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Intermolecular forces are weaker than intramolecular forces. Intramolecular forces in this case include bonding forces within a molecule from ionic and covalent bonds. Intermolecular forces are forces between different molecules and include things like London dispersion forces, Van der Waals forces, and dipole-dipole interactions. Intramolecular forces are stronger because they involve the actual sharing of electrons for covalent bonds. This sharing of electrons gives each element of the bond an octet of electrons in the valence shell which is a highly stable electronic configuration. Ionic bonds involve strong electrostatic interactions between ions. By comparison, intermolecular interactions do not involve the sharing or transfer or electrons and electrostatic interactions like hydrogen bonding only involve partial charges, not fully charged ions.
Molecules are electrically neutral; they contain equal numbers of positively charged protons and negatively charged electrons (often in a complicated arrangement). Portions of a molecule may have some degree of electrical charge because the charges within a molecule are unevenly distributed. For example, a water molecule is slightly negative where the oxygen atom is and slightly positive where the hydrogen atoms are. Ions, in comparison, have electrical charges, because they have either lost or gained electrons. Since all these forces, both the ionic bonds and the intermolecular forces, derive from electrostatic forces as described by Coulomb's Law, the greater the difference in charge, the greater the resulting force. Charged ions must necessarily exert more force than uncharged molecules.
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