hello everybody my name is Iman welcome back to my YouTube channel today we're starting a more detailed General chemistry playlist if you've been following me here for a while you know I already have a general chemistry 1 and general chemistry 2 playlist however I've learned a lot in the past two years that I've been doing YouTube and I have a lot of new ideas for how I want to teach General chemistry so here in this new playlist we're going to go into more detailed discussions about every topic and I plan on incorporating a lot more practice problems as well both in the lecture and in separate videos that are going to follow every lecture video so we're going to go ahead and start with chapter one it's titled chemical foundations and the objectives that we want to cover in this playlist are as follows first we're going to start with a brief overview so for a long time humans have believed that matter is composed of atoms and in the previous three centuries we've collected a lot of evidence to support this belief so here the goal is really to get you excited about chemistry by describing how recent technology allows us to quote unquote see individual atoms and how chemistry is in everything we see and do and in discussing the importance of chemistry we're going to move into the second objective where we're going to talk about the scientific method third we're going to move into a discussion on measurement here we're going to talk about base versus derived units and in addition we're going to discuss how units are modified through the use of metric prefixes we're going to learn that measurements also have some degree of uncertainty and that's the topic of objective 4 we're going to learn also how to distinguish between accuracy and precision with all of this background then we move into talking about significant figures in objective five we will cover rules for counting significant figures rules for for significant figures in mathematical operations and rules for rounding our sixth objective is on dimensional analysis this is the most important topic in the first chapter if there is any topic that I would recommend focusing on the most it is going to be dimensional analysis please make sure that you fully understand this topic because it is a reoccurring theme in general chemistry 1 and two dimensional analysis is a problem solving technique that's used in chemistry to convert between different units of measurements it also involves using conversion factors which are ratios that relate different units to cancel out unwanted units and ensure that The Final Answer has the desired units you're looking for then the next two topics are going to be temperature and density these are also important topics that will reemerge and will rediscussed throughout our our general chemistry course density is going to be defined as mass over volume and temperature here we're going to cover the different units of temperature we're going to encounter in this course that's going to be Celsius Fahrenheit and Kelvin and we're going to learn how to convert between each of these units and then last but certainly not least we're going to talk about classification of matter matter exists in three phases and it is composed of many levels of organization and we're going to get into all the details in this objective with that being said let's get started with objective one we're going to start with a brief overview again for a long time humans have believed that matter is composed of atoms and in the previous three centuries we've collected evidence to support this belief and it is in this invisible world of atoms that we find a lot of interesting information and it is this invisible world world of atoms that forms the foundation of chemistry and its countless applications in the world around us chemistry focuses on the composition and properties of matter causing it to occupy a really Central and critical position in science the study of chemistry it impacts virtually every field of science a fundamental understanding of chemistry is going to be required for success in many fields including biology medicine earth science and many many more now a an essential Foundation of chemistry is going to involve grasping the fundamentals of atomic structure which serves as a stepping stone to comprehending the complex nature of molecules and of compounds and this fundamental knowledge this foundational knowledge really paves the way for exploring the dynamic interaction and chemical reactions and into delving into principles of chemical bonding stochiometry and the mechanisms that really Drive Transformations at the molecular level to further motivate chemistry I really want to talk about two quick things first I want to talk about the power of quote unquote seeing individual atoms first obviously we can't see atoms with the naked eye but we can use something like a special microscope this one's called scanning tunneling microscope that we're going to focus on now we're not going to consider the details of its operation here but scanning tunneling microscopy really allows researchers to map a conductive sample surface atom by atom with ultra high resolution essentially the scanning tunneling microscope uses an electron current from a needle from a tiny needle you can see the tip right here to probe The Sur surface of a substance it was developed in 1981 and it actually earned its inventors the Nobel Prize in physics in 1986 now in addition to quote unquote seeing the atoms in materials we've learned how to isolate and view single atoms too and so at this point we're fairly sure that matter consists of individual atoms but the nature of these atoms it's really complex and the components of atoms they don't behave much like the objects we see in the world in our day-to-day experience and one of the main jobs of uh scientists is to delve into the macroscopic world discover its parts and then try to connect the microscopic with the macroscopic now something else that I want to talk about to motivate chemistry is chemistry in art the intersection of chemistry and art is is exemplified in the analytical techniques that allow us to probe the molecular and atomic composition of artistic materials so for instance polarized light microscopy has been a staple in the examination of pigments polarized light microscopy can differentiate pigment particles based on their Optical properties and that's typically influenced by the crystal structure and the interaction of light with the material and actually by comparing ing the optical signatures