Name: Period: Date: Unit 1 Part 1 Introduction to Chemistry. What is the equation for density and its rearrangements for mass and volume?

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1 Unit 1 Part 1 Introduction to Chemistry Which element has a type of chemistry devoted to it? What is the equation for density and its rearrangements for mass and volume? Chemistry is often referred to as the (1) science. It bridges the gap between the (2) sciences which study life and the (3) sciences which study non-living systems. This is an oversimplification of the major sciences and there is plenty of overlap between them as we will often encounter. For example, a substance such as (4) is not itself alive but is produced via photosynthesis and provides us with energy on a daily basis. At its most basic, a chemist studies (5), or anything that has (6) and takes up (7). Not everything around us is considered matter. For example, what is allowing you to see this paper, (8), and what is keeping the Earth from being a gigantic snowball in space, (9), have neither mass nor volume. However, the effects that light and energy have on substances are well documented and we take advantage of those effects to develop materials and live in the modern society we have. With such a broad subject with the only mandate relating to matter, it stands to reason that there are numerous types of chemistry that can be studied. A quick look around a chemistry classroom and your eyes will be drawn to the (10) that has a list of over 100 (11). Each one of these building blocks of our universe has unique properties and behaviors that separate it from the other elements. Just one of these elements, carbon, is the main player in the largest branch of chemistry: (12). The number of known organic compounds is in the millions and carbon is an incredibly abundant element. So while it is difficult to avoid carbon in a compound, when carbon is not the focus (even if it is present in the compound) of the scientist, they can be consider an (13) chemist. Some chemists are not too concerned about whether the compound is organic or inorganic but whether the compound is properly identified. Chemists focusing on identifying and quantifying compounds are known as (14) chemists. These chemists may be studying the concentration of heavy metal pollution in river water, which would be an example of (15) chemistry or perhaps pouring over data sent back by the Mars rover which would be (16) -chemistry. The (17) would study the behavior of DNA and protein inside living organisms. Some chemists will focus on the role of heat and energy and the actual movement of atoms and molecules in chemical processes which is known as (18) chemistry. The last (of a sample of the many branches of chemistry) is unfortunately overshadowed by their physics (think Einstein and Hawking) counterparts. These (19) chemists are using computer models and simulations to develop superconducting materials or the next vaccine or cure for a disease. The point is the substance or chemical does not exist yet but it could, in theory. During schooling chemists will encounter a multitude of these subjects and are likely to utilize the skills from more than one in their career.

2 Regardless of the specific type of chemistry being studied, all chemists will follow a logical approach to their research. This is also known as the (20). This is generally considered to include five steps, with a slight variation in how they are named. The first step is (21) and often includes the formulation of a question. This is not enough to move forward as the question that is formulated, may not actually be testable. Therefore, it is important to develop a (22) which is represents a testable statement in regards to the observations. Next up is (23) where data is collected that can confirm the hypothesis or lead the scientist down a different path of discovery. Once data has been collected it is time for (24) in which qualitative and quantitative data is examined with respect to the hypothesis or purpose behind the experiment. Finally, once the data has been analyzed it is time to develop the (25) in which the outcome of the experiment is explained and the validity of the hypothesis can be expressed. During the course of the experiment, all manner of measurements will be made and data collected. It is expected that using different instruments and measuring different properties will result in numbers with varying amounts of digits and different units. Do not worry, nothing is wrong; however, what we will want to be is clear and consistent when reporting this information. If you re thinking, well of course we have to be clear and consistent then I bring to your attention the case of the Mars Climate Orbiter. If you have never heard of it, look it up and write below why the orbiter failed. (26) Consistency and clarity is not simply for the units of measurement (which are coming up shortly) but for the number of digits you use in your calculations and answers. For example, if I were to call someone a millionaire, you could deduce that they have at least $1,000,000 in the bank. If I were to ask them how much money they had, they could respond $1,234,678. It would be painfully obvious to say that these two are different values but what if I were to suggest that they contain different numbers of digits? This concept is known as (27) figures and we will not apply the concept to the letter of the rules but rather to the idea. The first rule we will follow governs that of addition and subtraction and concerns the number of decimal places we are allowed to use in an answer. So let s say we utilized different scales to measure three different blocks. Block A has a mass of g, Block B has a mass of g, and Block C has a mass of g. The major difference between each number may not be obvious until you align each number by the decimal place in the chart below. Block A. Block B. Block C. Total. Each measurement has five total digits but differ in the number of (28) places. This is the key piece of information that we must carry forward. When we add the masses together to get the total, we still follow tried and true rules of addition. However, we have to make an assumption that every decimal place we do not actually have a number for is the number (29).

