Chapter 1 - Introduction: Matter and Measurement

Today we're going to discuss Chapter 1: Introduction to Matter and Measurements. The learning objectives for this chapter are to distinguish among elements, compounds, and mixtures. Also, we will be able to identify symbols of common elements, identify common metric prefixes, demonstrate the use of significant figures, scientific notation, and the SI units in calculation, and attach appropriate SI units to define quantities and employ dimensional analysis in calculation. Chemistry: Why is this important to study chemistry? Chemistry is the study of the properties and behavior of matter. It is central to our fundamental understanding of many science-related fields. So, chemistry is basically the base of a lot of different kinds of science because we try to learn about the properties and behavior of matter, which are important things for other sciences. Matter: Matter is anything that has mass and takes up space. That's the definition of matter. Matter can be composed of atoms of an element or molecules. In the case of atoms, we have just one type of atom in the matter. In the case of molecules, we have more than one atom attached to each other. So, when you have a molecule with just one type of atom, it is a molecule of an element. When you have more than one type of atom in the molecule, it is a molecule of a compound. Lastly, we can have mixtures of elements and compounds, where we see molecules of the same element and molecules of a compound because we have more than one type of element present. Atoms: Atoms are the building blocks of matter. Each element is made of a unique kind of atom. A compound is made of two or more different kinds of elements. Here, we will look at some examples. For example, a molecule of oxygen is made of two oxygen atoms, so it is denoted as O2. Water is a compound made of two different types of elements, oxygen and hydrogen. Ethanol is also a compound made of two carbon atoms, six hydrogen atoms, and one oxygen atom. Aspirin is another example. Classification of Matter: Let's talk a little bit about the state of matter and the composition of matter. The state of matter can be classified into three categories: solid, liquid, and gas. Here, we can see all three states represented by the same molecule. For example, in the case of water, we have ice as the solid state, liquid water, and water vapor as the gas state. So, we have the three states of matter represented by the same molecule. Substance: A substance has distinct properties and a composition that does not vary from sample to sample. For example, glucose or sugar always has the same composition, regardless of how much you have. Water, no matter the sample size, will always have the same composition, which is H2O. Elements and Compounds: Elements are substances that cannot be decomposed into simpler substances because they consist of only one type of element. Compounds, on the other hand, can be decomposed into simpler substances. Compounds have a definite composition, meaning the relative number of atoms of each element that makes up the compound is the same in any sample. This is known as the law of constant composition or the law of definite proportions. Mixtures: Mixtures exhibit the properties of the substances that make them up. Mixtures can vary in composition throughout a sample, which is called heterogeneous, or have the same composition throughout the sample, which is homogeneous. For example, a chicken soup is an example of a heterogeneous mixture because you can see and vary the composition of each scoop. On the other hand, a jar of iced tea is a homogeneous mixture because the composition remains the same regardless of the sample. In summary, matter can be classified into pure substances or mixtures. Pure substances can be elements or compounds, and mixtures can be either heterogeneous or homogeneous. Example of a pure substance that is an element is gold. The rods right here are made of gold. Another example of a pure substance compound is glucose or sugar. Basically, cubes of sugar are pure substances. Now, let's talk about mixtures. We have homogeneous mixtures and heterogeneous mixtures. In a homogeneous mixture, such as a cup of tea, you can't see the difference between the components. It looks like one body. In a heterogeneous mixture, like a mixture of water and oil, you can see the different components. The water and oil in this mixture are examples of a heterogeneous mixture. Now, let's discuss the classification of matter based on its composition. If matter is uniform throughout and you can't see the components, it is a homogeneous mixture. If you can see the components, it is a heterogeneous mixture. If matter is not uniform throughout and has a distinct composition, it is a pure substance. If the pure substance contains more than one atom, it is a compound. If it consists of only one atom, it is an element. Now, let's move on to the types of properties. Physical properties can be observed without changing the substance into another substance. Examples of physical properties are boiling point, density, and volume. Chemical properties can only be observed when a substance changes into another substance. Examples of chemical properties are flammability, corrosiveness, and reactivity with acids. Intensive properties are independent of the amount of substance present, such as density and boiling point. Extensive properties depend on the amount of substance present, such as volume, mass, and energy. There are two types of changes in matter. Physical changes do not change the composition of substances. Examples include changes of state, temperature, and volume. Chemical changes result in the formation of new substances. Examples include combustion, oxidation, and decomposition. Let's now discuss the characteristics of the different states of matter. In a solid, atoms or molecules are closely packed and in fixed locations. They can vibrate or oscillate but cannot move freely. Solids