of pigments from verified works of artists to those that are currently unattributed pieces a polarized light microscope becomes a really pivotal tool in authenticating artwork and potentially linking unsigned or disputed Works to specific artists regardless all right of these two examples I I hope that you have gotten excited about chemistry and and hopefully we can carry this excitement throughout the course and as we move into objective two in objective two we're going to talk about the scientific method and to motivate this objective I want to start by asking you a question how do you tackle the problems that confront you in real life so think about something basic like your trip to school if you live in a city traffic is undoubtedly a problem you confront daily how do you decide the best way to drive to school if you're new in town you might grab a map or you might open your Google Maps app and look at the possible ways you can make the trip then Additionally you might collect information from people who know the area about the advantages and disadvantages of certain routes and then last but not least you might try a couple of different routes yourselves yourself to see what Falls best with your preferred criteria for a route from your home to school and after after a few experiments with the various possibilities you're going to select the best way what you're doing in solving this everyday problem is actually applying the same processes that scientists do to study nature the first thing you did was you collected information all right you collected information and you made a prediction and then you tested it out so you made some observations you collected data you made a prediction so you formed a hypothesis and then you did the experiments to test the prediction scientists call this process the scientific method the scientific method is a rigorous protocol that guides researchers through the process of scientific inquiry it is a cyclical and iterative process that involves several key steps that are described in this image right here the steps are really designed to build on one another forming this continuous loop of hypothesis experiment observation and refinement so let's go ahead and go over the different components of the scientific method first and foremost you want to generate a testable question science begins with curiosity and questions these questions arise from observations about the world a good scientific question is one that can be tested through experience experiments after you formed a and generated a testable question you want to then gather data and resources so before you even form a hypothesis it's really important to go and gather existing information and resources that are related to the question this helps to ensure that the hypothesis you develop is informed and grounded in current understanding then you can finally form a hypothesis and a hypothesis thesis is an educated guess or prediction that can be tested it's usually a statement about the relationship between two or more variables then after you formed a hypothesis you can get out there and collect some data through experimentation through experimentation scientists collect data that's either going to support or refute the hypothesis and the step can involve quantitative measurements or it can um involve qualitative observation after you've collected data through experimentation and you've conducted your experiment more than once you can then begin to analyze the data so the data has to be analyzed to determine whether it supports the hypothesis this is going to involve statistical analysis to discern patterns or relationships in the data and after you've done that analysis you can then begin to interpret your data so the the results are then have interpreted to to draw conclusions this step involves considering if the data aligns with the hypo the hypothesis or if the data suggests a different conclusion now something that's important to talk about after this process is developing a theory or a model so when a hypothesis is supported by a substantial amount of data and it withstands repeating testing it may contribute to the development of a scientific theory or model that provides a conceptual framework for understanding and at this point it's going to be really important for us to make a distinction between what an observation is what a theory is and what a law is so a theory often called a model is a set of tested hypothesis that give an overall explanation of some natural phenomena it's really important to distinguish between observations and theories and observation is something that is witnessed and it can be recorded a theory is an interpretation a possible explanation of why nature behaves in a particular way theories can change as more information becomes available of course now as scientists observe nature they often see that hey the same observation it applies to many different systems and such generally observed behavior is then formulated into a statement that's called a law all right so for example the observation that total mass of materials is not affected by chemical change in those materials this is called the law of conservation of mass it's seen when you talk about chemical reactions and it's seen in other instances in in different fields as well hence why it's called a law all right let me reiterate now in a few points the difference between Theory and law a law summarizes what happens a theory is an attempt to explain why it happens so there's this distinction between what versus why when we discuss Theory and law with that we can move into our third objective which is titled units of of measurement chemistry obviously involves experimentation and measurement and in order to communicate those measurements it's really important to pay close attention to the units that are being used to describe them every measurement must be expressed in appropriate units now the agreed upon unit system among scientists is the SI system and it's based on the metric system there are seven base units in the SI system I have them listed here in this table all other units that you might be thinking about or are familiar with are just derived units that are obtained by combining the SI base units let's go ahead and go over them so the SI base unit for mass is the kilogram it's abbreviated kg the SI base unit for length is the meter it's abbreviated lowercase M the SI base unit for time is second it's abbreviated lowercase s the SI base unit for temperature is the Kelvin it's abbreviated capital K