Welcome to Chemistry I CHEM 1025
Philosophy: Why study chemistry?
Chapter 1 Matter and Measurement
Chemistry is the study of the properties of matter (material) and the changes that matter under goes into new materials.
Matter is the physical material of the universe; it is anything that has mass and occupies space.
The tremendous variety of materials (matter) in our world is due to combinations of only about 100 very basic substances called elements.
We seek to relate the properties of matter to its composition (I.e. elemental composition/ structure).
Atoms can combine together to form molecules. Molecules are held together is specific shapes.
Every change in the observable world -from boiling water to the changes that occur as our bodes combat invading viruses has its basis in the unobservable world of atoms and molecules.
Matter can exist in one of three states of matter: a gas, a liquid, or a solid. A gas is highly compressible and will assume both the shape and the volume of its container. A liquid is not compressible and will assume the shape but not the volume of its container. A solid also is not compressible, and it has a fixed volume and shape of its own.
Matter can also be classified according to its composition. Most of the matter that we encounter exists in mixtures, which are combinations of two or more substances. Mixtures can be homogeneous or heterogeneous.
Mixtures can be separated into pure substances, and pure substances can be either compounds or elements.
A Pure Substance: Matter that has a fixed composition and distinct properties (Pure substances contain only one kind of matter)
Elements: A substances that cannot be separated into simpler substances by chemical means into simpler substances by chemical means..
Compounds: A substance composed two or more elements united chemically in definite proportions.
Mixture: A combination of two or more substances in which each substance retains its own chemical identity.
Homogeneous: Having uniform composition throughout.
Heterogeneous: Having diverse composition
Mixtures can be separated into pure substances, and pure substances can be either compounds or elements.
The student should be able to classify various substances. Use the flow chart above to classify the follow substances:
Different types of matter have different distinguishing characteristics that we can use to tell them apart. These characteristics are called physical properties and chemical properties. Physical and chemical properties may be intensive or extensive. Intensive properties such as density, color, and boiling point do not depend on the size of the sample of matter and can be used to identify substances. Extensive properties such as mass and volume do depend on the quantity of the sample.
A physical property refers to those characteristics of a substance we can observe without changing the composition of the substance.
A chemical property of a substance describes its chemical reactions with other substances.
Chemical properties are only observed via chemical reactions.
Physical and Chemical Changes
In a physical change, the chemical composition does not change (a change of state occurs).
In a chemical change, the composition of the sample changes, and a new set of properties are observed.
In a chemical change, we usually observe one of the following:
(A chemical change is the same as a chemical reaction).
As we perform our experiments, we may begin to see patterns that lead us to a tentative explanation or hypothesis that guides us in planning further experiments.
A scientific law is a concise verbal statement of mathematical equation that summarizes a broad variety of observations and experiences.
At many stages of our studies we may propose explanations of why nature behaves in a particular way. If hypothesis is sufficiently general and is continually effective in predicating facts yet to be observed, it is called a theory or model.
A theory is an explanation of the general principles of certain phenomena with considerable evidence or facts to support it.
Ask the question: Is it measurable? If so, its' a law.
Ask the question: does it explain a behavior? If so, its' a theory
For example, the law of gravity is a measurable relationship for falling bodies (g=32ft/s2) and thus is a law. Chemical reaction rates are affected both by the concentrations of reactants and by temperature which is explained by the collision model of kinetic molecular theory.
The scientific community uses SI units for measurement of such properties as mass, length, and temperature. There are seven SI base units from which all other necessary units are derived.
Physical Quantity |
Name of Unit |
Abbreviation |
|
Mass |
Kilogram |
kg |
|
Length |
Meter |
M |
|
Time |
Second |
sec |
|
Temperature |
Kelvin |
K |
|
Amount of substance |
Mole |
mol |
|
Electric current |
Ampere |
A |
|
Luminous intensity |
Candela |
cd |
Although the meter is the base SI unit used for length, it may not be convenient to report the length of an extremely small object or an extremely large object in units of meters. Decimal prefixes allow us to choose a unit that is appropriate to the quantity being measured. Thus, a very small object might best be measured in millimeters (1 millimeter = 0.001 meters), while a large distance might best be measured in kilometers (1 kilometer = 1000 meters).