3 Block A Block B Block C Total This assumption is where the problem lies. In Block C, we capably measured (30) decimal places. So what prevented us from doing the same for Block A and Block B? It is an important question and this is why significant figures are an important concept. So we should not assume those missing decimal places have a value of zero because we never measured them. Instead, we simply do not know their value. Block A ?? Block B ? Block C Total If we do not know a value then how can we perform the proper mathematical operation? Well we can if we eliminate what we no longer know. Since we do not know the 4 th decimal place of each number, we cannot report the 4 th decimal place of the answer. Since we do not know the 3 rd decimal place of each number, we cannot report the 3 rd decimal place of the answer. Therefore we can only report the (31) and decimal places in the answer because we know at least those in each and every number. Block A ?? Block B ? Block C Total report as the mass of the three blocks as g. So our addition has to essentially ignore those decimal places and we have two options: 1) Ignore the numbers from the beginning or 2) add everything we have at the beginning and strike out the numbers we cannot use (shown in the boxes). This leaves the answer we can (32) = (33) = (34) = (35) = The rules for multiplication and division follow a similar idea in that you can only report what you at least know about both (or all) numbers in the calculation. Let s take a mass and volume and calculate density (D = m ). If an object has a mass of 10.1 g and a volume of 7.1 ml, what is V the density? Piece of cake (write down every digit your calculator shows you). (36) Density = g/ml Now how many digits are in the value for mass? (37) And how many digits are in the value for volume? (38) And how many digits are in your answer for density? (39) So compare your answers for 37 and 38 with 39. Explain below what you think is the problem here. (40)

4 It makes no sense to use a 3 digit value (mass) and a 2 digit value (volume) and report a 10 or 11 digit (even larger if your calculator can display them) answer! Like the addition/subtraction rule where we are limited to what we know about decimal places, in multiplication and addition we are limited to what we know about total digits. Therefore, since we know 3 digits of one value and only 2 of the other, we can only report our density with (41) digits. The proper answer, therefore, would be 1.4 g/ml. Since Density = mass / volume, we can rearrange that equation to solve for mass and volume respectively. You can remember how to rearrange the equation or the triangle below to help you get the two other equations D = m V m = V = Using the triangle, to solve for D you put m over V because that is how they are placed within the triangle! Since m is not next to neither D nor V, then you can never (42) mass by density or mass by volume. Likewise, since m is above D and V, you can never (43) D by m or V by m! Below are some practice problems involving the density equation where you will solve for density, mass, and volume. Remember to apply significant figures rules as well. The density of copper is 8.92 g/ml. If you have a block with a volume of ml, what is the mass of the block? (44) You have to samples of clear liquids and one is reported to be pure water and the other sea water. If Sample A has a mass of g and a volume of ml and Sample B has g in ml, which one is pure water and which one is sea water? (45) Sample A = Sample B = Determine the volume of mercury, which has a density of 13.6 g/cm 3 if you have a sample that has a mass of g. (46)

5 Unit 1 Narrative Part 2 Precision, Accuracy, and Scientific Notation QUESTION: If Person A is accurate and Person B is precise, which person would you choose to hit a game winning shot at the end of a game? QUESTION: How could be rewritten? Defined as closeness to an accepted value (or goal), (1) often gets confused with closeness of a set of measurements (or attempts) or (2). We often use the terms interchangeably but they have completely different meanings. It is tough to get an idea for how the terms differ simply by looking at their definitions so let s look at the targets below. If you are aiming at a target, the goal would be the (3). We must use that goal to determine whether the shooter is accurate. If we want to compare the precision of the shooter, we must only compare each of his shots to the other shots, not the bullseye. A person can be accurate, precise, both accurate and precise, or neither accurate nor precise. Presented below are four targets where the shooter took only four shots. Describe the shooter accordingly. (4-7) Shooter A Shooter B Shooter C Shooter D Shooter A is not (8) nor because the shots are neither (9) to the bullseye nor (10) to each other. Shooter B is (11) because the shots are not close to the bullseye but they are close to each other. Remember, precision compares only the shots to themselves, not a particular goal. Shooter C is (12) and because the shots all hit the center of the target. Lastly Shooter D is (13) because the shots are all the same distance from the bullseye. In other words, you cannot say that one shot is worse than the other. It may be easiest to identify Both Accurate and Precise or Neither Accurate nor Precise because those represent the best and worst possible shooters. Precision should be easier to notice because the shots will at least be very close together. Accuracy alone is likely the most difficult because you have to think of the shots in relation to each other and the bullseye.

