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From counting up all the lone pairs and bonds, you can calculate the total number of valence electrons for the compound. In this case, there are 32 VE. The diagram shows you how many Cl and O atoms are in the compound, so using that you can calculate the number of VE that come from those two atoms. 32 VE= 3(7) + 6 + E --> 5VE. It says that the unknown element is in period #, therefore you can deduce that the element is P because it's the only element in period 3 with 5 VE.
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