Prefix |
Abbreviation |
Meaning |
|
Giga |
G |
109 |
|
Mega |
M |
106 |
|
Kilo |
k |
103 |
|
Deci |
d |
10-1 |
|
Centi |
c |
10-2 |
|
Milli |
m |
10-3 |
|
Micro |
m |
10-6 |
|
Nano |
n |
10-9 |
|
Pico |
p |
10-12 |
|
Femto |
f |
10-15 |
The SI unit of temperature is the kelvin, although the Celsius scale is also commonly used. The Kelvin scale is known as the absolute temperature scale, with 0 K being the lowest theoretically attainable temperature.
K = ºC + 273.15
The common temperature scale in the United states is the Fahrenheit which is not used in scientific studies. The Fahrenheit and Celsius scales are related as:
Even the most carefully taken measurements are always inexact. This can be a consequence of inaccurately calibrated instruments, human error, or any number of other factors.
Two terms are used to describe the quality of measurements: precision and accuracy. Precision is a measure of how closely individual measurements agree with one another. Accuracy refers to how closely individually measured numbers agree with the correct or "true" value.
Whatever the source, all measurements contain error. Thus, all measured numbers contain uncertainty. It is important that these numbers be reported in such a way as to convey the magnitude of this uncertainty.
Consider a fourth-grade student who, when asked by his teacher how old the Earth is, replies "Four billion and three years old." (The student had been told by a first-grade teacher three years earlier that the Earth was four billion years old.) Obviously, we don't know the age of Earth to the year, so it is not appropriate to report a number that suggests we do.
RULES FOR DETERMINING SIGNIFICANT DIGITS
1. Nonzero digits are always significant.
2. Leading zeros that appear at the start of a number are never significant because they act only to fix the position of the decimal point in a number less than 1.
3. Confined zeros that appear between nonzero numbers are always significant.
4. Trailing zeros* at the end of a number are significant only if the number contains a decimal point or contains an over-bar (*may or may not be significant).
Examples
Nonzero digits are always significant- 457 cm (3 significant figures); 2.5 g (2 significant figures).
Zeros between nonzero digits are always significant–1005 kg (4 significant figures); 1.03 cm (3 significant figures).
Zeros at the beginning of a number (leading zeros) are never significant; they merely indicate the position of the decimal point–0.02 g (one significant figure); 0.0026 cm (2 significant figures).
Zeros that fall at the end of a number (trailing zeros) are significant when the number contains a decimal point –0.0200 g (3 significant figures); 3.0 cm (2 significant figures).
When a number ends in zeros but contains no decimal point, the zeros may or may not be significant–130 cm (2 or 3 significant figures); 10,300 g (3, 4, or 5 significant figures).
To avoid ambiguity with regard to the number of significant figures in a number with tailing zeros but no decimal point, such as 700, we use scientific notation to express the number.
If we are reporting the number 700 to three significant figures, we can leave it written as it is, or we can express it as 7.00 x 102.
There is no ambiguity in the latter regarding the number of significant figures, because zeros after a decimal point are always significant.
However, if there really should be only two significant figures, we can express this number as 7.0 x 102. Likewise, if there should be only one significant figure, we can write 7 x 102.
Scientific notation is convenient for expressing the appropriate number of significant figures. It is also useful to report extremely large and extremely small numbers. It would be most inconvenient for us to have to write all of the zeros in the number 1.91 x 10-24 (0.00000000000000000000000191).
Rules for Rounding Off
1. If the first non-significant digit is less than 5, drop it and the last significant digit remains the same. Thus, 47.21 (rounded to 3 sig. figs) is:
2. If the first non-significant digit is more than 5 or is 5 followed by numbers other than zeros, drop the non-significant digit(s) in increase the last significant digit by 1. Hence, 47.26 and 47.252 are both equal to 47.3 ( when rounded to 3 sig. figs)
3. If the first non-significant digit is 5 and and is followed by zeros, drop the 5 and.
A) increase the last significant digit by one if it is odd, or
b) leave the significant digit the same if it is even.
4. Non-significant digits to the left of the decimal point are not discarded, but are replace by zeros.
Thus 1781 becomes 1780 and not 178 when rounded to three significant digits.
Rule for Addition and Subtraction
The answer must not contain a smaller place (that is, decimal, units, tens, and so on) than the number with the smallest place.
25.1
+22.11
47.21 rounds to
47.2
In the above example, the data (25.1) limits the answer to the tenth place.Rule for Multiplication and Division
In multiplication and division, the answer must not contain any more significant digits than the least number of significant digits in the numbers used in the multiplication or division.
Rounds to 11.8
In the above example, a number with four significant digits is being diveded by a number with three signigicant digits. Thus the answer must be rounded to three singnificant digits.