the SI base unit for electric current is the Ampere it's abbreviated capital A the SI base unit for amount of substance is the mole it's abbreviated m o l and last but not least the SI base unit for luminous intensity is the Canda and it's abbreviated CD now we can use SI units to obtain derived quantities like volume density electric charge and many others volume is a good example so let's focus on that volume is the amount of space that's occupied by an object and its units are cubic MERS the formula for volume is length multiplied by width multiplied by height and you would Express length in units of meters you would Express width in units of meters and you would also Express height in units of meters so what really have here is meter time meter time meter hence why the unit for volume is cubic meters in the SI system Now units they're frequently modified through the use of metric prefixes you can add these prefixes to make it more reasonable to refer to different values of length mass or time depending on the system you're referring to so for example if you are discussing a human cell you don't want to say hey a human cell is anywhere between 0.000000001 and 0.0000001 M when you can instead say that a human cell is anywhere between 1 to 10 micro micro here is a metric prefix that's used to modify this quantity of length and here you see a a figure with the various prefixes and their values you should accommodate yourself with these because they're really important for a lot of future calculations we may do in general chemistry and as we do these problems of course we'll reference and remind ourselves what these metric prefixes reference but really quickly just a couple that are important we have mega it refers to 10 ^ 6 kilo 10 ^ 3 Millie 10 the- 3 micro 10- 6 and Nano 10-9 all right so this is familiar here micro now we know references 10 Theus 6 so for example when we say 1 micrometer we are essentially saying 1 * 10-6 m and we can also see that 1 * 10 to the- 6 m is equal to 0.000000001 M if we were to expand our scientific notation all right and just as a quick reminder of how scientific notation works if you have this 1 * 10- 6 meter this minus 6 tells you to move the decimal point six places down left so here we have our invisible decimal we would move this 1 2 3 4 five six units down to the left we would fill these positions with zeros and again we can see why 1 * 10- 6 m is equal to 0.000000001 M if we were to expand it away from scientific notation now something else that we want to talk about in this objective is mass 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 and 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 so for example your body mass is the same on Earth as it would be on the moon but your weight would be much less on the moon than on Earth because of the moon's smaller gravitational field with that we can now move into objective four which is a discussion on the uncertainty in measurement now any measured quantity always contains some uncertainty and we use significant figures to communicate the amount of uncertainty in a measurement this uncertainty it's it's not a flaw but a fundamental characteristic of any measurement process the Precision of the measuring device directly influences the uncertainty and yes more precise devices will reduce uncertainty but you can never eliminate it entirely now to understand this better let's consider this buet burettes are used in titrations they're filled up to this 0ml Mark and then when liquid is dispensed by opening the stopcock the liquid moves down and it reads out the amount dispensed what we notice in this buet is that the Precision of the buet is to the nearest milliliter as indicated by the graduation on the side so you can can see this graduation reference is 0 ml this is 1 2 3 4 5 so on and so forth now if we go ahead and dispense some amount of liquid and try to read how much liquid was dispensed by looking at this closeup of the buet we're going to be looking at the meniscus this is the curved surface of the liquid in the buet and here we can see it's somewhere between 16 and 17 milliliters of liquid that has been dispensed now if we try to estimate the next decimal place right we might describe the volume as oh it's about 16.4 milliliters that was dispensed in this measurement what that means is that there is an uncertainty here in the tenth place and this becomes a really good time for us to Define and distinguish between precision and accuracy the term Precision is used to describe how closely individual measurements agree with one another this graduated buet is precise to the nearest milliliter and there is uncertainty in the 10th place now Precision is not the same as accuracy the term accuracy is how close measured values agree with the true or correct value to designate the degree of position precision and the amount of uncertainty in a measurement we have to express each measured value with the appropriate number of significant figures now we're going to cover this in the next objective but significant figures in a measurement are going to include every digit we're certain of plus the first uncertain digit so in our value 16.4 16 the one and six are digits that we are certain of and then the first uncertain digit that's going to be our point4 hence again why we said in this measurement there is uncertainty in the tenth place now we can visualize precision versus accuracy in this figure all right this is like a Target and let's say that you're throwing darts at this target if you throw a couple of darts and they give this distribution here you notice that the darts are landing kind of close to the bullseye so they're accurate because they're close to the true value our true value is our bullseye but you have darts in various different quadrants in this Target and so your dart throwing is accurate but it's not precise if we compare the second one you notice that you're hitting really pretty much at the bullseye and every measurement is near the same area so you're being both accurate and precise in your dart throwing at the Target this third figure shows a distribution that's not accurate or precise it's nowhere near the bullseye and you have various darts Landing in very different places and so you can tell that there is not an agreement among the several darts that you've thrown in this figure here in this last one you don't seem to be hitting the bullseye so you're not accurate but all your darts are landing in the same area so you're precise but not accurate another thing that's important