Download Math of Chemistry PPt

Math Concepts
Chemistry
Observations

A large part of laboratory chemistry is
making observations.

Two types of observations:
 Qualitative observations = descriptive
observations, no numbers involved
 Quantitative observations = observations
described by a numbered measurement.
Accuracy and Precision

Chemists need to have to make exact and
reproducible results.
 Accuracy = measurements that only have slight
deviation from the true value.
 Depends on:
 Equipment used
 Precision = being able to reproduce a measured
value through several experimental runs or trials.
 Depends on:
 The person making the measurements
Accuracy and Precision
Accuracy and Precision

Experimental results:
 Sean: 2.56g
2.37g
2.41g
 Morgan: 3.12g
2.11g
4.32g
 Doug: 3.22g
3.25g
3.27g

If the true value of the
mass is 3.10g, explain
each students
measurements in
terms of the words
accuracy and precision.



Answer: Sean not
accurate, but precise
Morgan accurate, but
not precise
Doug: good accuracy
and very precise.
Why is it so important to be
accurate and precise as a chemist?




Medicine – certain amounts can turn into
lethal dosages
Work with flammable products
To insure reproducible products
(cosmetics, soap, hair products…)
To insure quality of our environments (air
and water quality)
How can a chemist achieve
exactness in measurements?


Significant
Digits/figures.
Sig figs = the
reliable numbers in
a measurement
and at least one
estimated digit.

Make readings for the following
measurements using significant figures.




1.
Rules for significant figures
All non-zero numbers
or digits are significant.
Ex: 23 g
2. All zero in-between 2
non-zero numbers are
significant. Ex: 2.002g
3. When working with a
small decimal number,
work your way over to
the right until you get to
your 1st non-zero
number - anything from
there over is significant.
Ex: 0.00250g
4. Final zeros 25.00g
are significant.



5. When working with
large numbers (no
decimals), look for your 1st
non-zero number –
anything from there to the
beginning of the number
are significant. Ex:
240100g
6. A line/bar over or
under a zero designates it
as significant.
7. Exact numbers =
numbers that you are use
to working with are
unlimited in terms of
significant figs. Ex: there
are 12 men on the football
field. = unlimited.
Significant Figures
An easy way to count the number of
significant figures in any number is:
DOT LEFT – NOT RIGHT
*If there is a visible decimal, look all the way
to the left of the value and move to the
right. Begin counting digits after your first
non-zero digit. Any numbers that follow a
non-zero digit are significant.
EX: 2.500 = 4 sig figs
500.00 = 5 sig figs

*If there is no visible decimal, look all the
way to the right of the value and move to
the left. Begin counting digits after your
first non-zero digit. Any numbers that
precede a non-zero digit are significant.
EX: 2500 = 2 sig figs
50000 = 1 sig figs
5001
= 4 sig figs





If an exponential number, look at
coefficient only.
If decimal at end all numbers are
significant.
A line over a zero indicates that zero as
the last significant digit.
Use decimal or line, not both.
No lines over nonzero digits.
Examples

How many sig
figs are in the
following:

20 kg






2 sig figs
90.4˚C


2 sig figs
0.010 s

3 sig figs
0.004 cm



1 sig fig
6 sig figs
5310 g


unlimited
2.15000 cm


4 sig figs
20 cars


3 sig figs
100.0˚C


2 sig figs
0.00900 l

2 sig figs
11 m
0.089 kg

1 sig fig
0.0051 g


3 sig figs
12050 m

4 sig figs
Calculations using sig figs


Adding or subtracting:

Look at the decimal
places. Choose the given
information that has the
least number of
decimal places. Make
sure to put your answers
in the least number of
decimals. Your calculator
does not do this! Your

final measurement can
not be more specific than
your least specific
measurement!
Multiplying or dividing:
Identify sig figs for each
number in your
information. Your
answer needs to be
altered to the least
number of sig figs
used when solving the
problem. (for the same
reason)
Addition
Subtraction
Multiplication
Division
Practice:
1. Give the correct number of significant figures
for:
4500
4500.
0.0032
0.04050
2. 4503 + 34.90 + 550 = ?
3. 1.367 - 1.34 = ?
4. (1.3 x 103)(5.724 x 104) = ?
5. (6305)/(0.010) = ?
Scientific Notation



Why is it that we use scientific notation in
science?
because many of the numbers, amount,
etc. that we use are either really big or
very small.
Examples: Distance from the Earth to the
Sun, size of an atom, the mass of an
electron, proton, or even neutron…..
Scientific Notation
If the number is large –
you will have a positive
exponent
 If the number is very
small – you will have a
negative exponent.
 Exponent decides which
direction and how many
spots you will move the
decimal
EX: 10000 = 1 x 104
0.00044 = 4.4 x 10-4

Must honor sig figs in
original value
 Root number or
coefficient is the only
number that is
significant (exponent
does not count)
EX: 2.4327 x 104
5 sig figs
7.8 x 10-3
2 sig figs

Examples

What is the correct scientific notation for:







25000
.00000801
12.87
What is the correct standard notation for:
1.98 x 103
2.609 x 10 -2
3.81 x 10-5
0.070 x 105
0.005 x 10-3
Calculations with scientific notation


