AT Chemistry
2014
Szkolar/Levine
Chapter 1 Notes
Before Chemistry
After Chemistry
CHEMISTRY
The study of matter and its properties, the changes matter undergoes, and the energy
associated with those changes.
Let’s first review some concepts you learned a couple of years ago in Regents chem.:
Substance
Matter that has definite, fixed composition and distinct properties.
Element
A substance that cannot be separated into simpler substances by physical or chemical
means
Compound
A substance composed of two or more elements which are chemically united in fixed
proportions. Compounds can be separated by chemical means but not by physical means.
Mixture
Matter composed a physical intermingling of two or more substances and whose
composition is variable. Mixtures can be separated by physical means.
Mixtures can be considered to be of two types:
Heterogeneous mixtures do not possess a uniform composition.
In a heterogeneous mixture some regions are richer in one component substance
than are other regions
Example:
Homogeneous mixtures have composition that is uniform right down to the
submicroscopic level.
Example:
It is often difficult to distinguish between heterogeneous and homogeneous mixtures (e.g.
milk “looks” uniform, but it’s not). Another term that means homogeneous mixture is
solution. If the major component of a solution is water, we call it an aqueous solution.
Many chemical reactions occur in aqueous solution.
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Property
A characteristic that can be observed
There are several kinds of properties we will study:
Physical property is one that can be measured/observed without changing the
composition or identity of a substance.
Physical change is a change in (physical) properties without any change in the
composition or identity of a substance.
Example:
Chemical property is one that can be observed only during a chemical change.
Chemical change is a change in the composition or identity of a substance (which is,
naturally, accompanied by changes in physical and chemical properties.
Example:
Every substance has a unique set of chemical and physical properties.
Macroscopic properties can be measured directly.
Submicroscopic properties cannot be measured directly (they are determined indirectly)
We make macroscopic measurements to determine macroscopic properties. Starting from
our macroscopic data, we deduce submicroscopic properties. We use our understanding
of the submicroscopic level to account for and explain macroscopic behavior.
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Classification of Matter:
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According to the Standard Model, elementary particles are classified into three families
which are made up of particles such as the electron, muon, up quark, down quark,
electron neutrino, charm quark, strange quark, tau-neutrino and several others. What
about dark matter and dark energy?
A new theory model has emerged called String Theory. This theory attempts to create a
universal theory of gravity by linking together two theories that are incompatible:
quantum mechanics, which describes how matter behaves at the scale of individual atoms
or smaller, and Albert Einstein’s General Relativity, which describes how gravity behaves
at scales that are larger than individual atoms. String theory says that all of the
fundamental particles and forces that make up the universe consist of tiny, vibrating
“strings.” The particular vibrational mode of the string determines how it expresses itself:
as an electron or an up quark, or a tau-neutrino, etc. These string are so small they are far
beyond human ability to detect them, and so far, there is no evidence from any
experiments to confirm them. What’s more, there are several varieties of string theory.
Some say the strings form loops, like wobbly rubber bands, while others say the strings
are open ended. And they require different numbers of dimensions beyond height, width,
depth, and time. If confirmed, string theory would give physicists a new basis for
modeling the birth of the universe, the formation of matter and energy, the mysterious
dark matter and dark energy, and other grand questions about matter, time, and space. In
other words, the theory of everything
Separation of Mixtures
Distillation - based on differences in the ease of vaporization of the compounds (i.e.
difference in boiling points)
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Filtration – method of separating the components of a mixture containing a solid and a
liquid; based on difference in particle size
Chromatography - The fundamental basis for all chromatography concerns the
distribution of the individual components of a mixture between two phases: the
stationary phase and the mobile phase. As the name implies, the stationary phase is a
nonmoving substance which may exist in a variety of forms (usually solid). Commonly it
is contained in a column or spread in a thin layer over a glass backing. The mobile phase
percolates over the stationary phase and may be either a gas, as with gas chromatography,
or a liquid, as with column chromatography. As the mobile phase flows over the
stationary phase it carries with it the sample mixture with all of its components. The
components are separated as a result of the sorption-desorption which occurs as they are
carried through the stationary phase. When an individual component favors (is more
strongly attracted to) the stationary phase, it tends to be held longer and, as a result,
moves more slowly through the stationary phase column than another component which
favors the mobile phase. It is these differences in equilibrium which allow for the
separation of compounds in multi-component systems.
