Is it compulsory to read periodic classification of elements before chemical bonding or Can I start chemical bonding before periodic classification?

Actually chemical bonding is based on the Atomic number and electronic configuration. And the main thing is valency which is based on the number of outer(valence) electrons. Valency decides that how many bonds can be made by an atom . Thus if you ignore periodic table, you have to learn atomic number and electronic configuration

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The electrons that gain enthalpy for metals is positive and negative for non metals. Also, if metals are bigger in size than non metals then, how can electrons gain enthalpy is inversely proportional to the atomic size?

The answer is simple, like you are hungry you can pay more to get the food than that of the person who is less hungry, Similarily here the non metals want electrons thus they spend the energy more , or they release the energy. By this they lose the energy. So smaller is the size

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