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Considering the nonmetals what is the relationship between the group number for an element (carbon, for example, belongs to group 4a; see the periodic table on the inside front cover) and the number of single covalent bonds that element needs to form to conform to the octet rule

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The Octet rule is essential to obey nature's law of stability. Among all the elements in the periodic table, the noble gases in Group 8 are the most stable in. Hence, all the other elements aim to achieve their electronic configuration. So, all elements must bond with others to conform to be a part of group 8. 

Bonds for non metals = 8 - Group number
Ex:
Bonds for oxygen = 8 - 4 = 4
Bonds for nitrogen = 8 - 5 = 3

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