MEASUREMENTS AND

CALCULATIONS

ChemistryChapter 2

Scientific Method

serendipity has played a role in science most of what we know has come by

careful research and experimentation scientific method- logical approach to

solving problems by observing, collecting data, formulating hypotheses, testing hypotheses, & formulating theories supported by data

quantitative data-involves numbers

measurements using rulers, thermometers, graduated cylinders, etc.

for ex- temp 25oC

qualitative data- is descriptive

for example- sulfur is a yellow chemical

experiments are controlled to test one variable and collect data

system- a specific portion of matter in a given region of space is studied in an experiment or observation

when scientists have a question they want answered, they usually state it in an “if-then” statement

hypothesis- testable statement (if-then)

control- part of experiment that remains the same

variable- part of experiment that is changed

during the experiment, any change observed is usually due to the effects of the variable

Units of Measurement

What is wrong with this recipe?

Banana Nut Bread

3 flour 1 vanilla

2 eggs 2 mashed bananas

2 sugar ½ nutmeg

measurements represent quantities

quantity- something that has magnitude, size, or amount (UNIT)

most ALL m’ments are a NUMBER and a UNIT

SI System

a standard system of m’ment 7 base units system is monitored by International

organizations

commas are NOT used in numbers = for example: 75 000 not 75,000

(many other countries use commas as decimal points)

few differences between SI system and metric

base units specific for certain quantities

(table 1) prefixes are used to indicate quantities

larger or smaller than the base unit prefixes are based on 10

(table 2)

Most common prefixes

kilo– means 1000

deci– means tenth (0.1)

centi- means hundredth (0.01)

milli- means thousandth (0.001)

commit these to memory

the prefixes are used with the base units to measure larger or smaller quantities

for ex: length of room- meter

distance to Sylacauga-kilometer

length of book- centimeter

width of fingernail- millimeter

MASS

measure of the quantity of matter

base unit:

SI- kilogram

metric- gram triple-beam

balance

Weight

measure of the force of gravity between 2 objects

can change, mass DOESN’T

SI unit - Newton scale

Time

interval between 2 occurrences

SI unit- seconds

stopwatch/clock

Length

distance between 2 points

SI unit- meter

ruler

Temperature

matter is composed of molecules, ions, and atoms which are in constant motion (i.e. have kinetic energy)

temp measure of the average kinetic energy of all these particles

increase heat, increase movement of particles, increase KE

SI unit- Kelvin (K)measures extreme

temps metric- Celsius

(oC) based on the

freezing and boiling point of water

thermometer

Derived Units

combinations of SI units

produced by multiplying or dividing std units

Volume amount of space an

object takes up SI unit- 1m3

metric- liter (L)1cm3 and 1mL are

smaller and usually used in the lab

1cm3 = 1mL graduated cylinder

Volume

can be calculated using a ruler and this formula: v = l x w x h

volume relationships:

1dm3 = 1L = 1 000cm3 = 1 000mL

1 000mL = 1 000cm3

Density

mass per unit volume density = mass

volume

D = m

v units can be g/mL, g/cm3 (whatever

units are used to measure mass and volume will be the units of density

can be used to identify substances

can use the formula to find mass or volume also

density of H2O = 1g/mL

How reliable are the measurements you make?

2 important terms indicate reliability:

1. accuracy- how close the m’ment is to the true value

2. precision- how close a set of m’ments for a quantity are to each other (regardless of accuracy)

% error

used to evaluate results obtained in lab

always positive number % error =

An automobile is traveling at 88 km/h. What is its speed in cm/s.

Density pop quiz1. A 30.0 cm3 sample of quartz has a

density of 2.65g/cm3. What is the mass?

2. The density of a sample of cork is 0.24g/cm3. What is the volume of a 35.0g sample?

3. What is the density of a piece of marble with the following dimensions: 552g and 212 cm3?

Significant Digits

In science, significance means measured, not importance.

the # of sig digs in a m’ment depends on the scale of instrument used

m’ment includes 1 uncertain, or estimated, digit

To find sig digs:

1. find decimal point

2. find 1st non-zero digit in the sequence

3. that digit and everything to the right is significant

4. if no decimal point, count from the 1st non-zero digit to the last non-zero digit

10.0

0.002

2 000 000

25.0010

0.100

260

100 100

2.550

when doing calculations on calculator, the answer cannot have any more sig digs than the value in the problem

answers in addition & subtraction must contain no more digits to the right than the # with the least digit to the right in the prob

52.63- 12.4

40.23=

40.2

answer in multiplication or division must contain no more sig digs than the # with the fewest digits in the prob

18.3

x 1.4

25.62=

26

5.356

x 0.793

4.247308=

4.25

Rounding Rules1. # 1-4 round down

21.31 =21.3

2. #6-9 round up36.7 = 37

3. # 5 -round down if # preceding 5 is even

32.5 = 32 688.5 = 688

round up if # preceding 5 is odd

43.5 = 44 759.5 = 760.

4. if there are #s after the 5, round up no matter what the preceding # is

42.52 = 43 78.571 = 79

Scientific Notation

very small and very large numbers are written in this shorthand method

#s are written in this format:

M x 10 n

M = 1 to 9.999

n = whole number exponent

convert into sci not:

650 000 000

6.5 x 108

0.000 000 974

9.74 x 10-7

convert into std numbers:

3.8 x 104

38 000

1.25 x 10-3

0.001 25

adding/subtracting in sci not

exponents must be same

moving decimal to LEFT increases exp

moving decimal to RIGHT decreases exp

4.5 x 105

+ 3.1 x 107

multiplying/dividing in sci not

multiply – ADD exponents

divide- SUBTRACT exponents

2.74 x 103 x 3.1 x 108 =

9.58 x 104

3.7 x 106

Proportions: 2 types

1. direct proportions- if 2 quantities can be divided and you get a constant value

y=kx

results in a straight line

as x increases, y increases

2. two quantities are inversely proportional if their product is constant

xy = k

forms a hyperbola

if x increases, y must decrease