37 9.2 Solution Stoichiometry

Water is by far the most important liquid solvent, partly because it is plentiful and partly because of its unique properties. In your body, in other living systems, and in the outside environment a tremendous number of reactions take place in aqueous

solutions. Consequently this section, as well as significant portions of many subsequent sections, will be devoted to developing an understanding of reactions which occur in water. Since ionic compounds and polar covalent compounds constitute the main classes which are appreciably soluble in water, reactions in aqueous
solutions usually involve these types of substances.

There are three important classes of reactions which occur in

aqueous solution: precipitation reactionsacid-
  • Precipitation reactions are useful for detecting the presence of various
    ions and for determining the concentrations of
  • Acid-
    base reactions and redox reactions are similar in that something is being transferred from one species to another.
    • Acid-base reactions involve proton transfers, while redox reactions involve electron transfers.
    • Redox reactions are somewhat more complicated, though, because proton transfers and other bond-making and bond-breaking processes occur at the same time as electron transfer.



In Binary Ionic Compounds and Their Properties we point out that when an ionic compound dissolves in water, the positive and negative


 originally present in the crystal lattice persist in solution. Their ability to move nearly independently through the solution permits them to carry positive or negative electrical charges from one place to another. Hence the solution conducts an electrical current.


Substances whose solutions conduct electricity are called electrolytes. All soluble ionic compounds are

strong electrolytes

. They conduct very well because they provide a plentiful supply of


 in solution. Some polar covalent compounds are also

strong electrolytes

. Common examples are HCl, HBr, HI and H2SO4, all of which react with H2O to form large concentrations of


. A solution of HCl, for example, conducts even better than one of NaCl having the same



Figure A shows a solution with many charged particles to represent the ions. The electrical measuring device connected to the opposite poles and the battery has the largest reading. Figure B shows a moderate number of ions and has a moderate current measurement while Figure C with the least ions has the least reading on the device.
Figure The conductivity of electrolyte

: (a) 0.1 M NaCl (b) 0.05 M NaCl (c) 0.1 M HgCl2. An electrolyte solution conducts electricity because of the movement of


in the solution (see above). The larger the concentration of ions, the better the solutions conduct.

Weak electrolytes, such as HgCl2, conduct badly because they produce few ions when dissolved (low concentration of ions) and exist mainly in the form of molecules.

The effect of the concentration of ions on the electrical current flowing through a solution is illustrated in Figure Part a of the figure shows what happens when a battery is connected through an electrical meter to two inert metal strips (electrodes) dipping in ethanol. Each cubic decimeter of such a solution contains 0.10 mol NaCl (that is, 0.10 mol Na+ and 0.10 mol Cl). An electrical current is carried through the solution both by the Na+ ions moving toward the negative electrode and by the Cl ions which are attracted toward the positive electrode. The dial on the meter indicates the quantity of current.

Figure 1b shows that if we replace the 0.10-M NaCl solution with a 0.05-M NaCl solution, the meter reading falls to about one-half its former value. Halving the

concentration of NaCl halves the number of ions between the electrodes, and half as many ions can only carry half as much electrical charge. Therefore the current is half as great. Because it responds in such a direct way to the concentration of ions, conductivity of electrical current is a useful tool in the study of solutions.

Conductivity measurements reveal that most covalent compounds, if they dissolve in water at all, retain their original molecular structures. Neutral molecules cannot carry electrical charges through the solution, and so no current flows. A substance whose aqueous solution conducts no better than water itself is called a nonelectrolyte. Some examples are oxygen, O2, ethanol, C2H5OH, and sugar, C12H22O11.

A repeating structure of mercury bromide represented by different colored circles. Two red circles of bromine is attached to each black circle which represents mercury.
Figure Mercury Bromide Crystals.

Some covalent substances behave as weak electrolytes—their solutions allow only a small current flow, but it is greater than that of the pure solvent. An example is mercury(II) chloride (seen in the Figure above). For a 100-M HgCl2 solution the meter reading shows only about 0.2 percent as much current as for 0.10 M NaCl. A crystal of HgCl2 consists of discrete molecules, like those shown for HgBr2 in Figure When the solid dissolves, most of these molecules remain intact, but a few dissociate into ions according to the equation


(The double arrows indicate that the ionization proceeds only to a limited extent and an

equilibrium state is attained.) Since only 0.2 percent of the HgCl2 forms ions, the 0.10 M solution can conduct only about 0.2 percent as much current as 0.10 M NaCl.

