Phosphorus Allotropes Exercises

Some of these questions make reference to the assigned papers for today, so please make sure to read them before attempting to answer the questions below.
  1. Is liquid P4 considered to be an allotrope of solid P4 (m.p. 44 °C)? Explain.
  2. What does it mean for P4 to be in a "plastic" phase at room temperature?
  3. Sketch out a predicted photoelectron spectrum for P4; here, you may find it helpful to refer to the interactive MO applet. Please note that the calculated orbital energies reported in the interactive applet do not correspond very well to the experimental PES ionization energies. Make an adjustment for this in your sketch by taking into account the fact that the experimental spectrum reveals ionization energies in the energy range from 8-12 electron volts. In addition, only MO numbers 21-26 are represented in the experimental spectrum in the 8-12 eV range, so only include the expected peaks corresponding to those MOs in your sketch. Label each peak in your sketch with the appropriate Mulliken symbol.
  4. Taking into consideration the detailed appearance of the HOMO for P4, predict the structure of [HP4]+ (i.e., protonated P4) and assign your predicted structure to its proper point group.
  5. What would need to be the charge on SP3 in order for this cluster to fulfill the criterion for spherical aromaticity?
  6. Viewing P4 as an example of a spherical aromatic system, how many filled pi type molecular orbitals does the system have?
  7. Considering the bond angles in P4, one might assume that this is a strained molecule, but the high thermal stability of P4 and the fact that no other all-phosphorus molecules are known experimentally suggest that this is a very stable structure. Take into account the molecular orbitals of P4, and comment on the issue of strain in this system.
  8. Using the interactive applets, examine and compare the experimentally determined structures of white, red, and black phosphorus. Write down the P-P bond distances, and comment on how sensitive is the P-P bond distance to the structure type.
  9. Write a balanced equation corresponding to the industrial synthesis of elemental phosphorus.
  10. What phosphorus compound is used as the electrolyte in lithium-ion batteries?