Units of Measurement

Chapter 1, cont’d: Units of Measurement

Measured quantities are associated with units!!

1. Base units in the SI system:

Mass kilogram (kg) Length meter (m) Time sec (s) Quantity mole (mol) Temperature Kelvin (K)

From the base units come derived units, e.g., Density = mass/volume Velocity = distance/time

9 Review of Exponential Notation (Appendix A1) e.g., express the following in scientific notation: 0.001453 m3 (what is this a measure of?) 33987.22 sec

SI system uses prefixes to indicate decimal fractions or multiples of units, e.g.,

Kilo- k 1x103

Centi- c 1x10-2

Milli- m 1x10-3

Micro-  1x10-6

Nano- n 1x10-9

LOOK OVER TABLE 1.5 (Common SI Prefixes)

10 e.g., use appropriate metric prefixes (k-, p, n, etc) to express the following measurements without an exponent:

6.5 x 10-9 m

3.5 x 103 L

6.54 x 105 s

Temperature What is temperature? Temperature scales Celsius

o 0 C= freezing point of H2O

o 100 C=boiling point of H2O (at sea level)

-What are the corresponding temps in oF?

Conversions between oC and oF

oC = 5/9(oF - 32o)

oF = 9/5(oC) + 32o

11 Kelvin scale

0 K = -273.15 oC (absolute zero)

K = oC + 273.15

Density (D) D = mass / volume

What are the base SI units of density?

More common: units of g/cm3 -Do density and weight describe the same thing? Is density an intensive property of matter or an extensive one?

Calculations using density

Find the density (g/cm3) of Hg if 1.00x102 g of this substance occupies a volume of 7.45 cm3

12 2. Uncertainty in Measurement Uncertainties always exist in measured quantities. Why?

Exact and Inexact Numbers Exact: any counted quantity; any conversion factor Inexact: any measured quantity

Precision and Accuracy precision: how closely individual measurements agree with each other

accuracy: how closely individual measurements agree with the "correct" value

Significant Figures Measured quantities are reported such that only the last digit is uncertain

13 e.g., a penny has a mass of 1.5576 g. This implies that the uncertainty in the mass of the penny is  0.0001 g.

How many significant figures are reported in the mass of the penny?

How do we determine the number of significant figures in a measured quantity? Rules to live by: all nonzero digits are significant (893 cm ; 17.57 L)

zeros between nonzero digits are significant (1.005 mol; 104 kg)

zeros to the left of the first nonzero digit are NOT significant (0.05 mol)

zeros at the end of a number AND to the right of the decimal point ARE significant (0.0200 mol; 3.0 cm)

14 OK, what about a number which ends in zeros that are not to the right of the decimal point? (120g, 11500 cm) write the number in scientific notation:

e.g., 120 g = 1.20x102 g (3 sig figs)

11500 cm = 1.1500x104 cm (5 sig figs)

Significant figures in calculations involving measured quantities The precision of the calculated result is limited by the least precise measurement!!!!!

Multiplication and division result must have no more sig figs than the measurement with the fewest sig figs e.g.: Suppose that a 1.05 g sample of a metal had a volume of 23.610 cm3. Find the density in g/cm3.

15 If the result has more than the correct number of sig figs, it must be rounded off: e.g., round 0.006543210 nm to four sig figs and report in scientific notation

In calculations with intermediate steps, retain an extra sig fig or two through the calculations and round the final result to the correct number of sig figs!

e.g.: The maximum allowable concentration of CO in urban air is 10.0 mg/m3 over an 8-hour period. At this level, what mass of CO in mg is present in a room measuring 8.0 x 12.1 x 10.1 m?

3. Dimensional Analysis/Conversions Length Given that 1 m = 1.0936 yd, and 1 inch = 2.54 cm, how many inches are in 2.5 m?

16 Convert 0.0023 mm to nm

Volume

SI unit of volume = m3

More common: cm3 (or cc) or dm3 1 liter (L) = 1000 ml = 1000 cm3 Given that 1 L = 1.057 qt, how many L is 5 gal of gasoline?

Convert 55.35 ft3 to cm3

17 The density of air is 1.19 g/L. What is the mass, in kg, of the air in a room that measures 12.5 x 15.5 x 8.0 ft?

18 Problems du Jour

Perform the following conversions: 5.0 x 10-8 m to nm

1.55 kg/m3 to g/L

5.0 pm/s to m/s

An individual suffering from high blood cholesterol has a count of 232 mg cholesterol/100 mL blood. If the total blood volume is 5.2 L, how many g of total blood cholesterol does this person contain?