Page 37 - Theory and Problems of BEGINNING CHEMISTRY

26 MATHEMATICAL METHODS IN CHEMISTRY [CHAP. 2

2.14. A certain mass is measured in kilograms and again in grams. Which measurement involves (a) the larger
number? (b) the larger unit?
Ans. The larger the unit, the fewer are required to measure a given distance. There are more grams because the
kilogram is larger. Compare this to Problem 2.13.

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2.15. (a) Would 0.22 m of water fill a thimble, a gallon jug, or an average bathtub? (b) 1.0 cm ?
Ans. (a) A bathtub (b) A thimble

2.16. What two instances are described in the text in which a standard for a type of measurement is different
from the unit with no prefix?

Ans. 1. The kilogram is the standard of mass, both in SI and legally by act of Congress in the United States.
2. The liter is a unit of volume in the (older version of the) metric system, but the cubic meter is the
standard.

2.17. Give the basic SI or metric unit and its abbreviation for each of the following types of measurements:
(a) mass, (b) volume, and (c) distance.
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Ans. (a) gram (g) (b) cubic meter (m ) or liter (L) (c) meter (m)

2.18. Make the following conversions:
(a) Change 46 cm to meters (c) Change 1.5 L to milliliters
(b) Change 0.28 kg to grams (d) Change 1.23 kg to milligrams

1m 1000 mL

Ans. (a)46 cm = 0.46 m (c) 1.5L = 1500 mL
100 cm 1L
1000 g 1000 g 1000 mg

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(b)0.28 kg = 280 g (d)1.23 kg = 1.23 × 10 mg
1kg 1kg 1g
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2.19. (a) How many 1 cm blocks can be placed on the bottom left edge of a 1 m box? (b) How many such
rows of these blocks can be placed on the bottom of the box? (c) How many such layers fit within the
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box? (d)Howmany1cm can fitinto1m ?(e) Cube the following equation: 100 cm = 1m.
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Ans. (a) 100 blocks (b) 100 rows (c) 100 layers (d) 1 million (10 ) cubic centimeters equal 1 cubic meter
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(100 × 100 × 100 = 10 ) (e) (100 cm) = (1 m) ,(100) (cm) = (1) (m) ,1 × 10 cm = 1m 3
2.20. What is wrong with the following problems?
(a) Change 13 cm to kilograms
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(b) Change 2.0 cm to mm
(c) Change 4.4 mL to cm 2
Ans. (a) You cannot convert a distance to a mass.
(b) You cannot convert an area to a distance.
(c) You cannot convert a volume to an area.
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2.21. (a) Change 0.0250 mi to square yards. (1 mi = 1760 yd). (b) Change 0.0250 km to square meters.
2
1760 yd
Ans. (a)0.0250 mi 2 = 77 400 yd 2
1mi
2

1000 m
(b)0.0250 km 2 = 25 000 m 2
1km