Multiplication:
multiply the
coefficients(roots)
and add your
exponents
Division: divide the
coefficients(roots)
and subtract your
exponents

Add or subtract:
Change your
exponents to equal
(largest one), then add
and put back into
correct scientific
notation. OR put your
numbers in standard
notation +/- and then
place back into
scientific notation
Practice:








(2.68 x
(2.95 x
(8.41 x
(9.21 x
(4.52 x
(1.74 x
(2.71 x
(4.56 x
x 103)
(3.05 x
10-5) x (4.40 x 10-8)
107) ÷ (6.28 x 1015)
106) x (5.02 x 1012)
10-4) ÷ (7.60 x 105)
10-5) + (1.24 x 10-2) + (3.70 x 10-4) +
10-3)
106) - (5.00 x 104)
106) + (2.98 x 105) + (3.65 x 104) + (7.21
106) x (4.55 x 10-10)
How can you decide if your
experiments are accurate/precise?


Percent error = calculations that will give
you a percent deviation from the true
value.
Formula: l True – experimental l x 100
True
Example


A student measured the density of an object to
be 2.889 g/ml, the true density of the object is
2.699g/ml. What is the percent error of the
experiment? Is the student accurate?
ANSWER: 7.000% error, anything below
10% is acceptable as accurate. The closer
to 0% the better!
Metric System



The Metric system was developed in France
during the Napoleonic reign of France in the
1790's.
The metric system has several advantages
over the English system which is still in place
in the U.S.
However the scientific community has
adopted the metric system almost from its
inception.

The advantages of the Metric system are:
1. It is based on a decimal system (powers
of ten).
2. It simplifies calculations by using a set of
prefixes.
3. In order to move from one prefix to
another you simply move the decimal.
4. It provides a standard measurement
system that is used by the scientific
community. (SI Base Units)
Prefix
Pico
Nano
Micro
Milli
Centi
Deci
no prefix
Deka
Hecto
Kilo
Mega
Giga
Decimal equivalent
0.000000000001
0.000000001
0.000001
0.001
0.01
0.1
1.0
10.0
100.0
1000.0
1,000,000.
1,000,000,000.
Exponent
10-12
10-9
10-6
10-3
10-2
10-1
100
101
102
103
106
109
SI Base Units
Table 1.
Base quantity

Length
Mass
Time
electric current
temperature
Name
Symbol
SI base units
meter
kilogram
second
ampere
kelvin
amount of substance mole
m
kg
s
A
K
mol
Common Base Units


The SI Base Units are standard for
Scientific Reports.
During your chemistry experience, you will
use these common base units:
-temperature  Celcius
°C
-length
 centimeter
cm
-mass
 gram
g
Common Prefixes
Converting Between Units of Metric
EX: Convert 500.0 mm  m
Step 1: Identify the prefixes in the given
values.
Step 2: Refer to the order of prefixes:
K h D m(base unit) d c m
Step 3: Find the direction that you will need to
move the decimal to achieve your new prefix.
Step 4: Move the decimal in that direction, the
same number of times.
Step 5: Express new value with correct unit
and sig fig.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
500.0 mm  m
(milli) (base unit of meter
so no prefix)
K h D Base Unit d c m
500.0
0.5000 m
EX: Convert 7.500 L  cL
Step 1:
(liters is (centi)
base unit)
Step 2: K h D Base Unit d c m
Step 3:
Step 4:
7.500
Step 5:
750.0 cL

•
•
•
•
•
•
•
Practice:
5000 mg  g
0.0076 km  m
1.000 hL  L
250000 mm  km
50.0 cg  mg
3.0 cm  dm
1.0 kg  mg

Density and Temperature
Mass

Mass = amount of matter that an object
contains. This is a physical property of
matter
 Golf ball or tennis ball?
 Golf ball is solid therefore has more
mass, tennis ball is made of empty
space.
 Lab instrument and unit?
 Scale and grams (g)
Volume

Volume = The amount of space an object
occupies. This is also a physical property
of matter
 1. Volume of a regular shaped object
like a cube, uses the formula:
 V = L x W x H
 What lab instrument would be used to
find and its unit?
 Ruler and cubic centimeters (cm3)
Volume

2. Volume by displacement
 Used when you have an irregular
shaped object. Ex: Marble or rock
 Lab instrument and unit?
 Graduated cylinder and milliliters (mL)
 How do you perform?
Density



Both mass and volume
make up density, it is
the relationship
between the two.
Density is also a
physical property of
matter
Formula = D = m/v
 M= mass
 V = volume
Density

Units for density are:
1. g/mL
 2. g/cm3


Question: A piece of metal
has a mass of 40 grams
and a volume of 80
milliliters, what is its
density?
 D= m = 40g =
v
80 ml
0.5g/mL
Density


A piece of wood has a density of 45
g/cm3, its mass is 5.0 grams. What is its
volume?
New formula: m/D = v

5.0 grams = 0.11 cm3
45g/cm3
Temperature




A measurement which describes the hotness
or coldness of a substance.
Instrument used = thermometer
We will commonly use ˚C in labs, but SI unit
is K = Kelvins
Formulas:




˚F = (˚c x 1.8) + 32
˚C = (˚F – 32) ÷ 1.8
˚C = K – 273
K = ˚C + 273