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).
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 |
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. |
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. |
Dimensional analysis: A method to convert a given result from one system of units to another.
The video (by Tyler DeWitt) below is an introduction to dimensional analysis. It discusses the reasons why & how it can be used in every day life.
Exploring more of the video discussion, let's discuss another conversion factor. Here is an equivalent statement: 2.54 cm = 1 in
If you divide both sides of that equation by 2.54 cm, you get:
1 in
1 = ------------
2.54 cm
This expression is called a unit factor. Since 1 inch and 2.54 cm are exactly equivalent, multiplying any expression by this unit factor will not change its value.
Problem:
A pin has a length of 2.85 cm. What is the length in inches (in)?
1 in 2.85 in
2.85 cm X ------------ = ------------ = 1.12 in
2.54 cm 2.54 in
We start off with our given, which is 2.85 cm and just like in the video, the centimeter units cancel out to give inches for the result. If you notice, the answer also has 3 significant figures just like our given 2.85. Remember the conversion factor are exact numbers and would not be considered for significant figures due to having infinite numbers.
The next video (by Tyler DeWitt) goes more into detail in the explanation and instruction of how to do dimensional analysis.
For a different explanation of Dimensional Analysis, view The Factor-Label Method video by Bozeman Science.
| Length |
|
SI unit: meter (m) 1 meter = 1.0936 yards 1 centimeter = 0.39370 inch 1 inch = 2.54 centimeters (exactly) 1 kilometer = 0.62137 mile 1 mile = 5280 feet 1 mile = 1.6093 kilometers 1 angstrom = 10-10 meter 1 angstrom = 100 picometers |
| Mass |
|
SI unit: kilogram (kg) 1 kilogram = 1000 grams 1 kilogram = 2.2046 pounds 1 pound = 453.59 grams 1 pound = 0.45359 kilograms 1 pound = 16 ounces 1 ton = 2000 pounds 1 ton = 907.185 kilograms 1 metric ton = 1000 kilograms 1 metric ton = 2204.6 pounds 1 atomic mass unit = 1.66056 x 10-27 kilograms |
| Volume |
|
SI Unit: cubic meter (m3) 1 liter = 10-3 m3 1 liter = 1dm3 1 liter = 1.0567 quarts 1 gallon = 4 quarts 1 gallon = 8 pints 1 gallon = 3.7854 liters 1 quart = 32 fluid ounces 1 quart = 0.94633 liter |
| Temperature |
|
SI Unit: kelvin (K) 0 K = –273.15 °C 0 K = –459.67 °F K = °C + 279.15 5 9 |
| Energy |
|
SI Unit: joule (j) 1 joule = 1kg • m2/s2 1 joule = 0.23901 calorie 1 joule = 9.4781 x 10-4 btu (British thermal unit) 1 calorie = 4.184 joules 1 calorie = 3.965 x 10-3 btu 1 btu = 1055.06 joules 1 btu = 252.2 calories |
| Pressure |
|
SI Unit: pascal (Pa) 1 pascal = 1 N/m2 1 pascal = 1 kg/m • s2 1 atomsphere = 101.325 kilopascals 1 atmosphere = 760 torr (mm Hg) 1 atmosphere = 14.70 pounds per square inch 1 bar = 105 pascals |
Sometimes, dimensional analysis is not a one-step process and can take multiple steps to solve a single problem.
The video (by Tyler DeWitt) below discusses, explains, and instructs how to do multi-step unit conversion problems.
Let's work out a multiple conversion problem going step-by-step!
A student has entered a 10.0 km run. How long is the run in miles?
First, we know that we have to convert kilometers to miles, and then we know that our given is 10.0 km.
Next, we need to know our equivalence statements, which are:
1 km = 1000 m
1 m = 1.094 yd
1760 yd = 1 mi
Now that we know our equivalence statements, let's figure out the strategy. We can follow this process:
kilometers → meters → yards → miles
Alright! Let's try to follow this process going step by step:
Kilometers to Meters
1000 m
10.0 km X ------------ = 1.00 x 104 m Note the km unit cancel out to give the meters result.
1 km
Meters to Yards
1.094 yd Note the m unit cancel out to give the yd result. Also, there should be
1.00 x 104 m X ------------ = 1.094 x 104 yd 3 significant figures in the answer, but this is an intermediate step and the
1 m FINAL result should round off to 3 significant figures.
