Explain why alkyl halides , though polar , are immiscible with water?

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The alkyl halides are polar in nature , but the molecules in them are strongly held by the hydrogen bonds formed between H and X (halide = F, Cl, Br atoms). these bonds are not easily broken, a lot of energy is required to break this interaction. Even the heat released at the time of interaction between water and halogens is not enough to break the hydrogen bond between H and X.

So being polar in nature still the alkyl halides are immiscible in water.

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