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Yes, I got phosphorus as well. The total number of valence electrons counted from the Lewis structure is 32 electrons. Subtracting 21 electrons for 3 chlorine atoms and 6 electrons for the oxygen, you obtain 5 valence electrons. The element in period 3 with 5 valence electrons is phosphorus.
For these types of questions, first find out how many valence electrons the unknown element adds to the total amount of electrons in the molecule. Take the total amount of electrons in the molecule and subtract the number of valence electrons of the known elements. For this specific problem, you end up with the unknown element having 5 valence electrons, and phosphorous is the one that fits the description.
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