Chapter 3 - Experimental Error - WH Freeman

60 3 Experimental Error
Cheryl Cynthia Carmen Chastity Figure for Problem 3-12.
3-12. Cheryl, Cynthia, Carmen, and Chastity shot the targets
above at Girl Scout camp. Match each target with the proper
description.
(a) accurate and precise (c) precise but not accurate
(b) accurate but not precise (d) neither precise nor accurate
3-13. Rewrite the number 3.123 56 (0.167 89%) in the forms
(a) number ( absolute uncertainty) and (b) number ( percent
relative uncertainty) with an appropriate number of digits.
Propagation of Uncertainty
3-14. Find the absolute and percent relative uncertainty and
express each answer with a reasonable number of significant
figures.
(a) 6.2 (0.2) 4.1 (0.1) ?
(b) 9.43 (0.05) 0.016 (0.001) ?
(c) [6.2 (0.2) 4.1 (0.1)] 9.43 (0.05) ?
(d) 9.43 (0.05) {[6.2 (0.2) 10 3 ]
[4.1 (0.1) 10 3 ]} ?
3-15. Find the absolute and percent relative uncertainty and
express each answer with a reasonable number of significant
figures.
(a) 9.23 (0.03) 4.21 (0.02) 3.26 (0.06) ?
(b) 91.3 (1.0) 40.3 (0.2) / 21.1 (0.2) ?
(c) [4.97 (0.05) 1.86 (0.01)] / 21.1 (0.2) ?
(d) 2.016 4 (0.000 8) 1.233 (0.002) 4.61 (0.01) ?
(e) 2.016 4 (0.000 8) 10 3 1.233 (0.002) 10 2
4.61 (0.01) 10 1 ?
(f) [3.14 (0.05)] 1/3 ?
(g) log[3.14 (0.05)] ?
3-16. Verify the following calculations:
(a) 23.141 5 (0.001 1) 1.772 4 3 (0.000 3 1 )
(b) log[3.141 5 (0.001 1)] 0.497 1 4 (0.000 1 5 )
(c) antilog[3.141 5 (0.001 1)] 1.385 2 (0.003 5 ) 10 3
(d) ln[3.141 5 (0.001 1)] 1.144 7 0 (0.000 3 5 )
20.104 (0.006)
(e) loga 0.80 0 (0.01 5 )
0.051 1 (0.000 9) b
3-17. When using Class 1 standard weights (Table 2-1) to calibrate
your balance, you want to place exactly 1 g on the balance.
Is it more accurate to use a single 1-g weight or the combination
500 mg 200 mg 200 mg 100 mg? Compare
the uncertainties in mass for the two choices.
3-18. Express the molecular mass (uncertainty) of
C 9 H 9 O 6 N 3 with the correct number of significant figures.
3-19. (a) Show that the formula mass of NaCl is 58.442 5
(0.000 9) g/mol.
(b) To prepare a solution of NaCl, you weigh out
2.634 (0.002) g and dissolve it in a volumetric flask whose volume
is 100.00 (0.08) mL. Express the molarity of the solution,
along with its uncertainty, with an appropriate number of digits.
3-20. What is the true mass of water weighed at 24°C in the air
if the apparent mass is 1.034 6 0.000 2 g? The density of air
is 0.001 2 0.000 1 g/mL and the density of balance weights
is 8.0 0.5 g/mL. The uncertainty in the density of water in
Table 2-7 is negligible in comparison to the uncertainty in the
density of air.
3-21. Twelve dietary iron tables were analyzed by the gravimetric
procedure in Section 1-4 and the final mass of Fe 2 O 3
(FM 159.688) was 0.277 4 0.001 8 g. Find the average mass
of Fe per tablet. (Relative uncertainties in atomic masses are
small compared with relative uncertainty in the mass of Fe 2 O 3 .
Neglect uncertainties in atomic masses in this problem.)
3-22. We can measure the concentration of HCl solution (a procedure
called standardizing the solution) by reaction with pure
sodium carbonate: 2H Na 2 CO 3
B 2Na H 2 O CO 2 .
A volume of 27.35 0.04 mL of HCl solution was required
for complete reaction with 0.967 4 0.000 9 g of Na 2 CO 3
(FM 105.988 0.001). Find the molarity of the HCl and its
absolute uncertainty.
3-23. Avogadro’s number can be computed from the following
measurable quantities for a particular element: 2 (1) the atomic
mass of the element (obtained from the mass and abundance of
each isotope), (2) the density of a crystal of the element, (3)
the size of the unit cell (the smallest repeating structural unit)
in the crystal, and (4) the number of atoms in the unit cell.
Extremely accurate measurements for silicon give an atomic
mass of m Si 28.085 384 2 (35) g/mol, where 35 is the
standard deviation in the last two digits. The density is
2.329 031 9 (18) g/cm 3 , the size of the cubic unit cell is c 0
5.431 020 36 (33) 10 8 cm, and there are 8 atoms per unit
cell. Avogadro’s number is computed from the equation
N A
m Si
(ρc 03 )>8
From the measured properties and their uncertainties (standard
deviations), compute Avogadro’s number and its uncertainty. To
find the uncertainty of c 03 , use the function y x a in Table 3-1.