7.S: Aqueous Solutions (Summary)

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Covalent bonds formed between atoms of differing electronegativity are polarized, resulting in a bond that is electron-rich on one end and electron-poor on the other. Covalent bonds that are polarized are said to have a dipole, where the term dipole moment refers to the direction and magnitude of the charge separation.
If a molecule is asymmetric (such as a molecule with a bend structure) local dipoles along covalent bonds can combine, generating a molecular dipole, in which the entire molecule has an imbalance with regard to electron distribution. This can be shown with an dipole arrow (with a positive end) indicating the direction of the charge separation in the molecule.
If a molecule is symmetrical (such as BH₃, which is trigonal planar), the individual dipoles associated with the covalent bonds cancel, leaving a molecule with no molecular dipole.
Water has a significant molecular dipole, allowing it to strongly interact with other polar molecules and with individual ions from ionic compounds. Because of this, water is able to break the electrostatic attraction between ions in compounds and to move the ions into solution. In solution, cations will be surrounded by a solvation shell where the water molecules are oriented so that the negative end of the water molecule interacts with the cation. Likewise, the cationic end of water will surround and solvate anions.
Molarity is simply defined as the number of moles of a solute dissolved in one liter of solvent, or (moles/L). The abbreviation for molarity is the uppercase M.
You should remember that concentration multiplied by volume gives the number of moles of solute; (moles/L)×L=moles.
When you are given the amount of solute in grams, remember, mass divided by molar mass gives moles. Dividing this by volume (in liters) gives molarity; \[\frac{\left ( \frac{grams}{grams/mole} \right )}{L}=molarity \nonumber \]
In a standard solution, we simply know the molarity of the solute(s). Because concentration (the molarity) multiplied by volume gives us moles, we can calculate the number of moles in given volume and use this value in standard stoichiometric calculations.
A sample of a solution of known volume is called an aliquot. When an aliquot of a solution is diluted into a larger volume, the final concentration can be calculated as: \[\left ( \frac{volume\; of\; the\; aliquot}{final\; volume} \right )=\left ( \frac{final\; concentration}{stock\; concentration} \right ) \nonumber \] or \[\left ( \frac{V}{V_{f}} \right )=\left ( \frac{C_{f}}{C_{i}} \right ) \nonumber \] where C_i and C_f are the stock and final concentrations, respectively, V is the volume of the aliquot and V_f is the final volume of the solution. This relationship is also often stated as V₁C₁ = V₂C₂, where the subscripts refer to the initial and final concentrations and volumes.