Page 32 - Modern Analytical Chemistry

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Chapter 2 Basic Tools of Analytical Chemistry 15

Since the relative uncertainty in both measurements is roughly 1% (101 ±1, 99 ±1),
the relative uncertainty in the final answer also must be roughly 1%. Reporting the
answer to only two significant figures (1.0), as required by the general rules, implies
a relative uncertainty of 10%. The correct answer, with three significant figures,
yields the expected relative uncertainty. Chapter 4 presents a more thorough treat-
ment of uncertainty and its importance in reporting the results of an analysis.
Finally, to avoid “round-off ” errors in calculations, it is a good idea to retain at
least one extra significant figure throughout the calculation. This is the practice
adopted in this textbook. Better yet, invest in a good scientific calculator that allows
you to perform lengthy calculations without recording intermediate values. When
the calculation is complete, the final answer can be rounded to the correct number
of significant figures using the following simple rules.
1. Retain the least significant figure if it and the digits that follow are less than
halfway to the next higher digit; thus, rounding 12.442 to the nearest tenth
gives 12.4 since 0.442 is less than halfway between 0.400 and 0.500.
2. Increase the least significant figure by 1 if it and the digits that follow are more
than halfway to the next higher digit; thus, rounding 12.476 to the nearest tenth
gives 12.5 since 0.476 is more than halfway between 0.400 and 0.500.
3. If the least significant figure and the digits that follow are exactly halfway to the
next higher digit, then round the least significant figure to the nearest even
number; thus, rounding 12.450 to the nearest tenth gives 12.4, but rounding
12.550 to the nearest tenth gives 12.6. Rounding in this manner prevents us
from introducing a bias by always rounding up or down.

2B Units for Expressing Concentration
Concentration is a general measurement unit stating the amount of solute present concentration
in a known amount of solution An expression stating the relative
amount of solute per unit volume or

amount of solute unit mass of solution.
Concentration = 2.1
amount of solution

Although the terms “solute” and “solution” are often associated with liquid sam-
ples, they can be extended to gas-phase and solid-phase samples as well. The actual
units for reporting concentration depend on how the amounts of solute and solu-
tion are measured. Table 2.4 lists the most common units of concentration.

2B.1 Molarity and Formality
Both molarity and formality express concentration as moles of solute per liter of solu-
tion. There is, however, a subtle difference between molarity and formality. Molarity molarity
is the concentration of a particular chemical species in solution. Formality, on the The number of moles of solute per liter
other hand, is a substance’s total concentration in solution without regard to its spe- of solution (M).
cific chemical form. There is no difference between a substance’s molarity and for-
mality if it dissolves without dissociating into ions. The molar concentration of a so- formality
The number of moles of solute,
lution of glucose, for example, is the same as its formality.
regardless of chemical form, per liter of
For substances that ionize in solution, such as NaCl, molarity and formality are solution (F).
different. For example, dissolving 0.1 mol of NaCl in 1 L of water gives a solution
+
–
containing 0.1 mol of Na and 0.1 mol of Cl . The molarity of NaCl, therefore,
is zero since there is essentially no undissociated NaCl in solution. The solution,