Yards to Miles
1 mi Note in this case that 1 mi equals exactly 1760 yd by designation, and therefore,
1.094 x 104 yd X ------------ = 6.216 mi making 1760 and exact number.
1760 yd
Since the given is 10.0 km, the result can only have 3 significant figures and should be rounded to 6.22 mi making the final answer:
10.0 km = 6.22 mi
Now if we combine the steps, it should look like this:
1000 m 1.094 yd 1 mi
10.0 km X ------------ X ------------ X ------------ = 6.22 mi
1 km 1 m 1760 yd
Helpful Tip:
In doing chemistry problems, you should ALWAYS include the units for the quantities used. ALWAYS check to see that the units cancel to give the correct units for the final result.
How do you do dimensional analysis problems with numbers that have a top and a bottom?
The video (by Tyler DeWitt) below will help explain and instruct on how to work out problems with numbers that have both a top and bottom unit.
Let's try out a problem of our own!
A car is advertised as having a gas mileage of 15 km/L. Convert to miles per gallon.
We already know how to do the initial part from changing km to mi, so let's start with doing that:
First, we need our equivalence statements:
1 km = 1000 m
1 m = 1.094 yd
1760 yd = 1 mi
1 L = 1.06 qt
4 qt = 1 gal
Now, let's do part one of our conversion problem:
15 km 1000 m 1.094 yd 1 mi Note that we were able to cancel out the km unit to mi, but we still
------------ X ------------ X ------------ X ------------ = 9.3238636 mi/L have yet to convert L to gallon.
L 1 km 1 m 1760 yd
We had to make sure that we canceled out the units by putting the same unit on the bottom of the next part of the equation (e.g., 15 km is on the top of the first step and 1 km is on the bottom of the second, 1000 m is on the top of the second step and 1 m is on the bottom of the third step).
Now, we are going to reverse the process. We have 1 L on the bottom of the first step so we need to make sure that the next L unit is on the top of the next step.
9.3238636 mi 1 L 4 qt Remember that we have to round the final result to obtain the
--------------------- X ------------ X ------------ = 35.18439 mi/gal = 35 mi/gal correct number of significant figures which should be 2 for
L 1.06 qt 1 gal this problem because our given is 15.
Here is what it would look like if it is done all together:
15 km 1000 m 1.094 yd 1 mi 1 L 4 qt
------------ X ------------ X ------------ X ------------ X ------------ X ------------ = 35.18439 mi/gal = 35 mi/gal
L 1 km 1 m 1760 yd 1.06 qt 1 gal
Everything that we did in the first step is done in purple while everything that we did in the second step is done in green.
Again, it helps when you write down your units and are able to cross them out as you go. This helps check your process to make sure that you are doing it correctly. ALWAYS INCLUDE UNITS!
The answers are located in the boxes: Highlight the text inside the box to reveal answer
Here are some conversion factors that you should probably know:
| 1 km = 1000 m | 1 cm = 10 mm | 1 L = 1000 mL | 1 g = 1000 mg |
| 1 m = 1000 mm | 1 m = 100 cm | 1 kg = 1000 g |
Here are other conversion factors:
| 1 mi = 1.61 km | 1 L = 1.06 qt | 1 oz = 28.3 g | 1 mL = 20 drops | 1 cm3 = 1 mL |
| 1 qt = 0.946 L | 1 lb = 454 g | 1 ton = 2000 lbs | 1 gal = 4 quarts | 1 in = 2.54 cm |
| 1 kg = 2.2 lbs | 1 mi = 5280 ft | 365 days = 1 year |
Convert 25.0 g to kg.
|
1 kg The answer should contain 3 significant figures because of the given 25.0. The leading zeros in the answer do not count as significant figures and the trailing zero does count because of the decimal point in the result. |
How many minutes are there in 1.6 years?
|
365 days 24 hr 60 min Because our given has 2 significant figures, our answer needs to have 2 as well. In this case, we can write the answer two different ways. The numbers that are underlined are the only numbers that count as significant figures. The trailing zeros in the first answer do not count because there is no decimal point in the result. |
If you are going 55 mph, what is your speed in m/s?
| 55 mi 1.61 km 1000 m 1 hr 1 min ------------ X ------------ X ------------ X ------------ X ------------ = 25 m/s 1 hr 1 mi 1 km 60 min 60 s |
These questions were obtained from Hudson High School Honors Course worksheet.