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Periodic Table: the student needs to have a good understanding of why the periodic table is organized the way it is. Knowing roughly where the main atoms reside in the table will be a huge help.
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Periodic Trends: knowing why the elements are organized in rows and groups based on their electronic structures will allow the student to make predictions on properties when the elements show up in Organic molecules.
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Electronegativity: since Organic Chemistry is full of terms such as "electron-poor" and "electron-greedy" the student needs to have the ability to assess electron density patterns within a molecule quickly.
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Valence: the number of bonds an atom may form, and the number of lone pairs that are (or are not) present, will dictate the reactivity of organic molecules and their ability to act as nucleophiles or electrophiles.
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Atomic Size: related to periodic trends, the size of atoms will play a very important role in their ability to hold a negative charge as conjugate bases and as leaving groups in substitution and elimination reactions.
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Acids & Bases: first studied in General Chemistry, Organic acid-base reactions are the first time students are required to put together all of the concepts studied thus far, including the mechanism of the proton transfer process.