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In a molecule of methane, carbon having four valence electrons binds to four hydrogen atoms how many lone pairs of electrons will be represented in the Lewis structure of methane

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None. To bind with an hydrogem atom, the carbon needs to ''share'' one of it's valence electron's with the hydrogen's valence electron. Therefore, forming 4 bounds means the carbon atom will share it's 4 valence electrons and there will be no lone electrons.
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