Page 283 - Physical Chemistry

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Chapter 9 M in (9.3) is the solvent molar mass (not molecular weight) and must have the proper
A
Solutions dimensions. The molecular weight is dimensionless, whereas M has units of mass per
A
mole (Sec. 1.4). The units of M are commonly either grams per mole or kilograms
A
per mole. Chemists customarily use moles per kilogram as the unit of molality.
Therefore it is desirable that M in (9.3) be in kg/mol. Note that it is the mass of the
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solvent (and not the solution’s mass) that appears in the molality definition (9.3).
The weight percent of species B in a solution is (w /w) 100%, where w is the
B
B
mass of B and w is the mass of the solution. The weight fraction of B is w /w.
B
Since V of a solution depends on T and P, the concentrations c change with
i
changing T and P. Mole fractions and molalities are independent of T and P.
EXAMPLE 9.1 Solution composition

An aqueous AgNO solution that is 12.000% AgNO by weight has a density
3
3
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1.1080 g/cm at 20°C and 1 atm. Find the mole fraction, the molar concentration
at 20°C and 1 atm, and the molality of the solute AgNO .
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The unknowns are intensive properties and do not depend on the size of the
solution. We are therefore free to choose a convenient fixed quantity of solution
to work with. We take 100.00 g of solution. In 100.00 g of solution there are
12.00 g of AgNO and 88.00 g of H O. Converting to moles, we find n(AgNO )
2
3
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0.07064 mol and n(H O) 4.885 mol. Therefore x(AgNO ) 0.07064/
2
3
4.955 0.01425. The volume of 100.00 g of this solution is V m/r
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(100.00 g)/(1.1080 g/cm ) 90.25 cm . The definitions c n /V and m
3
3
i
i
i
n /w [Eqs. (9.1) and (9.3)] give
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i
3
4
c1AgNO 2 10.07064 mol2>190.25 cm 2 7.827 10 mol>cm 3
3
4
3
3
3
17.827 10 mol>cm 2110 cm >1 L2 0.7827 mol>L
3
m1AgNO 2 10.07064 mol2>188.0 g2 0.8027 10 mol>g
3
3
3
10.8027 10 mol>g2110 g>kg2 0.8027 mol>kg
In this example, the weight percent was known, and it was convenient to
work with 100 g of solution. If the molarity is known, a convenient amount of
solution to take is 1 L. If the molality is known, it is convenient to work with an
amount of solution that contains 1 kg of solvent.
Exercise
A solution is prepared by dissolving 555.5 g of sucrose, C H O , in 750 mL
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11
12
of water and diluting with water to a final volume of 1.0000 L. The density of
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the final solution is found to be 1.2079 g/cm . Find the sucrose mole fraction,
molality, and weight percent in this solution. (Answers: 0.04289, 2.488 mol/kg,
45.99%.)
9.2 PARTIAL MOLAR QUANTITIES
Partial Molar Volumes
Suppose we form a solution by mixing at constant temperature and pressure n , n ,
1 2
..., n moles of substances 1, 2, ..., r. Let V* , ..., V* be the molar volumes of
r m,1 m,r
pure substances 1, 2, ..., r at T and P, and let V* be the total volume of the unmixed