Extraction – separation based on difference in solubility
Centrifugation – separation based on difference in density
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Energy
The ability to do work
We will study energy and energy transfer in chapter 6 (thermochemistry). Understanding
energy is crucial if we wish to understand chemistry, because chemical reactions always
involve energy changes. In fact, we will learn in the chapter on thermodynamics
knowledge of the energy change that would accompany a reaction should it happen to
occur is an important part of being able to predict whether or not that reaction is possible.
Most processes lead to a lowering of energy. Energy comes in two general forms:
Kinetic energy – energy due to motion
Potential energy – energy due to position
Energy can be converted from one form to another, but it cannot be created nor destroyed
(Law of Energy Conservation – the First Law!)
Measurements in Scientific Study
Almost all our calculations will be done in SI (Systeme Internationale) unit. Below is a
summary of SI base units
Base quantity
unit name
symbol
Mass
_______________
_____
Length
_______________
_____
Time
_______________
_____
Temperature
_______________
_____
Electrical current
_______________
_____
Amount of substance
_______________
_____
The base units are not always the most conveniently sized units for expressing some
measurements. Therefore, we can use multiple of base units (some of which are
“fractional multiples”) to express our measurements. We use a set of prefixes to
designate which multiple we are using and these are summarized below:
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Prefix
symbol
meaning
example
kilo
_____
_____
____________________
centi
_____
_____
____________________
milli
_____
_____
____________________
micro
_____
_____
____________________
nano
_____
_____
____________________
There are a few quantities that often confuse people. For example, mass and weight.
Mass – a measure of the quantity of matter in an object, measured with a ____________,
versus
Weight – the force that gravity exerts on an object, measured with a _______________.
Another example involves heat and temperature.
Heat – involves the transfer of thermal energy from a warm object to a cooler object.
Thermal energy is the kinetic energy possessed by the submicroscopic particles that make
up each object.
versus
Temperature – a measure of the amount of thermal energy that an object contains (or a
measure of the average kinetic energies of its particles).
There are three common temperature scales, summarized below:
Scale
freezing point H2O
boiling point H2O
symbol
Kelvin
________
________
_____
Celsius
________
________
_____
Fahrenheit
________
________
_____
Forget Fahrenheit as it is used only by weatherman in the US and Great Britain.
How do we convert between Celsius and Kelvin temperatures?
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Some quantities that we will measure do not correspond to any SI base units but to
combinations of these units. These combinations of base units are called “derived” SI
units.
Derived unit
base unit combinations
symbol
Volume
product of three lengths
m3 *
Density
mass/volume
kg/m3**
*
the m3 for volume is large and we often use cm3 in chemistry. As far as volume
measurements are concerned (for fluids, which refer to liquids and gases),
1 L = 1 dm3 and 1 ml = 1 cm3
**The kg/m3 for density is small and the more commonly used unit in chemistry is g/cm3
(for solids and liquids) and g/L (for gases).
The units we have seen can be separated into two classes:

Some apply to quantities that depend upon the amount of substance and are called
extensive properties.
example:

Other units apply to quantities that do not depend of the amount of substance and
are called intensive properties.
example:
text problems 4, 5,
Experimental Error
Precision and Accuracy
Precision refers to the degree of how close repeated determinations done the same
way are to each other. Precision is determined by the scale of the measuring instrument.
The more precise the scale (i.e, the greater the number of decimal places it can record),
the closer repeated measurements will be to each other. A balance measuring mass to
the ten-thousandth place will be more precise compared to one measuring mass to the
hundredth place. We like to be as precise as possible, but this does not always insure
accuracy. Recall that accuracy is how close our measurement is to some “accepted”
value.
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We assume that the error between repeated measurements is due to random errors.
Random error (or indeterminate error) means that a measurement has an equal
probability of being low or high. This error occurs when estimating the value of the last
digit of a measurement. This is the recorded uncertainty of the scale of an instrument –
the plus/minus or + in a measurement.
As a specific example, consider some actual results of an experiment performed
by AT chemistry students at Scarsdale High School on determining the molar mass of a
volatile liquid by the Dumas method. Listed below are the data they obtained:
trial
1
2
3
4
5
6
7
8
9
10
11
12
Molar mass (g/mol)
83.21
84.55
82.88
83.68
82.43
81.79
80.66
81.85
82.30
84.69
82.24
81.36
What do we choose to report for the best estimate of the molar mass? The proper
procedure is first to examine the data to see whether any of the results are especially far
from the rest (a value of 76.45 might be such an example). Such values are likely to
result from some mistake in carrying out or reporting that particular measurement, and
therefore are excluded from further consideration (although there have been cases in
science where just such exceptional results have led to significant breakthroughs). In our
data no such points should be excluded. To obtain our best estimate for the molar mass,
we calculate the mean or average value, by adding up the values found and dividing by
the number of measurements.
