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remember it is not technically breaking bonds, as in covalent bonds between Hydrogen and Oxygen molecules. It is breaking intermolecular forces between water molecules. Therefore, energy is needed to overcome and break the intermolecular forces which requires heat.
It is important to distinguish between breaking bonds and breaking the intermolecular attractions between molecules in a substance. During phase changes, the chemical bonds in the molecules of the substance aren't actually being broken. Rather, the energy added is being used to break the attractions between molecules in the substance. However the substance remains the same, so when water is evaporated it doesn't turn into H2 and O, it stays H2O.
The temperature stays the same because the energy going into the system is used to change the phase of the substance and not increase the temperature. Once the phase change is complete the temperature starts rising again.
Additionally, more heat energy is required to break bonds when a substance is vaporizing (liquid to gas) as opposed to when a substance is melting (solid to liquid) because bonds have to be completely broken in the gas phase.
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