Chapter 1
 Measurements

Chemistry: a science that deals with matter; its structure, its composition, and transformation or changes.

It is very important in allied health to be able to measure physical dimensions pertaining to matter. 

Matter is anything that has mass and occupies space (volume).

Mass is defined as the quantity of matter in an object; does not change with location even if it is in the moon or in any weightless condition.

Weight is a  measure of gravitational attraction on an object; it varies with location. An astronaut with a mass of 200 lbs has the same mass of 200 lbs in the moon; the weight, however, would be less. Compare gravitational attraction in the moon and on the earth.

1.1 Units of  Measurement

Metric System is used almost throughout the world, with the exception of a few countries, by scientists and allied health professionals.  In 1960, a modification of the metric system, Systeme Internationale (SI),  was adopted .  In this textbook, metric system and some SI units are used.

Table 1.1 shows comparison of the metric and SI units.

Measurements           Metric                    SI   

Length                     Meter (m)                Meter (m)

Volume                    Liter (L)                   cubic meter  (m3)

Mass                       Gram (g)                  Kilogram (kg)

Time                        Second (s)                Second (s)

Temperature            Celsius (oC)              Kelvin (K)

Temperature measures how hot or how cold an object is.  It is not the same as heat.  

How to use your text book:

Each topic is followed by  CONCEPT CHECK, SAMPLE PROBLEM, Study Check, and Questions and Problems.  Answers to Study check are found at the end of the chapter. Also, answers to red numbered problems are found at the back of the chapter. BE SURE TO DO EACH CONCEPT, SAMPLE PROBLEMS, and STUDY CHECKS for practice.

 

1.2 Scientific Notation: Exponential Form.

Large or small numbers can be converted into scientific notation by moving decimal. The number should be written as coefficient with a value between 1 - 10 and multiplied by 10 raised to some power or exponent.

** The exponent represents how many places the decimal has been moved.

(+) power or exponent means decimal has been moved to the left for number larger than 1.  Table 1.2

10000 = 1 x 104 = 10 x 10 x 10 x 10

7550000 = 7.55 x 106

(-) power or exponent means decimal has been moved to the right for number less than 1.

0.00001 = 1 x 10-5 = 1/10 x 1/10 x 1/10 x 1/10 x 1/10

0.0000755 = 7.55 x 10-5

***Do Sample problems 1.2, Study Check, and Questions and Problems (p. 21)

Make sure you know how to use your calculator with scientific notation. (p. 20) or go to the math lab at the library.

 

1.3 Measured Numbers and Significant Figure

Numerical values obtained from any measurement are never exact because of some degree of uncertainty due to the precision of the equipment and the skill of the operator.

Significant figures (SF) in measurement include all the digits (definitely known) and one estimated digit.

    Example: 355.87 ; 7 is an estimated digit

Significant Figures in Measured Numbers and rules of counting Significant Figures (SF).

Determining the number of significant figures:

1. A number is a significant figure if it is:

    (a) Non zero, therefore, digits 1 - 9 are significant :  Ex.  25g   2SF;          1.88cm     3SF  

    (b) Zero between nonzero digits (captive zeros):   Ex.    205L  3SF;        10.88kg     4SF

    (c) A zero at the end of a decimal :                    Ex.    25.0m   3SF      151.00 mg   5SF

    (d) Any digit in the coefficient of a number

        written in scientific notation                              Ex.   2.50 x 105 mm       3SF        2.1 x 10-3 lb   2SF

2.  A zero is not significant  if it is

    (a)  At beginning of decimal number not significant       0.068mg         2SF        0.00002 kg       1SF

    (b) Used as a placeholder in a large number without a decimal or  trailing zeros       1200m     2SF

        135 000mL     3SF

Exact Numbers are NOT measured; they are obtained by counting or from defined equalities in the same measuring system; they do not affect the number of SF in a calculated answer.

   Counted numbers                           U.S. System                                Metric System

    15 oranges                                    1 ft = 12 in.                                1 m = 10 dm

    25 persons                                    1 lb = 16 oz.                              1kg =  1000 g

 

1.4 Significant Figures in Calculations

    a) Rounding off:

        1.     If the first digit to be dropped is 4 or less, then it and all the following are dropped from the number.

                                           Two SF              Three SF                                                            

          Example:    5.21484  round off to             5.2                            5.21     

        2.    If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1.                

        Example:     5.21484 round off to four SF  5.215

Do Concept 1.4; Sample problem 1.4, and Study Check

  b) Multiplication and Division: the final answer will have the same number of SF as the measurement with the fewest SF.

        Ex.  2.34(3SF)  x 0.032 (2SF) = 0.07488 (calculator) = 0.075 (2SF) rounded to 2SF

               2.34/0.032 = 73.125 (calculator) = 73 (2SF) rounded to 2SF

c) Addition and Subtraction: the answer is written so that it has the same number of decimal places as the measurement with the fewest decimal places.

       Examples:  1.2 (one decimal place) + 1.22 (2 decimal place) = 2.42 (calculator) = 2.4 (one decimal place) rounded to one decimal place  

                        55(ones place) - 2.8 (one decimal) = 52.2 (calculator) = 52 rounded to ones place  

         Do Concepts, Sample problems, and Study Checks. 

d)  Adding Significant Zeros:  Significant zeros, sometimes, may be written to correct the number of SF displayed by the calculator.

