I admire the enthusiasm (and promise) the younger members show.
(Everyone is younger than me.
)
You need a mentor to point you in the right direction!
Was this posted on the High School forum? If so this explanation will probably
be over your head.
Consider the formation of PX5 (X = H, F, Cl, Br) from PX3
X3P: + X2 ⇋ PX5
-RTlnKeq = ΔG = ΔH - TΔS Let us ignore the ΔS term even though there is loss of entropy in forming the product (why?).
The ΔHrxn term may be broken down into three steps:
(1) Promotion energy: energy need to take a lone pair sp3 electron and place it in a 3d atomic orbital:
P 3s23p4(P:F bonds)p(↑↓)(lp) → P 3s23p4p(↑)3d(↑) ΔHprom +ve
We can also lump the reorganization energy into this term as well (change of F-P-F angles when forming the product)
and steric interactions. Electron excitation energies are large and positive.
(2) Dissociation energy of X2:
X2(g) → 2X. ΔHdiss +ve
(3) Energy of formation of two new P:X bonds = 2ΔHform(P-X) (-ve)
Hence ΔHrxn = ΔHprom + ΔHdiss(X2) + 2ΔHform(P-X)
Take ΔHprom = 340 kJ mol^-1 (I know I am fixing the result!) and get ΔHdiss(X2) and ΔHform(P-X) from the table.
If ΔHrxn is –ve it is thermodynamically allowed, if +ve it is not allowed
X ΔHdiss(X2) kJ mol^-1 ΔHform(P-X) kJ mol^-1
H 436 322
F 155 490
Cl 242 326
Br 193 264
Conclusion: the nonexistence of PBr5 could well be due steric factors,
but it is not the reason for the nonexistence of PH5. (What is the reason?)
P-Cl bond strength > As-Cl bond strength.
We can leave the discussion of why the P-X strengths vary the way they do to another day.
But it is a matter of overlap of the AOs.