Average = ___________ g/mol
The average by itself does not convey any estimate of uncertainty. If all the
measurements had given results falling between 81.00 and 82.00 g/mol, the uncertainty
would be less than if the results had ranged from 80 to 86 g/mol. Furthermore, an
average of 100 measurements should have less uncertainty than an average of 5.
Therefore, a measure of uncertainty should take into account both the spread of the data
and the number of determinations. How these ideas are made quantitative? A statistical
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measure of the spread of data, called standard deviation, s, is useful in this regard. It is
given by the formula
s = (sum of the squares of the deviations from the mean/number of observations - 1)1/2
n
s
(X
i 1
i
 X )2
n 1
where s = standard deviation from the mean, xi = members of the set, x = mean, and n =
number of members in the set of data. The symbol  means to sum over the members.
The simplest way for us to calculate the standard deviation is to take advantage of
our graphics calculators.
On the TI-89 calculator:
press 2nd and math (above number 5 key)
press 6
press 6 again
press 2nd and bracket {
enter data separated by comma
close bracket } and parenthesis )
press “green diamond” and ENTER
alternately on the TI-89 you may get a complete statistical analysis by following these
steps:
press APPS
press 6 (Data/Matrix Editor)
press 3 (New)
arrow down to variable box and type in any title (in letters)
ENTER twice
Use c1 to fill in your data
Press F5
Arrow right and then up to OneVar and ENTER
Arrow down and type c1
ENTER twice
The sx represents the standard deviation
Standard Deviation, s =
For practical purposes, standard deviation can be used to omit any data that are not really
valid skew the mean. As a rule of thumb, any individual measurement (Xi) that differs
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from the mean by two standard deviations or more (2s) must be discarded and a new
mean determined. In our example of data on the molar mass twice the standard deviation
is 2.46. Adding and subtracting 2.46 from the average gives a high value of 85.10 and a
low value of 80.18. All are measured data fall within this range and are thus statistically
valid.
Random error is only one source of error. The other source of error is called
systematic (or determinate) error. Systematic error causes a shift from the true value
and reduces the accuracy of the result. By making more measurements we can reduce the
random error and increase the precision of our results, but if systematic errors exist the
experimental result will still differ from the true (or accepted) value. Systematic errors
can result from miscalibration of the instruments or some error in the experimental
technique. Systematic error is measured by determining the percent error:
observed  accepted
X 100
accepted
Problem: If the accepted value for the molar mass of the volatile liquid is 86.07 g/mol,
calculate the percent error:
Uncertainty in Measurements
A measurement always has some degree of uncertainty. In recording a measurement, we
always use significant figures - these indicate the uncertainty of a measurement and are
related to precision.
In recording a measurement, we record only a limited number of digits (i.e. the ones we
got from the instrument, always regarding the last one as “less certain” or estimated). We
refer to these recorded digits as significant digits or significant numbers.
The more precisely a measurement is made, the more significant figures that can be
recorded.
When we are given a measured value (say, one measured by someone else) we assume
that the number of digits shown reflects the precision of the measurement (and that the
last digit is less “certain” i.e. estimated, than the other)s.
e.g.
27.13 + 0.01g
the 2, 7 and 1 are certain, the 3 is estimated
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Given a measured value, we count the number of significant figures as follows:
1.
2.
3.
4.
5.
All non-zero digits are significant.
All zeroes that are between non-zero digits are significant.
Leading zeroes are not significant.
Trailing zeroes to the right of a decimal point are significant.
Measured values that have trailing zeroes only to the left of the decimal point (or
which do not have a decimal point) are ambiguous and should be expressed in
scientific notation
For example, the quantity “one hundred” must be written as
1 X 102 if it has one sig fig
1.0 X 102 if it has two sig figs
1.00X 103 if it has three sig figs
(though 100.0 is perfectly fine to represent four sig figs)
Problem: How many sig figs are there in each of the following measurements?
a)
b)
c)
d)
e)
f)
g)
h)
i)
8.45 cm
1.234 kg
606 m
40, 501 J
0.08 L
0.0000349 g
2.0 mg
0.004200 s
400 cm
There are numerical values which are not subject to experimental error. These are the
“defined quantities” (e.g. 1 m = 100 cm exactly) and numerical values which represent a
counted number of objects (e.g. there are 5 boroughs in New York City). For such
values, there is no error and so we need not worry about significant figure restrictions for
such quantities. These quantities are called “exact numbers”. The important point is that
exact numbers are not used in determining the final number of significant figures in
any mathematical calculation of measured quantities (data).
