Chemistry - The study of the composition of matter and the changes that matter undergoes.
Five different branches of chemistry:
The following video by Bozeman Science (Mr. Anderson) gives a brief history of the scientific method and discusses it in step-by-step detail.
| Steps | Explanation |
|---|---|
| Problem | What is wrong? |
| Hypothesis | "Educated Guess" - Predict what will happen based on prior knowledge |
| Experiment | Test your hypothesis a) Control Group - This group will stay the same and is used for comparison b) Variable Group - This is what is being manipulated and changes 1. Independent Variable - This is what the experimenter changes (what I change) 2. Dependent Variable - This is what is being observed and measured (the dependent variable DEPENDS on the independent variable) 3. Control Variables - Things that are kept the same during each experiment Remember, a good experiment only has two variables that change (independent and dependent). All the rest of the variables must be the same. |
| Data Collection |
Observe the data that has been collected and apply statistical analysis. |
| Conclusion | Based on the observation and might support the hypothesis |
Observation - The act of gathering information (actually seeing it).
Inference - An opinion based on the observations.
Examples:
The sky is cloudy today = observation
It is going to rain = inference
Qualitative - Describes physical characteristics (e.g., color, odor, shape, sound, taste, texture)
Quantitative - Numerical information (e.g., How much?, How fast? How many? How tall?)
Scientific Law - Summarizing statement of many experiments (has been proven, usually stated in mathematical formula.
Scientific Theory - Thoroughly tested explanation of why experiments give certain results (helps predict natural systems; cannot be proven).
Matter: Takes up space and has mass. It is the material of the universe.
Three most common states of matter:
Most matter around us consists of mixtures of pure substances (e.g., wood, gasoline, wine, soil, and air).
Pure substances: A substance with constant composition. Pure water is composed solely of H2O molecules, but water found in nature is a mixture.
Two classifications of mixtures:
Heterogeneous mixtures usually can be separated into two or more homogeneous mixtures or pure substances (e.g., the ice cubes can be separated from the tea).
Example:
Methods for separating the components from a mixture:
Example:
High affinity (mobile phase) = moves quickly through the chromatographic system
High affinity (solid phase) = moves more slowly
Note: When a mixture is separated, the absolute purity of the separated components is an ideal.
Pure substances are either compounds (combinations of elements) or free elements.
Compounds: A substance with constant composition that can be broken down into elements by chemical processes (e.g., electrolysis of water - an electric current is passed through water to break it down into the free elements hydrogen and oxygen).
Elements: Substances that cannot be decomposed into simpler substances by chemical or physical means.
A quantitative observation (measurement) always consists of two parts: a number and a scale (unit).
There are two major systems of measurements: the English system used in the United States and the metric system used by most of the rest of the industrialized world.
For scientists, an international agreement set up a system of units called the International System (le Système International in French), or the SI system. This system is based on the metric system and units derived from the metric system.
| Physical Quantity | Name of Unit | Abbreviation |
|---|---|---|
| Mass | kilogram | kg |
| Length | meter | m |
| Time | second | s |
| Temperature | kelvin | K |
| Electric current | ampere | A |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
| Prefix | Symbol | Meaning | Scientific/Exponential Notation |
|---|---|---|---|
| exa | E | 1,000,000,000,000,000,000 |
1018 |
| peta | P | 1,000,000,000,000,000 |
1015 |
| tera | T | 1,000,000,000,000 |
1012 |
| giga | G | 1,000,000,000 |
109 |
| mega | M | 1,000,000 |
106 |
| kilo | k | 1,000 |
103 |
| hecto | h | 100 |
102 |
| deka | da | 10 |
101 |
| -- | -- | 1 |
100 |
| deci | d | 0.1 |
10-1 |
| centi | c | 0.01 |
10-2 |
| milli | m | 0.001 |
10-3 |
| micro | µ | 0.000001 |
10-6 |
| nano | n | 0.000000001 |
10-9 |
| pico | p | 0.000000000001 |
10-12 |
| femto | f | 0.000000000000001 |
10-15 |
| atto | a | 0.000000000000000001 |
10-18 |
An important point concerning mass and weight:
Mass is a measure of the resistance of an object to a change in its state of motion. Mass is measured by the force necessary to give an object a certain acceleration.
