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Does chloroform have a greater dipole because the $\ce{C-H}$ dipole is weaker than $\ce{C-Cl}$ dipole thereby making the overall net dipole greater in chloroform, as opposed to trichlorofluoromethane where the $\ce{C-F}$ bond dipole being more similar to the $\ce{C-Cl}$ dipole makes the molecule more stable with a smaller net dipole?

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    $\begingroup$ C-H and C-F dipoles are in opposite directions; which of them has greater absolute value is not immediately obvious. $\endgroup$ – Ivan Neretin Mar 2 at 6:16
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$\ce{C-Cl}$ in $\ce{CHCl3}$ all lies in same direction and hence net vector sum is downwards, which makes it's dipole moment greater, while in $\ce{CFCl3}$ three $\ce{C-Cl}$ bonds are in same direction while one $\ce{C-F}$ lies in opposite direction to them thus while adding dipoles as vectors we need to subtract dipole of $\ce{C-F}$ from dipole of three $\ce{C-Cl}$ thus reducing net dipole moment.

Hence dipole moment of $\ce{CHCl3}$ is greater than $\ce{CFCl3}$ .

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