Why are metal displacement reactions exothermic?

I'm doing a research paper on the causes of exothermic reactions. I need to know why there is a release of heat in the reaction between zinc and copper(II) sulphate.
Judy 3/27/99

Vocabulary
endothermic*
enthalpy*
enthalpy of hydration*
exothermic*
Hess's law*
redox*
spontaneous*
sublimation*
The reaction Zn(s) + Cu2+(aq) rightarrow Cu(s) + Zn2+(aq) is spontaneous and exothermic. To figure out exactly where the heat released comes from, we'll have to break the reaction down into simpler steps. Hess's law says that it doesn't matter how many steps we chose to write; the enthalpy changes for each step will add up to the enthalpy change for the net reaction.

One possible way of analyzing the reaction involves breaking it into separate sublimation, ionization, and hydration steps:

  1. Convert the aqueous copper(II) into gaseous copper(II).

    Cu2+(aq) rightarrow Cu2+(g)   DeltaH° = +2289 kJ

    This process is endothermic because strong attractive ion-dipole forces between the copper(II) ion and the water must be overcome to vaporize the ion.
  2. Convert gaseous copper(II) into gaseous copper.

    Cu2+(g) + 2 e- rightarrow Cu(g)   DeltaH° = -2703.4 kJ

    This process is the reverse of ionization; DeltaH is equal to minus the sum of the first and second ionization enthalpies for copper. Capture of electrons by a cation is always exothermic.
  3. Convert gaseous copper into solid copper.

    Cu(g) rightarrow Cu(s)   DeltaH° = -337.4 kJ

    DeltaH for condensation of gaseous copper is minus the heat of formation for gaseous copper. The process is exothermic because strong metallic bonds are formed in the condensation.
  4. Convert the solid zinc into gaseous zinc.

    Zn(s) rightarrow Zn(g)   DeltaH° = +130.5 kJ

    Vaporization of solid zinc is endothermic because strong metallic bonds are being broken.
  5. Convert gaseous zinc into gaseous Zn2+.

    Zn(g) rightarrow Zn2+(g) + 2 e-   DeltaH° = +2639 kJ

    Ionization of zinc atoms is endothermic because the strong attraction the valence electrons have for the nucleus must be overcome.
  6. Convert gaseous Zn2+ into aqueous Zn2+.

    Zn2+(g) rightarrow Zn2+(aq)    DeltaH° = -2247 kJ

    Hydration of zinc ion is exothermic because strong water-ion attractions are formed.
Adding all of these steps together gives

Zn(s) + Cu2+(aq) rightarrow Cu(s) + Zn2+(aq)   DeltaH° = -229 kJ

with a reaction enthalpy that is probably good to +/- 30 kJ, given the uncertainties in the hydration enthalpies we used.

Although the reaction doesn't actually proceed by a series of sublimation-ionization-hydration steps, the calculation does give us a valuable insight into where the energy is actually coming from in the reaction. Try the following questions to explore some reasonable deductions that can be made about the significance of ion-water interactions, metallic bonding, and attraction for valence electrons in determining the sign on DeltaH in this reaction.

1. If the heats of hydration for Cu2+ and Zn2+ are -2289 and -2247 kJ/mol, respectively, which ion is more tightly bound to water molecules in solution?
impossible to tell from this data aloneZn
Cu
2. If the heats of formation for Cu(g) and Zn(g) are 337.4 and 130.4 kJ/mol, respectively, which metal probably has stronger metallic bonding?
impossible to tell from this data aloneCu
Zn
3. If the formation of Cu2+(g) from Cu(g) absorbs 2703 kJ/mol, and the formation of Zn(g) from Zn2+(g) releases 2640 kJ/mol, give the reaction enthalpy for

Zn(g) + Cu2+(g) = Cu(g) + Zn2+(g)

+63 kJ-63 kJ+5343 kJnone of these-5343 kJ
4. The calculation outlined on this page suggests that displacement of Cu2+ ions from solution by zinc metal is exothermic because:
zinc ions release more heat than copper ions when hydrated
copper is harder to ionize than zinc
metallic bonding in copper is stronger than in zinc
copper holds on to its valence electrons more tightly than zinc

References

  1. Heats of formation and ionization energies were adapted from data given in the CRC Handbook of Chemistry and Physics, 58th ed.
  2. Enthalpies of hydration were converted from Fajan's data given in Physical Chemistry, E. A. Moelwyn-Hughes, 2nd ed., Pergamon, Belfast 1961, p. 875. The original reference is Z. Elektrochem., 34, 502 (1928).

Author: Fred Senese senese@antoine.frostburg.edu


General Chemistry Online! Why are metal displacement reactions exothermic?

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