Measurement of Matter

 

Metric system:

a)  Unit of length:       meter (m)

            Prefixes:                                

            micro (m)(1/1,000,000)                     milli (m)(1/1000)

            deci (d)(1/10)                                                 centi (c)(1/100)

            kilo (k)(1000)

      More in Table 1.2 of textbook.

                                                           

b)  Unit of mass:  kilogram (kg) = 1000 g

 

c)  Unit of volume: 

            V = l  x  w  x  h = dm x dm x dm = dm3

                                    1 dm3 = 1 liter (L)

                                    1 cm3 = 1 milliliter (mL) = 1/1000 L

                                   

d)  Unit of temperature:         Kelvin (K) scale

                                                                                                Celsius (C) scale

                        Conversions: K = °C + 273

                                                                 °F = °C x 1.8 °F  + 32°F

                                                                                    1.0 °C

                                                                        °C = 1.0 °C    x (°F - 32°F)

                                                                                    1.8 °F

 

e)  Unit of heat:  joule (J), calorie (cal)       

      • how much energy a sample contains

      • calorie:  amount of heat required to raise 1 g of water 1 °C

      Food Calorie  = 1000 calories =1 kilocalorie

 

Density

 

            •  Definition:  mass per unit volume

            •  Mathematical representation:

                        D         =          mass               =          g                      =          g         

                                                volume                        cm3                       mL

 

              •  Example:  Water = 1 g/mL

                                    Gasoline         = 0.66 - 0.69 g/mL

 

Calculate the density of an unknown substance which is determined to weigh 18.2 grams and have a volume of 6.74 mL.

 

 

 

Calculate the volume of a 200 gram piece of lead (see table 1.5).

 

 

 

Accuracy - the degree to which a measurement represents the “true” or accepted value

Precision        - the reproducibility of a measurement

 

Significant figures - help to communicate the uncertainty or reliability of a measurement.

•     includes all digits in a measurement known with certainty (what you read) plus the estimated next digit to the right.

Zero may or may not be a significant figure:

•     leading zeros are not significant figures

                        0.02 m                                    (1 sig fig)

•     captive zeros are significant figures

                        0.0203 m                                ( 3 sig figs)

•     trailing zeros with a decimal point shown are significant figures                  

                        0.02030 m                             ( 4 sig figs)

                        200 m                                     ( 1 sig fig)                  

                        200.0 m                                  ( 4 sig figs)

                        200.                                        ( 3 sig figs)

 

Express the following numbers to 3 significant figures.

 

421798.076

 

0.000993385

 

0.00099985

 

0.42

 

1

 

8222

 

1704

 

Scientific notation may be used to express very large or very small numbers

 

Example:  The mass of 1 molecule of water is

 0.000 000 000 000 000 000 000 029 916 grams

 

This may also be expressed as 2.9916 x 10-23

 

Notice the decimal place has been moved 23 places to the right to obtain a number between 1 and 10.

 

Moving the decimal to the right to express a very small number results in a negative exponent; moving the decimal to the left to express a very large number results in a positive exponent.

 

All significant figures are shown in scientific notation.  

 

Express the following numbers in scientific notation and report their number of sig figs.

 

602,217,000,000,000,000,000,000

 

0.000 000 000 000 000 420

 

 

 

Performing mathematical operations using sig figs . . .

 

Addition and subtraction:

•     The answer must not contain any significant figures beyond the place value common to all numbers.

 

Example:                                2.015

                                      +        4.8

                                                -------

                                                6.8                   (not 6.815)

 

Multiplication/Division

•     The answer must not contain more significant figures than the least number of sig figs in the measurements.

 

Example:                                4.01

                                      x        3.1

                                                ------

                                                12                                (not 12.431)

                       

14.085 + 9.4 =

 

11 m   x   12 m  =

 

 

Unit Conversions

 

Converting units requires that an equivalence between the two units be known.  The equivalence is referred to as a conversion factor.  (See Appendix 6).

 

Conversion factors can be used in either direction . . . Since 2.54 cm = 1 in, this equivalence can be used to convert cm to inches or inches to cm.

 

Ex.  Convert 4.52 inches to cm

 

 

Convert 0.29 cm to inches

 

 

 

Several conversion factors can be used together to perform a multi-step conversion.  Ex.  Convert 0.0287 miles to mm

 

 

 

Convert the density of water (1.0 g/ml) to the units of lb/gal

 

 

 

 

 

 

Convert the area of a square that is 1 in2 to the units of cm2