        Example: 55.0/1.1 = 5 (calculator gives one SF; from the calculation answer should have 2SF; therefore the correct answer is written as 5.0(2SF)

 

1.5 Prefixes and Equalities

    Table 1.6 Metric and SI Prefixes

Common Prefixes that increase the size of the unit: gram (m), Liter (L), meter (m), and seconds (s)  

Prefix                Symbol            Numerical Value                Scientific Notation                   Equality

giga                    G                    1000 000 000                    109                                        1Gm = 109 m

mega                   M                  1000 000                           106                                        1Mg = 106

kilo                     k                    1000                                  103                                         kL = 103L

Common Prefixes that decrease the size of the unit: gram (m), Liter (L), meter (m), and seconds (s)    

Prefix                    Symbol            Numerical Value                Scientific Notation                 Equality

deci                      d                      0.1                                    10-1                                     1dL = 10-1L

                                                                                                                                          1L =101dL

centi                     c                      0.01                                   10-2                                     1cm = 10-2 m

                                                                                                                                          1m = 100 cm

milli                       m                     0.001                                 10-3                                     1mg = 10-3 g

                                                                                                                                          1g = 1000 mg

micro                                          0.000 001                         10-6                                      1m = 10-6 m

                                                                                                                                          1m = 106 m

Some equalities:

1 meter = 100 cm             1dL = 100 mL

1L = 10dL                        1g = 106

1L = 1000 mL

1.6 Writing Conversion Factors

  a)  Table 1.9 Some Common Equalities

    Quantity                            US                         Metric (SI)                                    Metric-US

    Length                              1ft = 12 in.              1km = 1000 m                                 2.54 cm = 1 in.

                                            1 yard = 3 ft            1m = 1000 mm                                1m = 39.4 in

                                            1 mile = 5280 ft       1cm = 10 mm                                  1 km = 0.621 mi

____________________________________________________________________________________________________________________

 Volume                               1qt = 4 cups            1L = 1000 mL                                  946 mL = 1 qt

                                            1 qt = 2 pt               1 dL = 100 mL                                 1 L = 1.06 qt

                                            1 gallon = 4 qt          1 mL = 1cm3

____________________________________________________________________________________________________________________

Mass                                    1 lb = 16 oz               1 kg = 1000 g                              1 kg = 2.20 lb

                                                                              1 g = 1000 mg                             454 g = 1 lb

_____________________________________________________________________________________________________________________               

Time                                                                        1 hr = 60 min

                                                                                1 min = 60 s

____________________________________________________________________________________________________________________

b) Examples of conversion factors

 Equality                                                   Conversion factor

1 m = 100 cm                                 1m/100 cm and 100cm/1m

1 kg = 2.20 lb                                 1 kg/2.20 lb  and 2.20/1kg

c) How to set up problems using two or more conversion factors:

  Rules to follow in unit conversion:

(a)  Write down the known or given quantity including the unit.

(b)  Write down the conversion factors in fraction form.

(c)  Multiply (a)  by the conversion factor written in fraction such that units cancel.

(d) Determine the number of significant figures in the answer.

Examples:

How many mL are there in 1.75 gallons? (Two steps) Table 1.9
  (a) Given: 1.75 gallons (Ans. 6620 mL (3SF)

 (b) conversion factors:

        1 gallon/4qt and 4qt/1gal

(c) Multiply (a) by conversion factor so that units cancel:

Equalities: 1 gal = 4 qt; 1qt = 946 mL

       
 
 
  A 15.0 km distance is how many miles long?  (Ans. 9.32 mi)

 Equality:  1 km = 0.621 mi
 
 

How many cm/second are there in 120 miles/minute? (ans. 3.2 x 10 5 cm/s )

Equalities:  1 km = 0.621 mi; 1km = 1000 m; 1 m = 100 cm; 1 min = 60 seconds

1.7 Practice problems: PRACTICE  

1.8 Density (mass/volume):

It is a comparison of the mass of an object and its volume.

In metric system, the densities of solids and liquids are expressed as gram per cubic centimeter (g/cm 3) or gram per millimeter (g/mL); gases are expressed as grams per liter (g/L).

Example problems: 

Determine the density in g/mL of a liquid that has a mass of 61.5 grams and a volume 73.2 mL. (Ans.0.840 g/mL, 3SF)

 

A copper sample has a mass of 44.65 g and a volume of 5.0 mL.  What is the density of of copper?  (Ans. 8.9 g/mL, 2 SF) 

 

 

Density of Solids: 

Weigh the solid to get its mass. Calculate the volume of the solid by volume displacement because a completely submerged object displaces a volume of liquid that is equal to its volume.

Problem example:  

A metal has a mass of 226 g.  When the metal is placed in a graduated cylinder containing 200.0 mL of water, the water level rises to 220.0 ml.  What is the density of of the metal in g/mL?

Volume of the metal:  220.0 mL - 200.0 mL = 20.0 mL

Mass of the metal: 226 g

Density =m/v = 226g /20.0 mL = 11.3 g/mL (3SF)

Do the study checks 1.15 on p. 44 and  study check 1.16 p. 44

Do sample problem  1.17 p.46

 

Specific Gravity (spgr): It is a ratio between the density of a substance and the density of water which id 1.00g/mL at 4oC.  An instrument,  a hydrometer, is used to measure the specific gravity of fluid (battery fluids, urine, etc)

Specific gravity = density of substance /density of water; if units cancel  (NO UNIT)

If the hydrometer reading is 1.006, what is the density of the liquid?

Problem:

John took 2.0 teaspoons (tsp) of cough syrup with a specific gravity of 1.20.  If there is 5.0 mL in a teaspoon, what is mass in grams of the syrup? (Ans.12 g)    

    Equalities (conversion factor):

    1tsp=5.0 mL ; 1mL= 1.20g