On Earth, we use the force that gravity exerts on an object to measure its mass. We call this force the object's weight. Since weight is the response of mass to gravity, it varies with the strength of the gravitational field.
Fun fact:
Your body mass is the same on Earth and on the moon
Your weight would be much less on the moon than on Earth because of the moon's smaller gravitational field.
Imagine that five different people took a measurement reading from the same buret. They were measuring volume by reading the meniscus (bottom of the liquid curve). The results are as follows:
20.15 mL, 20.14 mL, 20.16 mL, 20.17 mL, 20.16 mL
These results show that the first three numbers are the all same (20.1) even though different people took the readings. Since that is the case, this is called certain digits. The digit to the right of 1 is estimated and that is why it is different in almost every answer. That last number is called an uncertain digit.
Measurements always have some degree of uncertainty. The uncertainty of a measurement depends on the precision of the measuring device.
Accuracy: The agreement of a particular value with the true value.
Precision: The degree of agreement among several measurements of the same quantity.
Precision is more on the reproducibility of the measurement while accuracy requires the measurement to be close with the actual answer. The illustration to the left is the results of several darts thrown and shows the differences between accuracy and precision.
a) Neither accurate nor precise
b) Precise but not accurate
c) Accurate AND precise
The numbers of scientific measurements are often very large or very small; thus making it convenient to express them using powers of 10. Scientific/Exponential notation expresses a number as N x 10M.
Examples:
The number 1,300,000 can be expressed as 1.3 x 106 - An easy way to remember is that the exponent (6) is the number the decimal moved to its wanted position.
1,300,000 is a whole number which means the decimal will be found at the end. 1,300,000.
From there, the decimal wants to be behind the first actual number; in this case it is the one. So, the decimal will move to be in the wanted position.
1,300,000.
1,300,00.0 = 1,300,00.0 x 101 Notice here that we moved the decimal once and changed the exponent to a number one. Remember, the decimal WANTS to be behind the first actual number (which is the one) so it needs to keep moving.
1,300,0.00 = 1,300,0.00 x 102 The exponent changes each time you move the decimal.
1,300.000 = 1,300.000 x 103 Again, we moved the decimal three times already, so the exponent is the number three.
1,30.0000 = 1,30.0000 x 104
1,3.00000 = 1,3.00000 x 105
1.300000 = 1.300000 x 106 or 1.3 x 106
Let's do another example! This time we are going to do the number 0.0034. Now, the question you may be having is, "Well, it's already behind a number, should we just leave it alone?" The answer is no. In this case, zero does not count as an actual number so the decimal wants to move behind the three. Whenever you are making your answers to scientific notation and wondering where to move the decimal, the actual numbers to consider are 1 - 9.
0.0034 We already have a decimal there. Now, we just need to move it behind the three.
00.034 = 00.034 x 10-1 Notice the exponent. This time when we moved the decimal one place, the exponent is now a negative one.
Helpful Tip:
If the start number is more than one (1,300,000), the exponent will be positive.
If the start number is less than one (0.0034), the exponent will be negative.
000.34 = 000.34 x 10-2
0003.4 = 0003.4 x 10-3 or 3.4 x 10-3
What if the teacher wants all your answers in scientific notation, but the answer is 5.6?
5.6 We need to move the decimal behind the first actual number. Well, it already is so we don't need to move it. This means your answer should be this:
5.6 x 100 Since you move the decimal zero times, your exponent will be zero.
| Number | Answers: Highlight the text inside the box to reveal answer |
|---|---|
| 1985 | 1.985 x 103 |
| 9.9 | 9.9 x 100 |
| 0.011 | 1.1 x 10-2 |
| 0.00000000519 | 5.19 x 10-9 |
For more practice problems, visit the University of Missouri-Rolla's self test page.
