Bond length comparison in substituted phosphorus pentahalide

Question

What would be the comparison between $\ce{P-F}$ and $\ce{P-Cl}$ bond length in phosphorus tetrafluoride chloride $\ce{PF4Cl}$ and phosphorus trifluoride dichloride $\ce{PF3Cl2}$ in the equitorial hybrid orbital arrangements?

While determining the bond length between the two compounds I am using Bent's rule, since in the case of $\ce{PF4Cl}$ there are two $\ce{F}$ atoms in equatorial region and thus they decrease their %s character in turn resulting in a larger bond length and since there are two $\ce{F}$ atoms here the %s would be relatively less as compared to the $\ce{P-F}$ bond in $\ce{PF3Cl2}$, so this decrease in %s character in flourine atom should result in increase of %s character in $\ce{P-Cl}$ bond and reducing the bond length and $\ce{P-F}$ bond length would be greater in $\ce{PF4Cl}$.

8. Bond lengths (pm) in substituted phosphorous pentahalides are given below:

$$ \begin{array}{lcc} & \ce{PF4Cl} & \ce{PF3Cl2} \\ \ce{P-F_{eq}} & x & y \\ \ce{P-Cl_{eq}} & a & b \end{array} $$

$$\text{(I)}~x > y \qquad \text{(II)}~y > x \qquad \text{(III)}~a > b \qquad \text{(IV)}~b > a$$

Choose correct code:

(a) Only I
(b) II and IV
(c) I and III
(d) Only IV

So if I'm assuming things right my answer about the $\ce{P-F}$ bond length is right, but here in the option for $\ce{P-Cl}$ bond length is that it's greater in $\ce{PF4Cl}$. Why? Can someone please explain?

Answer 1

According to (1) and (2), the values in your table would be as follows (all values in Å):

$$\begin{array}{c c c} & \ce{PF4Cl} & \ce{PF3Cl2} \\ \ce{P-F_{eq}} & 1.541 & 1.546 \\ \ce{P-Cl_{eq}} & 1.999 & 2.004 \\ \end{array}$$

we have $x < y$ and $a < b$, which means that (b) is the correct answer

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According to Bent's rule:

atomic s character concentrates in orbitals directed towards electropositive substituents

Bonds with larger s-character are shorter in nature. Keeping these two points in mind and analyzing the structures, in $\ce{PF4Cl}$, almost all the s-character is directed towards $\ce{Cl}$, which means that $\ce{P-Cl}$ bond length in $\ce{PF4Cl}$ is less than that in $\ce{PF3Cl2}$. Similarily, considering that the $\mathrm{sp^3d}$ hybridization can be considered as $\mathrm{sp^2+pd}$, in the equatorial plane, the s-character shared between the two fluorine atoms in $\ce{PF4Cl}$ would be more than the s-character given to the single fluorine atom in $\ce{PF3Cl2}$, hence the shorter bond length.

Another perspective is that the above set of arguments are largely hand-waving, as Bent's rule is at best empirical and the bond length differences are $\pu{\approx 5 pm}$, which is very small. An easier question would be to compare bond lengths between $\ce{PCl5}$, $\ce{PF3Cl2}$ and $\ce{PF5}$, but for this question, I don't have a 'solid' explanation per se, other than the lengths from the references and the elaboration of Bent's rule above.

References:

1. Leiding, Jeff, et al. “Bonding in PF2Cl, PF3Cl, and PF4Cl: Insight into Isomerism and Apicophilicity from Ab Initio Calculations and the Recoupled Pair Bonding Model.” Theoretical Chemistry Accounts, vol. 133, no. 2, Feb. 2014, p. 1428. doi:10.1007/s00214-013-1428-7.
2. French, Richard J., et al. “Dichlorotrifluorophosphorane (PCl2F3): Molecular Structure by Gas-Phase Electron Diffraction and Quadratic Force Field.” Inorganic Chemistry, vol. 24, no. 18, Aug. 1985, pp. 2774–77. doi:10.1021/ic00212a014