for us to to Define really quickly is random versus systematic error Rand error also known as indeterminant error this is defined um as when your measurement has an equal probability of being high or low so this is the type of error that occurs in estimating the value of the last digit of a measurement it has equal probability of being high or low the second kind of error is systematic error also known as determinant error this type of error error occurs in the same direction each time it's either always high or always low now we've made lots of mention of significant figures so it's about time we move into the fifth objective where we talk about significant figures and calculations now calculating the final result for an experiment it usually involves adding subtracting multiplying or dividing the results of various types of measurements since it's very important that the uncertainty in the final result is known exactly we have developed rules for counting the significant figures in each number and for determining the correct number of significant figures in the final result so first and foremost we're going to cover rules for counting significant figures and then we'll cover rules of significant figures in mathematical operations for the rules for counting significant figures the first rule is that nonzero integers always count as significant figures so if you have a number like 15 this number has two significant figures the one counts as a significant figure and the five does as well because they are both non-zero integers the next three rules have to do with zeros there are three classes of zeros first there are leading zeros leading zeros are zeros that preed all the nonzero digits these do not count as significant figures so in a number like like 0.0025 this number only has two significant figures that's going to be the two and the five but these leading zeros are not significant the next class of zeros we have are captive zeros these are zeros between nonzero digits and they always count as significant figures so if we have the number 1.008 this number has four significant figures the one and the eight and the two zeros that are captive between those one that between that one and eight the last class of zeros that we want to talk about then is trailing zeros trailing zeros are zeros at the right end of the number they are significant only if the number contains a decimal point so if we look at a number like one 100 just like this this only has one significant figure that's going to be that one right there but if we have 100 and there's a decimal point very clearly demonstrated for us then this number now has three significant figures those trailing zeros now count as significant because of the presence of the decimal point and then the last rule for counting significant figures is exact numbers so exact numbers many times in calculations um calculations involve numbers that were not obtained using measuring devices but that were determined by Counting Like You Can Count you did 10 experiments you have three apples there's eight molecules there's 10 books Etc these numbers are called exact numbers and they can be assumed to have an infinite number of significant figures all right and again they are not going to technically affect a lot of the calculations so they're assumed to have an infinite number of significant figures awesome with the rules for counting significant figures now we can confidently move to talking about rules for significant figures in mathematical applications and operations we'll start first and foremost with talking about multiplication and division for multiplication or division the number of significant figures in the results is the same as the number in the least precise measurement used in the calculation so for for instance let's say you're multi multiplying 4.56 by 1.4 you put this into a calculator the calculator spits out 6.38 that's not the end of the operation here you have to correct this to have the N correct number of significant figures to do that you have to determine how many significant figures does 4.56 have that would be three and how many significant figures does 1.4 have that would be two which one of these is the least precise measurement that's used in the calculation that's going to be 1.4 with only two significant figures and that means our final answer has to only have two significant figures so in short the product should only have two significant figures since 1.4 is our limiting term and it only has two significant figures then for addition and subtraction the rule is that the result has the same number of decimal places as the least precise measurement used in the calc calculation so for example let's say that we're adding up the following numbers 12.11 + 18.0 + 1.013 plug that into a calculator it spits out the following number 31.12 3 okay now in trying to correct that value to have the appropriate number of significant figures you're going to have to look at each number and determine how many significant figures it has after the decimal place the number of decimal places right so 12.11 has two decimal places 18.0 has 1 and 1.013 has three okay which is our limiting term our limiting term is 18.0 it has one decimal place and so we correct 31123 to be 31.1 the correct result is 31.1 since 18.0 has only one decimal place the next thing we also want to talk about is rounding because you just saw me correct these two values and the way that it was done was through rounding so let's also cover what the rules for rounding is so that we can properly express our final answers with the correct number of significant figures the first and the most important rule for rounding is that in a series of calculations carry all the extra digits through to the final answer and then you round at the end nowhere in between the calculations okay the second rule is look at the digit that needs to be removed if the digit to be removed is less than five all right then the preceding digit is going to stay the same so looking at here 31.12 3 we knew that we only want to keep one decimal point that means that the digit that we are going to remove is going to be this two right here first and foremost okay now if that digit is less than five which it is because two is less than five then the preceding digit this one that we're keeping stays the same this is why our final answer was written as 31.1 the second rule is if the digit to be removed is greater than or equal to I should say or equal to five then the preceding digit increases by one so when we we