6 The terms accuracy and precision can be applied to measurements taken too but of course we cannot compare the accuracy of a measurement unless we know what the measurement should be. If the accepted value for the mass of a block is g, identify the sets of measurements below as accurate, precise, both, or neither. Group 1 Group 2 Group 3 Group 4 Measurement g g g g Measurement g g g g Measurement g g g g Description (14-17) The easiest group to identify is the Both Accurate and Precise one which is (18) Group because the three measurements are very close to the goal and each other. The next easiest group to identify should be the Neither Accurate nor Precise one which is (19) Group because the three measurements are neither close to the goal nor each other. With accuracy and precision, it should be easiest to identify Precise as you are simply looking for a set of values that are close to each other and that would be (20) Group. By process of elimination you will leave the Accurate group for last which will have numbers roughly equally above and below the target which in this case is (21) Group. There is no point discussing the accuracy or precision of measurements if the units of the measurements are questionable. In the case of science, the only acceptable units are (22) units. There is another name for this international system of units which is the (23) System. Many countries have non-standard units of measurement in every day discussion such as England where the word stone (14lb, 6.35kg) is a reference for weight. However, there are only two (as of this typing) that use the Standard system as its official unit system and not metric. One of them is the United States so now we must refresh our memories of what exactly the metric, or the SI System, is. For this paragraph, only use the abbreviation of the unit. The SI system units that we will encounter are used for length (24) or for longer lengths, mass (25) or for larger masses, and volume (26) or for smaller volumes. We will utilize a few others such as (27) or for temperature and (28) for amount. Yes, #28 sounds like an animal but it s not. The beauty of the SI system is in its ease of use. Think of inches, feet, yards, and miles. 1 mile = 1760 yards = 5280 feet = inches. Of course, no one would really ever measure the length of a mile in inches but there is not really a nice way to go from one unit to the next. Now consider centimeters, meters, and kilometers. 1 km = 1000 m = cm. All that happened was the addition of zeroes to change one unit to the next and there is a very simple way to remember how, unlike our standard system which we probably all know just fine from using our entire lives. Consider King Henry the Eighth and his love of chocolate milk. King Henry Died by Drinking Chocolate Milk

7 This mnemonic device is useful for remembering unit prefixes in the following order (29) * * base * The * refers to unit prefixes we will really never use but we must remember they exist when we convert one unit prefix into another. kilo (k) hecto (h)* deca (da)* 1 0. BASE 1. deci (d)*. 1 centi (c). 0 1 milli (m) kilo is 1000 units of the base m 1 km base units are found here: gram (g), meter (m), liter (L) centi is 1/100 units of the base. 1 cm.01 m milli is 1/1000 units of the base. 1 mm.001 m Note: when the letter m is all alone, that implies meter. Milli is a prefix which means it comes before something, in this case a unit. k h da b d c m To change from one unit prefix to the next, all we need to do is follow the list of letters above. Let s convert 4875 mm to m. (30) mm stands for which means we start at the letter (31). (32) m stands for which means we will stop at the letter (33). (34) so the we must move the decimal (35) times to the (36). Since the decimal point is not shown in the number, we can rightfully assume it is located at the end of the number Move the decimal accordingly and 4875 mm is (37) m As long as you know 1) the starting unit, 2) the new unit, and 3) the location of the decimal point, converting SI units is very simple. Practice Unit Conversion (38) km = m (39) mg = g (40) ml = L (41) cm = mm (42) L = ml (43) mm = km (44) g = kg (45) m = cm

8 During the course of analyzing data and using formulas, the possibility of using or generating incredibly massive or incredibly tiny numbers is rather high. Consider you are in chemistry class and that chemists study atoms which you already know are incredibly small. The rough estimate for the number of atoms in the universe is The really big numbers are not to be outdone by their really small counterparts such as the so called Planck Time which, in seconds, is There is no way anyone in their right mind would ever want to write such numbers which is why (46) notation was created. This format converts really large (by large meaning number of digits in the value) numbers to ones that are much easier to write. The format of every number in scientific notation is: #.## x 10 +/-## A couple of notes: 1) There is always one exactly one non zero digit THEN the decimal point 2) There is no limit to the number of digits (both zero and nonzero) after the decimal 3) The exponent can be positive (but never write the + sign) or negative (must write sign) Often students will say the exponent represents the number of 0s in the decimal form of the number but this is not quite accurate. The exponent represents the number of places the decimal moved in order to have ONE non-zero digit to the left of the decimal. For the first number on this page, the decimal would need to move (47) times and for the second number (48). If the value is greater than 1, then the exponent will be greater than 1 too (positive) and if the value is less than 1, then the exponent will be less than one too (negative). Since the number of atoms is much bigger than 1, the exponent will be 80 and since the Planck time is much smaller than 1, the exponent will be -44. So the number of atoms written in scientific notation is (49) x 10 and the Planck time written in scientific notation is (50) x 10. Taking numbers out of scientific notation simply means applying the reverse process. 1) The sign of the exponent tells you the direction you must move the decimal point This means for positive exponents you move the decimal point (51) and for negative exponents you move it (52). 2) Add a 0 for every decimal place you move where there is not already a digit The speed of light is often rounded to 3 x 10 8 m/s or In decimal form (53) m/s. Likewise the wavelength of red light is 7 x 10-7 m or in decimal form (54) m. Convert to Scientific Notation Convert from Scientific Notation (55) m (radius of H atom) (56) x kg (mass of proton) (57) m (distance to Sun) (58) 9.46 x m (length of a light year) (59) K (temp of Sun s core) (60) x m 2 kg/s (Planck constant)