Question

The average P-P bond enthalpy in $ {{\text{P}}_{\text{4}}} $ molecule is-

A) $ 102KJ $
B) $ 201KJ $
C) $ 104KJ $
D) $ 120KJ $

Answer 1

Hint :The white phosphorous is in solid form so it will first change into gaseous form. First we need to know the enthalpy of sublimation and atomization of Phosphorus molecule $ {{\text{P}}_{\text{4}}} $ .Then, Find the number of bonds in P-P.
Formula used-Average enthalpy= (Enthalpy of atomization-Enthalpy of sublimation)/no. of bonds.

Complete Step By Step Answer:
Given, Change in Enthalpy $ = - 104{\text{ }}KJ/mol $
We know that white phosphorus exists as molecules made up of 4 atoms in tetrahedral structure. Each mole of $ {{\text{P}}_{\text{4}}} $ has $ 6 - 6 $ bonds.
We know that white phosphorus exists in a solid state so to perform the reaction first it will be converted into gaseous state. The reaction is given as-
 $ {P_4}\left( s \right) \to {P_4}\left( g \right) $
In this reaction first the bonds between molecules of phosphorus are broken to obtain the atoms in gaseous state so the energy required to break the bonds is called atomization energy. Here, the enthalpy of atomization is $ 1265KJ/mol $ .
But since the molecule undergoes phase transition so some energy is required to change the phase from solid state to liquid state which is called sublimation energy. So the enthalpy of sublimation is $ 59KJ/mol $ .(These are the standard values we are using since it is not given in the question).
 Now we will use a formula to find the average bond enthalpy.
Average Enthalpy= (Enthalpy of atomization-enthalpy of sublimation)/No. of bonds
On putting the given values in the formula, we get-
Average enthalpy= $ \dfrac{{1265 - 59}}{6} = 201 $ KJ
Hence, the correct answer is option B.

Additional Information:
Phosphorus is an element which does not exist in nature in Free State, it is always found in a combined state. Its two main forms exist-
Red Phosphorous- which is an amorphous solid. It is an allotrope of phosphorus which is deep red in color. It is non-toxic. It is also more stable than white phosphorus.
White Phosphorous-It is a waxy solid which is poisonous in nature. It glows in the dark and is flammable when it reacts with oxygen present in the air.

Note :
Phosphorus is used as-
Red phosphorus is used as a flame retardant in thermosetting polymers.
It is used as a smoke device that quickly creates a smoke screen.
It is used in making emergency flares.
White phosphorus is used in incendiary devices.
Phosphorus is also used as fertilizer and in production of steel.