Why is carbon's covalent bond stronger than oxygen bond to hydrogen?

This has to do with electronegativity, which is the affinity an atom has for electrons. Oxygen is more electronegative than carbon, so it has a greater affinity for the electrons that make up the covalent bond. This means that it is much easier for the oxygen atom to sort of kidnap the electrons away from the bond, leaving a positive hydrogen ion and a negative oxygen ion.In a C-H bond, the electrons are shared more equally between the two atoms, making the bond stronger.

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