have a fixed volume and rigid shape. In a liquid, atoms or molecules are close to each other but can move around and by each other. Liquids have a fixed volume but assume the shape of their containers. In a gas, atoms or molecules are separated by large distances and are free to move relative to one another. Gases assume both the shape and volume of their containers. Gases are also compressible, unlike solids and liquids. In a chemical reaction, the reacting substances are converted to new substances. For example, the elements hydrogen and oxygen react to form water. In the water, oxygen will react and produce water molecules. The reactants are on the left side of the arrow, and the product is on the right side.If we want to separate a mixture, we can separate the components based on their physical properties. Some commonly used methods are filtration, distillation, and chromatography. Filtration is used to separate solid substances from a liquid solution. The solution is poured into a filter, where the liquid collects in a beaker while the solid remains in the filter. Distillation uses the differences in boiling points to separate a homogeneous mixture into its components. For example, if we have a mixture of water and alcohol, both liquids will form a homogeneous solution. By boiling the mixture, the water evaporates and turns into a gas. It then goes through a condenser, where cold water causes it to condense back into a liquid form, which can be collected. After the water has boiled away in the distillation process, the remaining solid, such as salt, can be separated as well. Chromatography is another technique used to separate components of a mixture. It relies on the substances' ability to adhere to a solid surface. A column with an absorbent material is used, with the mixture added at the top and a solvent added to allow the components to move through the absorbent. The solvent interacts with the different components, separating them as they move down the column. Numbers play a significant role in chemistry, as many topics are quantitative. We need to express measurements numerically using units and understand concepts such as significant figures and uncertainty. The SI units, or the International System of Units, are used for physical quantities. The units include kilogram (mass), meter (length), second (time), Kelvin (temperature), mole (amount of substance), ampere (electric current), and candela (luminous intensity). The metric system, which uses the base units of gram (mass), meter (length), second (time), Celsius or Kelvin (temperature), mole (amount of substance), liter or cubic centimeter (volume), is also commonly used. Prefixes are used to convert base units into appropriate measures for very large or small numbers. For example, kilo- represents 1000 times the base unit, while milli- represents one thousandth. In the next slides, we will discuss the metric system and measurement techniques further. Measure of the amount of material in an object. As I mentioned before, the kilogram is the base unit for mass in the metric system, while the gram is also a unit for mass but not a base unit. Moving on to volume, we know that it is not a base unit in the SI system, but is derived from the measurements of height, depth, and length. For example, one cubic meter is equivalent to one meter multiplied by one meter multiplied by one meter. The most commonly used metric units for volume are the liter and the milliliter. A liter is a cube with each side measuring one decimeter, while a milliliter is a cube with each side measuring one centimeter. Therefore, one milliliter is equal to one cubic centimeter. Next, let's discuss temperature. In general usage, temperature refers to the hotness or coldness of an object and determines the direction of heat flow. Heat flows spontaneously from an object with a higher temperature to an object with a lower temperature. There are different temperature scales, such as the Kelvin, Celsius, and Fahrenheit scales. In scientific measurements, the Celsius and Kelvin scales are most often used. The Kelvin scale ranges from 273 Kelvin to 373 Kelvin, while the Celsius scale ranges from 0 to 100 degrees. Fahrenheit is commonly used in weather reports but not in scientific measurement. The equations below can be used to convert between Celsius and Fahrenheit, as well as between Celsius and Kelvin. Let's move on to the property known as density. Density is a physical property of a substance that is characteristic to each substance. It is measured in units derived from mass and volume, such as grams per milliliter or grams per cubic centimeter. The equation for density is density equals mass divided by volume. This equation can be rearranged to find mass or volume if the other variables are known. Depending on what information is given, you can rearrange the equation to solve for the desired variable. Now, let's discuss some strategies for solving mathematical problems. First, identify the starting and ending points. What information is given in the problem and what are you trying to find? Then, devise a plan to get from the starting point to the ending point, using the given information and any additional knowledge or resources. You can use a solution map to visually represent the steps required to solve the problem. Start by sorting the information in the problem and creating a step-by-step plan to reach the desired solution. It's like creating a map to navigate from your house to a Starbucks, where each step is carefully planned out. In those are the series of steps that you need to go through to get to the Starbucks. So this is the same concept, okay? It's a map that you need to create to solve the problem. So the third part is going to be solving it by carrying out the mathematical operations, paying attention to the rules for significant figures in calculation. We're going to talk a little bit about that later. Also, cancelling units as needed. And finally, you need to check if the answer