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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.
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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.
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If a molecule is symmetrical (such as BH
3
, which is trigonal planar), the individual dipoles associated with the covalent bonds cancel, leaving a molecule with no molecular dipole.
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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
.
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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
.
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You should remember that
concentration
multiplied by
volume
gives the number of
moles
of solute; (
moles/L
)×
L=moles.
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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
; \[\frac{\left ( \frac{grams}{grams/mole} \right )}{L}=molarity \nonumber \]
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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.
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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 V
1
C
1
= V
2
C
2
, where the subscripts refer to the initial and final concentrations and volumes.