1. Measurements and Calculations
Chapter 2
Measurements and Calculations

2. 2-1 The Scientific Method
A logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses and formulating theories that are supported by data
Hypothesis – testable statement, if-then
Hypotheses not supported by data must be rejected

3. 2-1 Observing and Collecting Data
Qualitative data – descriptive, what is it like?
The ice water was clear and colorless.
Quantitative data – numerical, how much?
The ice water was 4˚C.
The volume of the ice water was 125 mL.

4. 2-1 System
A specific portion of matter in a given region of space that has been selected for study during an experiment or observation.
The scientist determines the system.
Anything outside of the system is called the surroundings.

5. 2-1 Hypotheses, Models and Theories
Scientists form hypotheses – a hypothesis is a testable statement, if-then
Scientists test hypotheses – a hypothesis is tested through experimentation.
If a hypothesis is not supported by data it must be rejected.
If a hypothesis is supported by experimental data, a model is constructed – a model is an explanation of how data and events are related.
If a model successfully explains a phenomenon, it may become part of a theory – a theory is a broad generalization that explains a body of facts.

6. 2-2 Units of Measurement Measurements represent QUANTITIES.
A quantity is anything that has magnitude, size or amount.
Length, width, temperature, mass, area, volume and time are examples of quantities.

7. 2-2 SI Measurement Quantity SI Base Unit length meter (m) mass
kilogram (kg)
time
second (s)
temperature
kelvin (K)
amount of substance
mole (mol)
electric current
ampere (A)
luminous intensity
candela (cd)
SI is the International System – a version of the metric system used by all scientists

8. 2-2 Mass Mass – amount of matter, SI unit is kilogram
Based on International Prototype Kilogram – a cylinder of platinum-iridium alloy kept near Paris
Scientists also use grams, milligrams

9. 2-2 Weight
Weight – measure of gravitational pull on matter, can vary with location because gravity is not the same everywhere, directly proportional to mass
Weight can vary. Mass can NOT vary

10. 2-2 Other Base Quantities
Length – distance between 2 points, SI base unit is meter, scientists also use decimeter, centimeter, millimeter
Temperature – hotness or coldness, average kinetic energy, SI base unit is degree kelvin, scientists also use degree Celsius
Time – interval between events, base unit is second

11. 2-2 SI Prefixes

12. 2-2 Derived Units Derived units are formed by combining SI base units
Quantity
symbol
unit
unit abbreviation
derivation
area A
square meter m2
length x width
volume V
cubic meter m3
L x W x H
density D
kilograms per cubic meter
kg/m3
mass/volume
Molar mass M
kilograms per mole
kg/mol
mass/amount
concentration c
moles per liter
mol/L
amount/volume
Molar volume Vm
cubic meters per mole
m3/mol
volume/amount
energy E
joule J
force x length

13. 2-2 Volume Amount of space occupied by an object
SI derived unit is cubic meters
Scientists often use liters (L) or milliliters (mL) for liquid volume.
1 L = 1 dm3
1 mL = 1 cm3

14. 2-2 Density The ratio of mass to volume
Each pure substance has a characteristic density
Density can sometimes be used to identify substances.
What is the mass of a 12.4 cm3 sample of gold? (Gold’s density is g/cm3.)

15. 2-2 Conversion Factors
A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other
example: 1 m = 10 dm

16. 2-2 Using Conversion Factors
Express g in milligrams and kilograms

17. 2-2 Using Conversion Factors
Express m in centimeters and kilometers.

18. 2-2 Using Conversion Factors
Express 1500 cm3 in cubic meters.

19. 2-2 Using Conversion Factors
Express 15 km/hr in meters per second.

20. 2-2 Using Conversion Factors
Express g/cm3 in kilograms per cubic meter.

21. 2-3 Accuracy and Precision
Accuracy refers to closeness of measurements to correct or accepted value.
Precision refers to closeness of measured values to each other.

22. 2-3 Accuracy and Precision
The boiling point of acetone is 56.3˚C.
student 1: 50.6˚C, 61.7˚C, 51.0˚C
student 2: 50.1˚C, 49.9˚C, 50.2˚C
student 3: 56.1˚C, 56.5˚C, 56.9˚C
Which student was accurate and precise?
Which student was only precise but not accurate?
Which student was neither precise nor accurate?

23. 2-3 Percent Error Percent error is a measure of accuracy.
P.E. = Valueaccepted – Valueexp x 100
Valueaccepted
If acepted value is greater than experimental value, PE is positive.
If accepted value is less than experimental value, PE is negative.

24. 2-3 Percent Error
A student measures the mass and volume of copper and calculates its density to be 8.50g/cm3. The accepted value is 8.92g/cm3. What is the percent error of this measurement?

25. 2-3 Significant Figures Any measurement contains some uncertainty.
Scientists use significant figures to show how certain they are of a measurement.
Example:
Which measurement represents a greater degree of certainty?
4000 g g

26. 2-3 Significant Figures
Represent any position for which real measurement has been made, plus one final digit which is an estimated position
The number of significant figures you can record when measuring with an instrument depends on the sensitivity of the instrument

27. 2-3 Significant Figures
Record all digits that you can read off the instrument, plus ONE ESTIMATED digit.

28. 2-3 Significant Figures All nonzero digits are significant.
Zeros between nonzero digits are significant.
Zeros in front of all nonzero digits are NOT significant.
Zeros at the end of a number and to the right of a decimal point are significant.

29. 2-3 Significant Digits
Determine the number of significant digits in the following measurements: g km
1002 m
400 mL cm kg

30. 2-3 Significant Figures and Calculations
Addition/subtraction – go by smallest number of decimal places
Multiplication/division – go by smallest number of significant figures
4.57 g g
7.77g  g m
X m
m2  m2

31. 2-3 Significant Figures and Conversions
Equalities are definitions, and therefore have NO uncertainty.
There are EXACTLY 100 cm in a meter, by definition.
When you convert a value, your answer will have the SAME number of significant figures as the original value.
4.608 m x 100cm/1m = cm

32. 2-3 Scientific Notation
Numbers are written in the form M x 10n, where M is a number greater than or equal to one but less than 10 and n is a whole number.
Express the following in scientific notation:
67000
621.0

33. 2-3 Direct Proportions
Two quantities are directly proportional to each other if dividing one by the other gives a constant value
y/x = k
k is the proportionality constant
Ratio between the variables remains constant
Rearrange to get y = kx (straight line)
Therefore, a graph of a directly proportional relationship will be linear. (e.g. density)

35. 2-3 Inverse Proportions
Two quantities are inversely proportional to each other if their product is a constant
xy = k
k is the proportionality constant
A graph of an inversely proportional relationship produces a curve called a hyperbola

36. Gas Volume v. Pressure