makes physical sense and if the units are correct. These are the questions you're going to ask at the end of the problem. Basically, this is the strategy that we suggest you to use for any problem from now on. A solution map is a visual outline that shows the strategic route required to solve a problem. For unit conversion, the solution map focuses on units and how to convert from one unit to another. Units can be very helpful in knowing where you are on the map and what you need to do next in order to go to the next step. So, sometimes, units can be very helpful. A solution map involving the equation for density. Let's do an example for this. In a problem involving an equation, the solution map shows how the equation takes you from the given quantities to the find quantity. For example, if we have mass and volume, and we want to determine the density of a desk, we can start with this and go through using the equation mass over volume. This is the initial data that we have. We need to create or find a mathematical operation that will help us determine the quantity we're looking for, which in this case is the density. Let me introduce you to a concept known as a conversion factor. We can use the density of a substance as a conversion factor between the mass of the substance and its volume. A conversion factor is a tool that you're going to find very useful because it helps you go from one unit to another. That's why it's called a conversion factor, as it helps you go from unit A to unit B. In this case, let's take an example of a liquid substance with a density of 1.32 grams per cubic centimeter. What volume should be measured to deliver a mass of 68.4 grams? Here, you can see that grams per cubic centimeter is a fraction. Every number is a fraction. The number 1.32 is a fraction. The number at the bottom part of 1.32 is 1. So, you don't represent it as 1.32 over 1, because that is 1.32. But you need to remember that there is a 1 below the 1.32. So, that means that you have 1.32 grams over 1 cubic centimeter. We can represent this as 1.32 grams over 1 cubic centimeter. We can also flip this and have 1 cubic centimeter over 1.32 grams. From here, we have two conversion factors. Both of them came from the same source, which is the density. From one density, you can obtain two different conversion factors. You're going to use the one that you need to cancel your initial unit. In this case, our initial unit is grams, so we need to use the conversion factor where we can find this unit in the bottom part. So, from these two conversion factors, the one that we need is 1 cubic centimeter over 1.32 grams. In that way, we can cancel the unit of mass. So, here, we start with mass and go to cubic centimeters using the density of 1.32 grams over 1 cubic centimeter. We can cancel the units of grams and we're left with cubic centimeters. But we want to express this in milliliters, so we find another conversion factor. One cubic centimeter is equal to one milliliter, as we mentioned before. So, this definition also creates two conversion factors: one milliliter over one cubic centimeter or one cubic centimeter over one milliliter. Any definition will always produce two conversion factors, and you're going to use just one, the one that you need to cancel your previous unit. In this case, we have this result in cubic centimeters, so we want to cancel the cubic centimeters. We can use this conversion factor as it is, so we can cancel the units of centimeter and, in the end, use milliliters. Therefore, we need to measure 51.80 milliliters to obtain 68.4 grams of the liquid. So, in a sample of 51.8 milliliters, that volume represents a mass of 68.4 grams. Now let's talk a little bit about numbers. Exact numbers are counted or given by definition. For example, there are 12 eggs in one dozen. You can count eggs, so that 12 is an exact number. Also, the definition of one dozen being equal to 12 is an exact number because it is a definition. Inexact or measured numbers depend on how they were determined. Scientific instruments have limitations. Some balance measures to the second decimal place, while others measure to the fourth decimal place. These are two different measurements. Whenever you measure something, whether it's volume, length, mass, or anything else, you need to use an instrument to determine that quantity. That number is an inexact or measured number and is always going to have some degree of error because it's not exact. You use an instrument to measure that quantity, and all instruments have errors. That's why, at the end, when you measure something, whether it's length, mass, or volume, that number is always going to have some error and is not exact. Now, let's talk about uncertainty in measurements. Different measuring devices have different uses and different degrees of accuracy. All measured numbers have some degree of accuracy. Here, we have different instruments like a graduated cylinder, a syringe, a pipette, and a volumetric flask. These can all be used to measure volumes. Each instrument has its own limitations and accuracy. Doesn't matter how exact they will be, they are the measure. They're going to obtain that value is going to always have an error, always always. So let's talk about accuracy and precision. Accuracy refers to the proximity of measurements to the true value of a quantity, while precision refers to the proximity of several measurements to each other. So accuracy is how close you are to the real value or the true value, and precision is how many times you are close to a specific value. It doesn't matter if it is the true value, but it could be any kind of value. Okay, so for example, here we have the dart table, and this represents very high accuracy and precision. Because both, you have accuracy because you're hitting the bull's eye, and good precision because all of them are hitting close to that, basically the bullseye. This one represents good accuracy but good precision. So let's talk now about significant