Homework, Chapter 1 answer key
1.
Explain the difference between: (a) A hypothesis and a theory, (b) A theory and a
scientific law. A hypothesis is a tentative explanation of the facts, and a theory
is a well-established hypothesis with facts to prove it. A general principle
explaining natural phenomena that can be stated using a simple sentence is a
law. A theory cannot be stated in a single sentence.
3.
How many phases are present in the graduated cylinder? Six.
8.
Which liquids in Table 1.1 are not mixtures? Mercury (an element), oil and water
(pure compounds).
9.
Which of the gases in Table 1.1 are not pure substances? Air (a homogeneous mix.)
12. Is the system that contains only one substance necessarily homogeneous? No,
because the substance can be in different physical states. For instance, ice
floating on water is a heterogeneous mixture because it contains two phases (ice and
water), and the phase boundary is clearly seen.
Homework, Chapter 2 answer key
4.
State the abbreviation for each of the following units: (a) milligram – mg; (b)
kilogram – kg; (c) meter – m; (d) nanometer – nm; (e) microliter – L.
Note the symbol for micro is a Greek symbol!
7.
How many significant digits are in each of the following numbers? (a) 0.025 – 2
sig.figs.; (b) 22.4 – 3 sig.figs; (c) 0.0404 – 3 sig.figs.; (d) 5.50 x 103 – 3 sig.figs.
9.
Round each of the following numbers to three significant figures: (a) 93.246 – 93.2;
(b) 0.02857 – 0.0286; (c) 4.644 – 4.64; (e) 34.250 – 34.2.
13. Solve the following problems.
(a) 12.62 + 1.5 + 0.25 = 14.4 (must round up to the most uncertain number: +/- 0.1)
(b) (2.25 x 103) (4.80 x 104) = 10.8 x 104+3 = 10.8 x 107 = 1.08 x 108.
Remember: When two numbers in scientific notation are multiplied, the two preexponent numbers multiply first, and than the exponents add together. After the
multiplication you get the number 10.8 x 107. However, a number in scientific
notation must have the pre-exponent number equal or greater than one, but less than
ten. Thus, the resulting number is not in written in correct scientific notation, you
must change it so that the pre-exponent number becomes less than ten. Move the
decimal point left by one, and increase the exponent by one: 1.08 x 108. Check the
significant figures – each of the two original numbers have three sig.figs, so that the
resulting number also has 3 significant figures.
(c) (452) (6.2) / (14.3) = 195.972… = 2.0 x 102.
The result must have the number of significant figures equals to that of the
multiplier that has the least. The number 6.2 has two significant figures, thus the
result must have two as well. Rounding 195.972… to two significant figures gives
two hundred, but it cannot be expressed with 2 significant figures using the regular
notation. (Check: with the decimal point, the number (200.) has 3 significant
figures, while the number without the decimal point (200) has only one significant
figure.) Thus, the result must be expressed in scientific notation: 2.0 x 102.
(d) (0.0394) (12.8) = 0.50432 = 0.504, or 5.04 x 10-1.
(e) (0.4278) / (59.6) = 0.0071778… = 0.00718, or 7.18 x 10-3.
(f) 10.4 + (3.75) (1.5 x 104) = 10.4 + 56250 = 56260.4 = 56000 or 5.6 x 104.
18.
(b) Solve the equation for the variable x:
8.9 g/mL = 40.90 g / x.
First multiply both sides of the eq. with x, and then divide both sides with 8.9 g/mL.
x = (40.90 g) / (8.9 g/mL) = 4.5955… mL = 4.6 mL.
23.
After you have worked out at a gym on a stationary bike for 45 min, the distance
gauge indicates you have traveled 15.2 miles. What was your rate in km/hr?
(conversion factors: 1 mile = 1.609344 km, 1 hour = 60 min)
15.2 mi
1.609344 km
60 min
x(
( 45 min ) x (
)
1 mi
1 h ) = 16.09344 km/h = 16 km/h.
Conversion factors are chosen so that a new (wanted) unit is introduced and the
unwanted one cancelled. Keep multiplying the number with conversion factors until
the desired unit is reached. In the above example, the first conversion factor
converts miles into km, the second one converts minutes to hours. The result has
two significant figures, as the number 45 min. Note that numbers 1 mi, 1 h, 60 min
are all EXACT numbers. Exact numbers are thought of as if they have as many
significant figures as needed for the calculation, so that the result depends only on
the number of significant figures in measured quantities.
41. A textbook is 27 cm long, 21 cm wide and 4.4 cm thick. What is the volume in:
(a) cubic centimeters; V = 27 cm x 21 cm x 4.4 cm = 2494.8 cm3 = 2.5 x 103 cm3.
(b) liters; 1 L = 1 dm3, 1 dm = 10 cm. Express all numbers in dm, then multiply:
1 dm
1 dm
1 dm
(2.7 cm x 10 cm ) x (2.1 cm x 10 cm ) x (0.44 cm x 10 cm ) = 2.5 dm3 = 2.5 L
(c) cubic inches; express all numbers in inches, then multiply them:
1 in
1 in
1 in
(27 cm x 2.54 cm ) x (21 cm x 2.54 cm ) x (4.4 cm x 2.54 cm ) = 152.242… in3 = 150 in3.
49. The normal boiling point of ethanol is 173.3 oF. What is this temperature in oC?
o
C = (5/9) (oF – 32) = (5/9) (173.3 – 32) = (5/9) (141.3) = 78.50 oC.
Note that numbers 5, 9 and 32 are exact numbers, thus the result has 4 significant
figures as the number 173.3 oF. Your calculator gives you 78.5 oC (three sig.figs),
you must add a zero to make it 4 significant figures!
55. Concentrated hydrochloric acid has a density of 1.19 g/mL. Calculate the mass of
250 mL of it. d = m / V  m = d x V. m = 1.19 g/mL x 250 mL = 297.5 g =
3.0 x 102 g.
As in the Question 13, you must use scientific notation to express
the correct number of significant figures (two).