}}\)

(c) \({\bf{HgO(s)}} \to {\bf{Hg(l) + }}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

Calculate ΔG° using

(a) free energies of formation and

(b) enthalpies of formation and entropies(Appendix G). Do the results indicate the reaction to be spontaneous or nonspontaneous at 25 °C?

\({{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{4}}}{\bf{(g)}} \to {{\bf{H}}_{\bf{2}}}{\bf{(g) + }}{{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{4}}}{\bf{(g)}}\)

Calculate the free energy change for the same reaction at 875 °C in a 5.00 L mixture containing 0.100 mol of each gas. Is the reaction spontaneous under these conditions?

Write conversion factors (as ratios) for the number of:

(a) yards in 1 meter

(b) liters in 1 liquid quart

(c) pounds in 1 kilogram

An important source of copper is from the copper ore, chalcocite, a form of copper(I) sulfide. When heated, the \({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{S}}\) decomposes to form copper and sulfur described by the following equation:

\({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{\;S(s)}} \to {\bf{Cu(s) + S(s)}}\)

(a) Determine \({\bf{\Delta G}}_{{\bf{298}}}^{\bf{^\circ }}\)for the decomposition of \({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{S(\;s)}}\).

(b) The reaction of sulfur with oxygen yields sulfur dioxide as the only product. Write an equation that describes this reaction, and determine\({\bf{\Delta G}}_{{\bf{298}}}^{\bf{^\circ }}\)for the process.

(c) The production of copper from chalcocite is performed by roasting the \({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{S}}\) in air to produce the \({\bf{Cu}}\). By combining the equations from Parts (a) and (b), write the equation that describes the roasting of the chalcocite, and explain why coupling these reactions together makes for a more efficient process for the production of the copper.
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