figures. The term significant figures refers to digits that were measured. Whenever you measure something, you need to determine the significant figures. When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers. And we need to discuss some rules for the significant figures. First of all, all nonzero digits are significant. Second, zeroes between two significant figures are themselves significant. Third, zeroes at the beginning of a number are never significant, and zeroes at the end of a number are significant if a decimal point is written in the number. If you have a decimal point after the zeroes, those zeroes are significant. When addition or subtraction is performed, answers are rounded to the least significant decimal place. And when multiplication or division is performed, answers are rounded to the number of digits that correspond to the least number of significant figures in any of the numbers used in the calculation. So, if we are in addition or subtraction, we need to look at the decimal places in the initial numbers. If we are doing multiplication or division, then we need to identify the significant figures of each of the initial data so we can represent our final answer with the least number of significant figures. These are the rules for rounding: Use only the last or leftmost digit being dropped to decide in which direction to round. Ignore all digits to the right of it. Round down if the last digit dropped is four or less, and round up if the last digit dropped is 5 or more. In multiplication and division, the result carries the same number of significant figures as the factor with the fewer significant figures. For example, here we have a multiplication of 5.02 times 89.665 times 110. If you use a calculator, the result is going to be 45.0118. But we need to represent this with the same number of significant figures as the lesser one. That has the fewest in our initial data, so three. Five and two. That means that we need to represent this as two significant figures. We need to remove this number. And at the end, our answer is going to be 45. For multiplication and division, the intermediate results in blue are rounded to the two significant figures to reflect the least precisely known factor. That is the point 10. This one is the least precisely known factor, which has just two significant figures. Now, what about addition and subtraction? In addition and subtraction, the result carries the same number of decimal places as the quantity carrying the fewest decimal places. So here we have an example, 5.74 plus 0.823 plus 2.651. This has two decimal places, three decimal places, and four decimal places. So that means that the one with the fewest decimal places is this one. So we need to express our result in two decimal places. That's why the result is 9.21. In subtraction, it's the same concept. We have here 4.8 minus 3.965. We need to express the result in one decimal place because this is the one with the fewest number of decimal places. So that's why we have here 0.835, and the result is going to be 0.8. Remember that we need to look at the first number that's going to be dropped. If that number is four or lower, you don't do anything. You just keep that number intact. It doesn't matter. This five, don't get confused. This five is not going to be significant. So this is the one that you need to see, the three. And in this case, the three is lower than four. So that's why I just drop this number and keep the other one. So the result is going to be 0.8. Now, what happens when we have both multiplication, division, addition, and subtraction in the same calculation? You should perform the multiplication and division first. Then, you round the result to the correct number of significant figures. Finally, you perform the addition and subtraction and round the result to the correct number of decimal places. For example, let's solve the expression 3.489 * (5.67 - 2.3). We start by solving the subtraction within the parentheses: 5.67 - 2.3 = 3.37. We need to consider the decimal places in both numbers: 5.67 has two decimal places and 2.3 has one decimal place. Therefore, the answer is 3.37, and we underline or mark the decimal place to remind ourselves to keep it. Next, we multiply 3.37 by 3.489. Since this is a multiplication, we need to consider significant figures, not decimal places. In this case, the answer has four significant figures: 3.37 has three significant figures, and 3.489 has four significant figures. When multiplying, we keep the least number of significant figures, which is two. So the result is 11.758, and since the 7 is greater than 5, we round up and the final answer is 12. Now, let's talk about dimensional analysis. In calculations, units are treated the same way as numbers. Units can be multiplied, divided, or canceled just like any other algebraic quantities. Using units as a guide to solving problems is known as dimensional analysis. It's important to always include units in calculations and make sure they flow logically from beginning to end. When converting units, we use conversion factors. Conversion factors are constructed from two known quantities that are equivalent to each other. For example, we know that 2.54 centimeters is equal to 1 inch. We can construct a conversion factor by dividing both sides of this equality equation by 1. So we have 2.54 centimeters over 1 inch (or 1 inch over 2.54 centimeters). This conversion factor can be used in calculations to convert between centimeters and inches. When using conversion factors, it's important to cancel out units. The given unit should be in the denominator of the conversion factor so it cancels out with the unit we want to convert. Always check that the final units in the answer are correct, and consider whether the magnitude of the answer makes sense. In summary, we have covered the importance of studying chemistry, the classification and properties of matter, units and measurements, uncertainty in measurements, and dimensional analysis.