Significant Figures: the certain digit and the first uncertain digit of measurement.
| Rule # | Rules | Examples |
|---|---|---|
| 1 | Nonzero integers. Nonzero integers always count as significant figures. | Numbers 1 - 9 |
| 2 | Leading zeros are zeros that come before all the nonzero digits and DO NOT count as significant figures. | 0.0034 - There are 2 significant figures (the 3 & 4). The zeros before do not count. |
| 3 | Zero sandwich. Zeros between nonzero digits count as significant figures. |
303 - There are 3 significant figures. The zero in between the three's count. |
| 4 | Trailing zeros are zeros at the right end of the number and they only count if the number contains a decimal point. |
100 - There is 1 significant figure. There is no decimal point so the trailing zeros do not count. |
| 5 | Exact numbers. Sometimes calculations involve numbers that were determined by counting and not using measuring devices (10 experiments, 3 apples, 8 molecules). These are exact numbers and can have an infinite number of significant figures. If a number is exact, it DOES NOT affect the accuracy of a calculation nor the precision of the expression. | 1 foot = 12 inches - Depending on how you use it in the equation it can either have 1 significant figure or 2. So, neither of those numbers can limit the number of significant figures used in the calculation. |
For a video tutorial on the rules regarding zero, view Significant Figures and Zero by Tyler DeWitt.
Example Problems for Significant Figures
| Example Problems | Answers: Highlight the text inside the box to reveal answer |
|---|---|
| 3.0800 | 5 - The first zero is sandwiched between the 3 & 8 making it significant and the trailing zeros are significant because of the decimal. |
| 0.004180 | 4 - The leading zeros do not count and the trailing zero behind the 8 counts because of the decimal. |
| 7.09 x 107 | 3 - The zero is sandwiched and there is a decimal. It counts. |
| 30,800 | 3 - The zero between the 3 & 8 is significant because it is sandwiched, but the trailing zeros do not count because there is no decimal point. |
Rules for Significant Figures in Mathematical Operations:
Multiplication or division: The number of significant figures in the result is the same as the number in the least precise measurement used in the calculation.
4.56 X 1.4 = 6.38 - Because the 1.4 has the least number of significant figures in the equation, your answer should also have 2.
Corrected answer: 6.4 - Now, the answer has 2 significant figures. The same amount as the 1.4 which is the least number.
Addition or subtraction: The result has the same number of decimal places as the least precise measurement used in the calculation.
12.11 + 18.0 + 1.013 = 31.123 - 18.0 only has one number after the decimal point and that will be considered the limiting term. So, your answer should only have one number after the decimal point.
Corrected answer: 31.1
Helpful Tip:
Multiplication and division - ALL the significant figures are counted.
Addition and subtraction - Only the numbers AFTER the decimal are counted.
| Example Problems | Answers: Highlight the text inside the box to reveal answer |
|---|---|
| (1.05 x 10-3) ÷ 6.135 | 1.71149 x 10-4 - Corrected to 1.71 x 10-4 because the term with the least amount of significant figures is (1.05 x 10-3) which has 3. |
| 21 - 13.8 | 7.2 - Corrected to 7 because 21 does not have any numbers after the decimal which makes the number zero the least number of decimal places. |
| 3.461728 + 14.91 + 0.980001 + 5.2631 | 24.614829 - Corrected to 24.61 because 14.91 has the least number of significant figures after the decimal, which is 2. |
For more practice problems, visit the University of Missouri-Rolla's self test page.
In most calculations, you will need to round numbers to obtain the correct number of significant figures.
Rules for Rounding:
In a series of calculations, carry the extra digits through to the final result, then round.
If the digit to be removed
| Instructions for Examples | Examples | Answers: Highlight the text inside the box to reveal answer |
| Round the example to three significant figures. | 22.528 | 22.5 - The 2 after the 5 is less than 5 and must be removed. |
| Round the example to one significant figure | 103,007 | 100,000 - The 0 after the 1 is less than 5 and the other numbers will be "removed". This number still has only 1 significant figure because the trailing zeros do not count since there is no decimal. |
| Round the example to two significant figures. | 0.000847 | 8.5 x 10-4 - The leading zeros aren't significant. The 7 after the 4 is higher than 5, so the 4 rounds up to become 5. |
There are three systems of measurement widely used for temperature:
Note: The size of the temperature unit (degree) is the same for Kelvin and Celsius scales. The difference is the zero points.
Conversions:
Temperature (Kelvin) = temperature (Celsius) + 273.15
or
Temperature (Celsius) = temperature (Kelvin) - 273.15
Example:
Convert 400.0 K to the Celsius scale.
400.00 K - 273.15 = 126.85 °C
Helpful Tip:
Kelvin does not use a degree symbol for its unit unlike Celsius and Fahrenheit; it is symbolized by the letter K.
