Stability of α-chlorocarbocations

Question

I'm trying to compare the relative stability of two carbocations:

$$\ce{CH3-\overset{+}{C}H-Cl}\quad\text{vs}\quad\ce{CH3-\overset{+}{C}H2}$$

Does the $\ce{Cl}$ exert a +M effect to stabilise the carbocation, or does it exert a −I effect to destabilise it?

Answer 1

As Oscar Lanzi suggested, both $+M$ and $-I$ applies here, but $\ce{Cl}$ stabilizes carbocation, meaning $+M$ is more effective than $-I$. This fact was confirmed by this peer-reviewed paper (Ref.1):

The lowering of $\ce{C_\beta–H}$ stretching frequencies in carbocations 1a–d and 2a–c induced by hyperconjugation was tested as a possible probe for estimating the electron donating ability of $\alpha$-substituents. Conclusions are based on the results of high level quantum chemical calculations confirmed with experimental FT-IR spectra. Because the decrease in the $\ce{C_\beta–H}$ stretching frequency is comparable in 1b and in 1c, and in 2b and 2c respectively, it follows that $\alpha$-substitution $\color{red}{\text{by a methyl group}}$ or $\color{red}{\text{by chlorine}}$ stabilizes a carbocation with $\color{red}{\text{almost the same effectiveness}}$.

The effect of the chlorine $n$-electron back donation is evident by a partially double bond character of the $\ce{C+–Cl}$ bond in $\alpha$-chlorocarbocations observed experimentally in IR spectra (Ref.2). In this experiment, FT-IR spectrum of $\ce{Cl3C+}$ cation has displayed the $\ce{C–Cl}$ stretching frequency at $\pu{1040 cm–1}$, which is $\pu{250 cm–1}$ higher than in neutral alkyl chlorides (e.g., characteristic $\ce{C–Cl}$ stretching frequency of $\ce{CCl4}$ is $\pu{785 cm-1}$). This is indicative of partial double bond character of $\ce{C+–Cl}$ bond suggested by the resonance structures:

$$\ce{Cl2C+-Cl <-> CH2C=Cl+}$$

The pioneering work of Olah and coworkers has also predicted this phenomena by $\ce{^{13}C}$-NMR studies of trihalocarbocations (Ref.3):

$$ \begin{array}{c|c|c|c} \ce{HCX3} & \delta\ce{^{13}C}\text{ of }\ce{CHX3} & \ce{^+CX3} & \delta\ce{^{13}C}\text{ of }\ce{^+CX3} & \Delta \delta\ce{^{13}C} \\ \hline \ce{HCCl3} & 77.7 & \ce{^+CCl3} & 236.3 & 158.6 \\ \ce{HCBr3} & 12.3 & \ce{^+CBr3} & 207 & 194.7 \\ \ce{HCI3} & -139.7 & \ce{^+CI3} & 95 & 234.7\\ \hline \end{array} $$

Olah has suggested that the decreasing trend of $\Delta \delta\ce{^{13}C}$ by going $\ce{I}$ to $\ce{Br}$ to $\ce{Cl}$ is in agreement with the positive charge stabilization by back-bonding in order of $\ce{Cl > Br > I}$.

References:

1. Milan Mesić, Igor Novak, Dionis E. Sunko, Hrvoj Vančik, "$\ce{C–H}$ Hyperconjugation in $\alpha$-chlorocarbocations," J. Chem. Soc., Perkin Trans. 2 1998, (11), 2371-2374 (https://doi.org/10.1039/A805772I).
2. Hrvoj Vančik, Ksenija Percač, Dionis E. Sunko, "Chloromethyl cations in cryogenic antimony pentafluoride matrixes and the generation of carbocations from hydrocarbons," J. Am. Chem. Soc. 1990, 112(20), 7418–7419 (https://doi.org/10.1021/ja00176a065).
3. George A. Olah, Ludger Heiliger, G. K. Surya Prakash, "Stable carbocations. Part 276. Trihalomethyl cations," J. Am. Chem. Soc. 1989, 111(20), 8020–8021 (https://doi.org/10.1021/ja00202a056).

Answer 2

You get both, but the +M effect wins. See the discussion of the effect of atoms with lone pairs over here.

Answer 3

I would say that many books suggest that +m effect overshines the -I effect but I feel it depend upon the reaction where thee intermediates are formed and type of reaction is happening and stability of intermediate involves the thermodynamics for a general exam like situation you can mark A is more stable than B.