Conductivity measurements can tell us more than whether a substance is a strong, a weak, or a nonelectrolyte. Consider, for instance, the data in Table which shows the electrical current conducted through various aqueous

solutions under identical conditions. At the rather low
concentration of 0.001 M, the strong electrolyte
solutions conduct between 2500 and 10 000 times as much current as pure H2O and about 10 times as much as the
weak electrolytes

 HC2H3O2 (acetic acid) and NH3 (ammonia).

Closer examination of the data for

strong electrolytes reveals that some compounds which contain H or OH groups [such as HCl or Ba(OH)2] conduct unusually well. If these compounds are excluded, we find that 1:1 electrolytes (compounds which consist of equal numbers of +1 ions and –1 ions) usually conduct about half as much current as 2:2 electrolytes (+2 and -2
ions), 1:2 electrolytes (+1 and -2 ions), or 2:1 electrolytes (+2 and -1 ions).
TABLE Electrical Current Conducted Through Various 0.001 M Aqueous
Substance Current /mA Substance Current /mA
Pure Water 1:2 Electrolytes
H2O 3.69 x 10-4 Na2SO4 2.134
Weak Electrolytes
Na2CO3 2.24
HC2H3O2 0.41 K2CO3 2.660
NH3 0.28 2:1 Electrolytes
1:1 Electrolytes MgCl2 2.128
NaCl 1.065 CaCl2 2.239
NaI 1.069 SrCl2 2.290
KCl 1.273 BaCl2 2.312
KI 1,282 Ba(OH)2 4.14
AgNO3 1.131 2:2 Electrolytes
HCl 3.77 MgSO4 2.00
HNO3 3.75 CaSO4 2.086
NaOH 2.08 CuSO4 1.97
KOH 2.34 ZnSO4 1.97

* All measurements refer to a cel1 in which the distance between the electrodes is 1.0 mm and the area of each electrode is 1.0 cm². A potential difference of 1.0 V is applied to produce the tabulated currents.

There is a simple reason for this behavior. Under similar conditions, most

ions move through water at comparable speeds. This means that
ions like Mg2+ or SO42–, which are doubly charged, will carry twice as much current through the solution as will singly charged
ions like Na+ or Cl. Consequently, a 0.001 M solution of a 2:2 electrolyte like MgSO4 will conduct about twice as well as a 0.001 M solution of a 1:1 electrolyte like NaCl.

A similar argument applies to

solutions of 1:2 and 2:1 electrolytes. A solution like 0.001 Na2SO4 conducts about twice as well as 0.001 M NaCl partly because there are twice as many Na
ions available to move when a battery is connected, but also because SO42–
ions carry twice as much charge as Cl
ions when moving at the same speed. These differences in conductivity between different types of
strong electrolytes can sometimes be very useful in deciding what
ions are actually present in a given electrolyte solution as the following example makes clear.

A second, slightly more subtle, conclusion can be drawn from the data in Table When an electrolyte dissolves, each type of ion makes an independent contribution to the current the solution conducts. This can be seen by comparing NaCl with KCl, and NaI with KI. In each case the compound containing K+ conducts about 0.2 mA more than the one containing Na+. If we apply this observation to Na2CO3 and K2CO3, each of which produces twice as many Na+ or K+

ions in solution, we find that the difference in current is also twice as great—about 0.4 mA.

Thus conductivity measurements confirm our statement that each ion exhibits its own characteristic properties in aqueous

solutions, independent of the presence of other
ions. One such characteristic property is the quantity of electrical current that a given
concentration of a certain type of ion can carry.


At 18°C a 0.001-M

aqueous solution of potassium hydrogen carbonate, KHCO3, conducts a current of 1.10 mA in a
cell of the same design as that used to obtain the data in Table 11.1. What
ions are present in solution?


Referring to Table 6.2 which lists possible

polyatomic ions, we can arrive at three possibilities for the
ions from which KHCO3 is made:
  1. K+ and H+ and C4+ and three O2–
  2. K+ and H+ and CO32–
  3. K+ and HCO3

Since the current conducted by the solution falls in the range of 1.0 to 1.3 mA characteristic of 1:1 electrolytes, possibility c is the only reasonable choice.



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