The degree size and zero points are different when considering Fahrenheit. As seen in the illustration above, The degree size for Fahrenheit is 180° and 100° for Celsius. So, the unit factor is:
180 °F 9 °F
------- or -------
100 °C 5 °C
This is because 180 ÷ 100 = 1.8 and in fraction form that is 9/5. You will also have to use the reciprocal depending on the direction that is needed.
Now, for the difference in zero points. To obtain the temperature in Celsius, you must subtract 32 °F from the given temperature in Fahrenheit and then multiply the unit factor to adjust for the difference in degree size.
5 °C
(TF - 32 °F) X ------- = TC
9 °F
As you can see in this equation, the reciprocal was used.
If the degree is needed in Fahrenheit and you have Celsius, then the following equation is used.
9 °F
TF = TC X ------- + 32 °F
5 °C
Example:
Convert 98.6 °F to the Celsius and Kelvin scales.
First, convert to Celsius:
5 °C
(98.6 °F - 32 °F) X ------- = 37.0 °C
9 °F
Next, convert the Celsius answer you just obtained to the Kelvin scale:
TK = TC + 273.15
TK = 37.0 °C + 273.15
TK = 310.2 K
Density: A property of matter used as an "identification tag" for a substance - the mass of the substance per unit volume of the substance.
mass
Density = -------------
volume
| Compound | Density in g/cm3 at 20 °C |
|---|---|
| Chloroform | 1.492 |
| Diethyl ether | 0.714 |
| Ethanol | 0.789 |
| Isopropyl alcohol | 0.785 |
| Toluene | 0.867 |
Example:
Identify the unknown liquid. 25.00 cm3 of the substance has a mass of 19.625 g at 20 °C. Use the chart on the right to solve for what the unknown liquid could possibly be.
The first thing needed, is to find the density of the unknown liquid:
mass 19.625 g
Density = ------------- = ----------------------- = 0.7850 g/cm3
volume 25.00 cm3
The density obtained matches with the density of isopropyl alcohol.
Note: Ethanol is also very close and you would need to run more tests in order to ensure that isopropyl alcohol is the correct unknown liquid.
| Substance | Physical State | Density (g/cm3) |
| Oxygen | Gas | 0.00133 |
| Hydrogen | Gas | 0.000084 |
| Ethanol | Liquid | 0.789 |
| Benzene | Liquid | 0.880 |
| Water | Liquid | 0.9982 |
| Magnesium | Solid | 1.74 |
| Salt (sodium chloride) | Solid | 2.16 |
| Aluminum | Solid | 2.70 |
| Iron | Solid | 7.87 |
| Copper | Solid | 8.96 |
| Silver | Solid | 10.5 |
| Lead | Solid | 11.34 |
| Mercury | Liquid | 13.6 |
| Gold | Solid | 19.32 |
FUN FACTS:
The liquid in your car's lead storage battery changes density when the sulfuric acid is consumed as the battery discharges. If the battery falls below a certain amount, the battery will have to recharge.
You can determine the amount of antifreeze, which tells you the level of protection against freezing in the cooling system of your car.
The center of a black hole (the singularity) is infinitely dense.
Saturn has the lowest density of all the planets in our solar system. Saturn has a density of 0.687 g/cm3 which is less than water. So, if you have a large enough pool filled with water, Saturn will float!
Silver has a density of 10.5 g/cm3 and gold has a density of 19.3 g/cm3. Which would have a greater mass, 5 cm3 of silver, or 5 cm3 of gold?
|
Silver: mass mass = density X volume Gold: mass = (19.3 g/cm3) X (5 cm3) Answer: gold has more density. |
One of the body's responses to an infection or injury is to elevate its temperature. A certain flu victim has a body temperature of 102 °F. What is the temperature on the Celsius scale?
|
Converting °F to °C 5 °C 5 °C Answer: 38.9 °C |
An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 2.0 mL. The height of the water rose to 7.0 mL. If the mass of the stone was 25 g, what was its density?
|
You must find the difference in the volume of water from the initial point to after the stone was dropped. 25 g Answer: density = 5 g/mL |
Convert -196 °C to the Kelvin scale.
|
Temperature (Kelvin) = temperature (Celsius) + 273.15 Answer: TK = 77 K |