A Special Rule: Exact Numbers
Exact numbers are precisely know and can have as many significant digits as a calculation requires, so they are not used to determine the number of significant digits for an answer. For example there are exactly 12 inches in 1 foot. So if you were told to calculate the amount of feet in 26.89 in you would set up the problem as below:
Rounds to 2.248 ft
In the above example, just the data (26.89 in), which has four significant digits, is used to determine the significant digits in the answer.
Dimensional Analysis: A method of problem solving in which units are carried through all calculations. Dimensional analysis ensures that the final answer of a calculation has the desired unites.
More inportantly, units will show you how to set up the problem. If you learn this one concept, all those "hard" chemistry word problems will become simple! (Dimensional analysis can be a tool used to help you solve the problem with out algebra).
In general, we begin any conversion by examining the untis of the given data and the units we desires. We then ask ourselves what conversion factor is need to yield the desired unites.
The key to dimensional analysis is the correct use of conversion factors to change one unit into another. A conversion factor (also known as a unit factor) is a fraction whosenumberator and denominator are the same quantity expresed in different units. For example, 12 inches and 1 foot are the same lenght, 12in = 1ft. This relationship allows us to write two conversion factors:
In the above example where 26.89 in. is converted into feet, one does not have to ponder whether to multiply or divied by twelve (the number of inches in one foot). Because the units of inches is in the given data one must divide by 12 inches in order for inches to factor out as shown below.
On your calculator that's: 26.89 [¸] 12 [=]
Most word problems that you come accross will take the above form. The student should read the problem to find the "given" then write that value along the units on the lefthand side of the paper. Next, place the conversion factor which has the units of the given in the denominator next to the given. The units of the given then cancel leaving the units in the numerator in the calculated answer.
Example A If a woman has a mass of 115 lb, what is her mass in grams? Here, the given value is 115 lb. The back inside cover of your textbook tells you that: 1 lb = 453.6 g On your calculator that's: 115 [x] 453.6 [=]
Density is widely used to characterize substances. It is defined as the amount of mass in a unit volume of the substance:
Notice that density has units of mass per volume (g/cm3). All density problems involve solving for one of three things: mass, volume, or density. Here is an example. Calculate the density of mercury if 100.0g occupies a volume of 7.36 cm3(Notice the units in the problem are "g" and "cm3").
How much would a liter(1000cm3) of mercury weigh, given that the density of mercury is 13.6g/cm3?
What volume would 1000.0 g of Balsa wood occupy given, that the density of Balsa wood is 0.160 g/cm3?
Once again, one does not have to ponder whether to devide or multiply by density. Use the unit factor which will cancel grams and yield volume (cm3 in this case).
Chemist and other scienist would solve the above problem using the below format A horizontal line is used with a vertical line to seperate various unit factors.
Now to illustrate how dimensional analysis helps one to solve the problem. As you can see from examples B and C sometimes you need to multiply by density and other times you divide. If you work out with paper and pencil by writing units, your mistakes will become obvious. Lets say the student (I see this done year after year) attempts example C by doing the exact same thing they did in example B. The student would then come up with the following expression:
Doing the math on the calulator and algerabra on the units yields the answer below:
At this point the student should ask themselves the all important question: "Does the answer make sense?" No, it doesn't make sense. The question was how many cubic centimeters of balsa wood are there in a 1000 grams of balsa wood. The density (0.169g/cm3) of balsa wood tells you that one cubic centimeter (1cm3) has a mass of 0.160 grams (1cm3=0.160g). Another way to say the same thing would be: 6.25 cm3 has a mass of one gram (6.25 cm3=1g). Thus, one should expect to calculate a value that is larger than the given value (6.25 times larger). Lastly, the units grams squarded per cubic centimeter should tell you the answer is not correct and that the student needs to multiply by the recipcal of the unit factor that they used.
One can put as many unit factors together as needed to solve the problem. Below is a good example of using multiple unit factors:
A political leader wants to flee his homeland and take with him one million dollars. Rather then leave with currency, he will take a million in gold. Given that gold is $300/oz and has a density of 19.32g/cm3, what size (volume) of attaché case is needed and what mass of gold (kilograms please) will be in the attaché case?
Looks like about 5 liters. Should have a little volume to spare in the attaché case.
Now how heavy?
Chemistry teachers call this the railroad track method. Millions of chemistry students have found this method to be quit useful. It behooves you to make use of it. Must know knowledge from chapter one * Answer must have correction number of significant digits.
Example B
Notice that in the above expression, the units cm3 cancel out leaving units of mass in grams.
Example C