Calculations involving Significant Figures
1) The number of significant figures in the result depends upon the lweast
precise piece of data.
2) If only addition and/or subtraction is performed, round the result to the same
decimal place as the least precise piece of data. For example, suppose that
you weigh a beaker on a crude balance and find that the weight is 52 g.
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Reporting this result to two sig figs implies that there is some uncertainty in
the second digit. The weight could be 51 or 53. (It may actually be less
precise than this. If no uncertainty is explicitly stated, you should assume that
the uncertainty is 1 in the last sig fig). If you weigh a sample of KHP
(potassium hydrogen pthalate) on an analytical balance and obtain 1.2345 g as
the weight, what is the combined weight of the beaker plus the salt? If you
report a combined weight of 53.2345 g, you will be wrong. Think of the
addition as written below:
52.
+ 1.2345
53.?????
You should report 53 g as the combined weight of the beaker plus salt.
3) If any multiplication and/or division is performed (even if there was
addition/subtraction too!), round the result to the same number of significant
figures as the least precise piece of data.
For example, 2.8 X 4.5039 = 13
4) We will follow Dr Halpin’s convention at NYU and never round off during a
multistep calculation!!! Only round off when reporting an answer!!!
Uncertainty Analysis
This is a tool for analyzing uncertainties introduced into experiments by the process of
measuring. Such an analysis might be useful for several reasons.
(1) You might need to know how much you can trust your results
(2) It is important to figure out where the weakest link in an experiment is so that it can
be improved.
(3) If there is a previously measured or theoretical number, one might wish to know
whether there is agreement or not with experiment. Is the difference “real” or is it an
experimental quirk?
(4) If you have measured something in two different ways, you will wish to know
whether the numbers are in agreement within experimental uncertainty or are
significantly different.
Rather than rely on blind prejudice, a formal system for calculating the maximum
probable uncertainty has been developed. This system computes the largest reasonable
uncertainty in a measurement derived from data whose uncertainty is known.
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The process of uncertainty analysis is a three step process:
 Make estimates of uncertainty in each measurement
 Derive uncertainty in calculated result
 Use uncertainty of result to bolster the argument
Definitions
Absolute Uncertainty: the uncertainty in a measurement or derived quantity expressed
in some absolute unit. e.g. a weight reported as 1.00 g + 0.01 g.
Relative Uncertainty: the uncertainty expressed in terms of the magnitude of the
quantity reported, usually as a percentage.
Relative uncertainty = absolute
uncertainty/measurement X 100. Continuing the above example, relative uncertainty is
0.01
X 100 = 1.0%.

1.00
The process of calculation of uncertainty in results starts from an estimate of uncertainty
of measurement. The instrument may indicate the uncertainty. In the absence of
specific instructions, it is safe to use half the smallest readable value.
Once you have an estimate of the uncertainty in the data, you may easily calculate an
uncertainty in a result using the rules below:
(i) If the result is determined by addition or subtraction, add absolute
uncertainties of measured quantities.
Final answer = _____ + _____ unit
(ii) If the result is determined by multiplication and division, add relative
uncertainties of measured quantities.
Final answer = _____ + _____ %
The final step is to use your calculated uncertainty to bolster your argument.
for example, you have calculated that a given value is 2.0 + 0.2 (a 10% error) and
accepted value is 2.1, your number agrees within experimental uncertainty. But if
accepted value is 2.5 + 0.1, then there is a problem with either your number or
accepted value.
If,
the
the
the
This problem usually turns out to be that you did not measure what you thought
you measured: “systematic error.” Either you made an outright blunder (such as dropping
some of the compound you just weighed) or there is a systematic error somewhere. All
that you ever look at is scale readings and those scale readings may not reflect the
quantity they are supposed to. If, for example, you are measuring length, and your meter
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stick expands, this will produce a systematic error that will make the length seem too
short.
