254
6 The Thermodynamics of Solutions
The molar concentration of component i is defined by
c i
n i
V
(6.2-14)
where n i is the amount of the solute in moles and V is the volume of the solution. In SI
units the molar concentration is measured in moles per cubic meter (mol m −3 ). If the
molar concentration is measured in moles per liter (mol L −1 , sometimes abbreviated
as M), it is called the molarity. A common symbol for the molarity is the formula for
the substance inside square brackets:
c i [F i ]
(6.2-15)
where F i is an abbreviation for the formula of substance i. The molar concentration depends on the temperature because of thermal expansion, although the molality
does not.
E X A M P L E 6.7
Assuming that the coefficient of thermal expansion of an aqueous solution is the same as that
of water, 2.07 × 10 −4 K −1 , find the molarity at 25.0 ◦ C of a solution that has a molarity of
0.1000 mol L −1 at 20.0 ◦ C.
Solution
Consider a quantity of solution that has a volume at 20 ◦ C of 1.000 L. The amount of solute is
n 2 (0.1000 mol L −1 )(1.000 L) 0.1000 mol
At 25 ◦ C, the volume of the solution is
V (1.000 L)
1 + (2.0661 × 10 −4 K −1 )(5.0 K)
1.0010 L
The molarity (molar concentration) at 25.0 ◦ C is
c 2
0.1000 mol
1.0010 L
0.0999 mol L −1
In a dilute solution, the amounts of solutes are small and the volume of the solution
is nearly equal to the volume of the solvent used to make the solution
V ≈ n 1 V
∗
m,1
(6.2-16)
where V ∗
m,1 is the molar volume of the pure solvent (substance number 1). In this case
c i ≈
n i
n 1 V ∗
m,1
≈
x i
V ∗
m,1
(dilute solution)
(6.2-17)
E X A M P L E 6.8
Show that for a dilute solution, Henry’s law becomes
P i k i V ∗
m,1 c i k
(c)
i c i
(6.2-18)
6 The Thermodynamics of Solutions
The molar concentration of component i is defined by
c i
n i
V
(6.2-14)
where n i is the amount of the solute in moles and V is the volume of the solution. In SI
units the molar concentration is measured in moles per cubic meter (mol m −3 ). If the
molar concentration is measured in moles per liter (mol L −1 , sometimes abbreviated
as M), it is called the molarity. A common symbol for the molarity is the formula for
the substance inside square brackets:
c i [F i ]
(6.2-15)
where F i is an abbreviation for the formula of substance i. The molar concentration depends on the temperature because of thermal expansion, although the molality
does not.
E X A M P L E 6.7
Assuming that the coefficient of thermal expansion of an aqueous solution is the same as that
of water, 2.07 × 10 −4 K −1 , find the molarity at 25.0 ◦ C of a solution that has a molarity of
0.1000 mol L −1 at 20.0 ◦ C.
Solution
Consider a quantity of solution that has a volume at 20 ◦ C of 1.000 L. The amount of solute is
n 2 (0.1000 mol L −1 )(1.000 L) 0.1000 mol
At 25 ◦ C, the volume of the solution is
V (1.000 L)
1 + (2.0661 × 10 −4 K −1 )(5.0 K)
1.0010 L
The molarity (molar concentration) at 25.0 ◦ C is
c 2
0.1000 mol
1.0010 L
0.0999 mol L −1
In a dilute solution, the amounts of solutes are small and the volume of the solution
is nearly equal to the volume of the solvent used to make the solution
V ≈ n 1 V
∗
m,1
(6.2-16)
where V ∗
m,1 is the molar volume of the pure solvent (substance number 1). In this case
c i ≈
n i
n 1 V ∗
m,1
≈
x i
V ∗
m,1
(dilute solution)
(6.2-17)
E X A M P L E 6.8
Show that for a dilute solution, Henry’s law becomes
P i k i V ∗
m,1 c i k
(c)
i c i
(6.2-18)