This reaction is already in the literature (peer-reviewed paper), so I don't want to change any outcome already explained by Waylander. But, I like to explore the reaction a bit more for the benefit of novice students of organic chemistry. The reaction seemingly follows the same mechanism as that of a general free radical reaction: Initiation; propagation; and termination. The starting material is active enough to get initiated by light:
$$\ce{Br-CCl3 ->[$h\nu$] Br^. + ^.CCl3} \tag1$$
$$\ce{Ph-CH3 + Br^. -> Ph-CH2^. + HBr} \tag2$$
Now propagation begins:
$$\ce{Ph-CH2^. + Br-CCl3 -> Ph-CH2-Br + ^.CCl3} \tag3$$
$$\ce{Ph-CH3 + ^.CCl3 -> Ph-CH2^. + HCCl3} \tag4$$
After all limiting reagent is used up, the remaining radicals react with each other to terminate the reaction:
$$\ce{Cl3C^. + ^.CCl3 -> Cl3C-CCl3} \tag5$$
According to the reactions shown in the original paper (Ref.1), the most probable limiting reagent should be toluene. If that's the case, the propagation ends at equation $(3)$ after going through many propagation cycles. At the end, what remains are
two $\ce{^.CCl3}$ radicals from the equation $(1)$ and last circle of the equation $(3)$. The reaction ends with dimerization of these two radicals.
As pointed out by Waylander, the ratio of $\ce{HBr:Ph-CH2Br}$ is ~$1:20$. This result supports the mechanism since formation of $\ce{HBr}$ is only by the initiation reaction $(2)$. The formation of $\ce{Ph-CH2Br}$ is by the propagation (chain) reactions $(23)$ and $(4)$, hence the larger portion. For the same reason, amounts of $\ce{Ph-CH2Br}$ and $\ce{CHCl3}$ are equimolar.
Note: When the same reaction applied to toluene derivatives with substituted aromatic nucleus, a relatively large polar effect was found in the reaction rates. The effect is depend on $\sigma^+$-values of the substituents (Ref.2).
References:
- Earl S. Huyser, "The Photochemically Induced Reactions of Bromotrichloromethane with Alkyl Aromatics," J. Am. Chem. Soc. 1960, 82(2), 391–393 (https://doi.org/10.1021/ja01487a034).
- Earl S. Huyser, "Relative Reactivities of Substituted Toluenes Toward Trichloromethyl Radicals," J. Am. Chem. Soc. 1960, 82(2), 394–396 (https://doi.org/10.1021/ja01487a035).