It is important to distinguish between systematic errors and the experimental
uncertainty. They are totally different concepts. Repeated measurements will reduce
experimental uncertainties, but the systematic errors will remain. (If, in the above
example, you measure the same length ten times with an expanded meter stick, your
average length will still be wrong). Systematic error can be reduced by careful
experimental design and the use of control experiments.
One of the real purposes in teaching you the technique of propagation of
uncertainty is so that you will know how much variation in results is to be expected from
the act of measurement itself. Scrutinize measurements that look off for systematic errors
or student blunders.
Examples of Basic Types of Uncertainty Analysis Calculations
1. Uncertainty in a concentration. A solution is made up in a 100.0 ml volumetric flask
(volume is a measured quantity). The substance has a MW of 120.0 (the MW is
defined quantity) and 2.6754 g are weighed out (the mass is a measured quantity).
What is the error in the concentration?
Conc =
2.6754 g
1
X
= 0.2230 M
120.0mol 0.1000L
Weighing is done by weighing a vial containing the solid, then transferring the solid
quantitatively to the flask, then reweighing the vial. The absolute uncertainty in each
weighing is + 0.0001 g.
Mass vial and solid
Mass empty vial
Mass solid
15.1254 g + 0.0001 g
12.450 g + 0.0001 g
2.6754 g + ?
Since two weighings are needed, the total absolute uncertainty is + 0.0002 g. This
0.0002
is
X 100 = 0.0075% in relative uncertainty.
2.6754
The volumetric flask has an uncertainty of + 0.2%. The relative uncertainty in the
concentration is the sum of the relative uncertainties of the volume and weight
measurements. Total uncertainty in concentrations = 0.2% + 0.0075% = 0.2%
In absolute terms the uncertainty is (0.2230 X 0.002) = 0.0005M and the concentration
should be reported as 0.2230 M + 0.0005M.
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2. Uncertainty in a burette reading. If the liquid level in the burette was initially at 1.05
mL and at 26.74 mL after the solution ran out, what is the uncertainty in volume?
26.75+ 0.05mL
1.05 + 0.05mL
25.70 + 0.10 mL
here we are adding measured quantities, se we add
the absolute uncertainties to get the uncertainty
in the final volume.
Correctly reading and recording a scale measurement:
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A measurement is
precise
accurate
if it is in agreement with
repeated measurements
made by the same
procedure
the true value
in other words, it is
reproducible
correct
The extent of agreement can be expressed as the
range or standard
deviation of repeated
measurements
absolute error or
percent error of
the measurement
Text problems 8, 11, 13, 16, 31, 33, 35, 37, 39, 47, 51, 61, 71, 73, 77, 79, 81, 84, 87, 89
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The College Board’s revised AP Chemistry curriculum reflects more of a focus on those
learning skills that we in the Science Department felt were more important when we
transitioned from AP to Advanced Topics (AT) several years ago. Our goals include the
following:









To develop critical thinking skills to enhance a student’s ability to perform
conceptual and abstract reasoning using the scientific method.
To develop proficiency in investigative scientific skills through hands-on
laboratory experiences.
To enhance problem-solving skills by helping students to become organized,
active and creative thinkers.
To develop an understanding of data collection and analysis using mathematical
techniques.
To develop an understanding of science through the use of modeling.
To foster an environment that leads to the use of independent inquiry and research
To foster an environment that leads to the use of independent inquiry and
research.
To foster an environment of active student involvement.
To develop the skills to use current technology as applied to information
gathering, modeling, data analysis and problem solving.
The College Board has developed a “Big Idea Concept Chart” which we have outlined
below. These ideas are organized around a few underlying principles which are already
interwoven throughout the AT curriculum,
Big Idea 1. The chemical elements are fundamental building blocks of matter, and all
matter can be understood in terms of arrangements of atoms. These atoms retain their
identity in chemical reactions.
Big Idea 2. Chemical and physical properties of materials can be explained by the
structure and the arrangement of atoms, ions, or molecules and the forces between them.
Big Idea 3. Changes in matter involve the rearrangement and/or reorganization of atoms
and/or the transfer of electrons.
Big Idea 4. Rates of chemical reactions are determined by details of molecular
collisions.
Big Idea 5. The laws of thermodynamics describe the essential role of energy and
explain and predict the direction of changes in matter.
Big Idea 6. Any bond or intermolecular attraction that can be formed can be broken.
These two processes are in dynamic competition, sensitive to initial conditions and
external perturbations.
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