1. Measurements and Calculations
World of Chemistry

2. Numbers and measurements
Quantitative observations like measurements must have units
Measurements can be very small or very large
Example:
Distance from Earth to Sun = 93,000,000 miles
Average size of eukaryotic cell: meters
For very large and small measurements, use scientific notation

3. In writing in scientific notation, you will
Make the number between 1 and 10 (move the decimal)
Determine the power of 10
- if the regular number is >1, move decimal to the right, positive exponent
- if the regular number is <1, move decimal to left, negative exponent
Example
93,000,000 miles = 9.3 x 106 miles
metes = 6.2 x 10-6 meters

4. Put the following numbers into standard scientific notation:
238,000 =
1,500,000 =
24.7 =
0.135 = =

5. Units All measurements must have units
USA – English system, most international countries – metric system
Science community – International System (SI)
when it comes to scale, use prefixes

6. SI Units for chemistry Quantity Unit Abbreviation Symbol Mass Kilogramkg m
Time
Second s t
Temperature
Kelvin K T
Amount of substance
Mole
mol n
Although not included, volume is measured in liters (L) and represented by V.

7. Unit Prefixes Prefix Symbol Power of 10 Mega M 106 kilo k 103 centi c
10-2
milli m
10-3
micro υ
10-6
nano n
10-9
mega – million times, k = thousand times, c – hundredth, m – thousandth, micro – millionth, nano – billionth size

8. Unit prefixes
Prefixes can be used to replace powers of 10 in scientific notation
Examples:
5000 m = 5 x 103 m = 5 km
L = 3.15 x 10-3 L = 3.15mL
s = 4.65 x 10-9 s = 4.65 ns
33000 m = 33 km
L = 0.56υL (microliters)

9. Practice Problems Convert the following 382 g = _____kg
0.0056g = _____mg
490 mL = _____L
6,560,000 m = _____Mm (Megameters)
99 Mg = ____________g
8.8υg = ______g
1) ) ) ) ) 9,900,000 6)

10. Measurement Uncertainty
Measuring anything (especially mass, volume, length):
certain and uncertain numbers
meter stick

11. Uncertainty in measurements
4.75 cm

12. Measurement Uncertainty
Determine the “certain” numbers of the measurement
Meter stick broken down into centimeters and millimeters
4.7 cm
Determine “uncertain” numbers (estimate)
value between millimeters
4.75 cm
Every measuring device (ruler, graduated cylinder, balance) has some degree of uncertainty…except for digital measuring devices

13. Significant Figures
In a measurement, specific numbers are considered significant figures
What counts as sig fig?
What does not count as sig fig?
All regular integers (1457 = 4 sig figs)
Leading zeros ( = 2 sig figs)
Trapped zeros (12059 = 5 sig figs)
Trailing zeros (only if there is a decimal involved)
sig figs
78.0 = 3 sig figs
100 = 1 sig fig

14. Practice Problems Determine the number of sig figs: 0.000304g
1.270 x 102m.
125g
10 A L
6.5 x 103g
6.5mg
9.02 g
10.0 mL
21.40 s

15. Calculating using Sig Figs
1) Multiplication/Division: # of sig figs in answer is the same as the measurement with smallest # of sig figs Example: 4.56 x 1.4 = = 6.4
3 sig figs
2 sig figs
Round off
2 sig figs

16. Calculating using Sig Figs
Example: ÷ 298 = =
4 sig figs
3 sig figs
Round off
3 sig figs

17. Calculating using Sig Figs
Examples 5.4 / 3 = 2.5 x = (8.62 x 103) / (33) = (0.54 / 6.4) x =

18. Calculating using Sig Figs
2) Addition/subtraction: sig figs in answer determined by measurement with smallest number of decimal places Example: =  31.1
1 decimal place
1 decimal place

19. Calculating using Sig Figs
Example: – 0.1 =  0.6
1 decimal place
1 decimal place

20. Calculations Examples
Multiplication and division – count sig figs
Addition and subtraction – count decimal places =
103.4 – =
(1945)(17.1) =
/ 270 =
(13.3 x 105)(45.45) =

21. Dimensional Analysis Dimensional analysis is used to convert units
Ex: g  mol g  L
Use conversion factors as bridges
Examples of conversion factors include..
1 lb = 453g
1 in = 2.54cm
1 mol carbon = 12.01g
Use railroad method to cancel out units

22. Dimensional Analysis
Convert the following 12 ft into cm 3.2 L into ounces 32.0 ft in km

23. 5.7 Temperature Temperature is the measure of heat Three scales:
Celsius (°C)
Fahrenheit (°F)
Kelvin (K)

24. Celsius Anders Celsius Original 1742 “Centigrade” scale
100°C water boils
0°C water freezes
100 degree scale

25. Fahrenheit Daniel Gabriel Fahrenheit
Scale based on three fixed points:
“Brine” mixture: water, ice, ammonium chloride = 0°F
Water and ice mixture = 32°F
Human body = 96°F
180 degree scale
32°F water freezes
212°F water boils

26. Kelvin William Thomson (Lord Kelvin) SI unit 273 K water freezes
373 K water boils
100 degree scale
Absolute zero = 0 K
all molecular motion ceases
has never been reached

27. Temperature Conversion Equations
°C to °F  T°F = (1.8)T°C + 32
°F to °C  T°C = (T°F - 32) x (0.56)
K to °C  TK =T°C

28. 5.8 Density Physical property, specific for a pure substance
Ratio of mass and volume
Density = mass
volume
Volume units
solids cm3
liquid mL
gas L

29. World of Chemistry, pg. 143

30. Determining Density Example: Mass = 55.64 g Volume = 10.0 mL
Density = 55.64g = g/mL
10.0mL