looking at our multiplication and division example problem we said that the final answer needs to have only two significant figures so the six and the three the digit to be removed is eight8 is greater than five that means that this preceding digit this three is increased by one hence why we wrote our final answer as 6.4 so those our those are our rules for rounding now that we've covered all of this talk of significant figures I'm going to go ahead and just like scroll down here a little bit we're going to do a couple of practice problems together to ensure that we really understand what's going on here so this first problem says give the number of significant figures for each of the following results a shows us a number 0.0105 let's recall a couple of our rules specifically for zeros if you remember that the zeros to the left all right the zeros to the left of this first nonzero integer these are called leading zeros and we said that leading zeros are not significant so we are not going to count this zero or this zero as a significant figure however this other zero right here this is a captive zero it's between two nonzero integers one and five that zero is significant in addition of course nonzero integers are also significant so one and five are significant and so is that captive zero this number has a total of three significant figures this next number is 0.0500 wait 0.058 okay again we have a couple of these leading zeros that we don't count as significant leading zeros are not significant but what we noticed is that we have these two captive zeros between five and 8 those will count as significant in addition there is also some trailing zeros here now this trailing zero is going to be signif significant because there is a presence of a decimal point so now we can count up the total significant figures we have for this number it's going to be 1 2 3 4 five this number has a total of five significant figures fantastic let's do this next example problem it says carry out the following mathematical operations and give each result with a correct number of significant figures the first problem we have is 1.05 * 10us 3 divided by 6135 all righty so if you go ahead and you just plug those numbers into a calculator your calculator is going to spit out a number that's like 17115 * 10-4 now what is our rule for multiplication and division for significant figures the N for 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 so what we have to do is we have to go back and look at each of these individual numbers and decide how many significant figures they have this number right here has 1 2 three significant figures and this number has 1 2 3 four significant figures the limiting term here is going to be this one where there's only three significant figures so our final answer can only have three significant figures that means that we're going to have to look at our answer and modify it so if we look at our Answer 1 2 3 those are our three significant figures that we're going to keep that means that this digit right here is going to be removed this digit is less than five so our rule for rounding is that the preceding digit stays the same and our final answer for this calculation is 1.71 * 10 to the minus I wrote five but it should be four here I apologize all right it's time 10 Theus 4 so let me correct that for us regardless the rules for what we just discussed stays the same I just accidentally put four instead uh five instead of four wonderful let's do the second calculation the second calculation is is 21 -3.8 all righty if you plug this into a calculator what you're going to get as an answer is 7.2 now this is a subtraction so what are our rules for significant figures for addition or subtraction it was that the result has the same number of decimal places as the least precise measurement used in the calculation 21 has zero decimal places 13.8 has one 21 is our limiting term as it has zero decimal places so our final answer is just going to be seven and the number that we discard is this two now two is less than five and in our rounding rules that means the proceeding digit stays the same and our final answer is just seven now that we've done a couple problems for significant figures let's go ahead and move into our sixth objective which is about dimensional analysis now it's often necessary to convert a given given result from one system of units to another and the best way to do this is by a method called the unit Factor method or more commonly dimensional analysis to illustrate the use of this method we're going to consider several unit conversions and conversion factors are really used to cancel unwanted units and it can be extremely helpful to move from one unit to another now here are a couple that I would recommend we know here from this start we're going to build on this as we do more enal chemistry but this is a good start this will help you get some of the through some of the example problems we do in this lecture and through some of the example problems we'll do in the problem set that will follow this lecture so 1 meter is equal to 1.94 yards 2.54 cm is equal to 1 in 1 cubic cm is equal to 1 ml this is going to be very important 1 kilogram is equal to 2.205 lb 43.6 G is equal to 1 pound 1 mile is equal to 1760 yard or 5,280 FT 1 lit is equal to 1.06 quart 1 cubic feet is equal to 2832 l 1 gallon is equal to 4 quarts and one pound is equal to 16 in now how are we going to be able to do this dimensional analysis I'm going to scroll past a couple of problems here just to talk about the steps and then we'll go back to that problem that dimensional analysis problem and do it together so how are we going to do this easy we're going to follow these three steps every time we try to tackle a dimensional analysis problem first you want to do is write down what you want to know what's the goal unit and then you also want to write down what you were given in the problem what is the given measured quantity you're starting off with and so now you have what you're starting off with what you want to get to you can start to think think about the different conversion factors that you want to do in order to cancel unwanted units now the best way to really learn this is through a practice problem so let's go ahead and do this one together it says a Japanese car is advertised as having a gas mileage of 15 km per liter convert this rating to miles per gallon so we're going to go ahead we're going to write what we know we know that the mileage is 15 kilomet per liter and our goal is to get this into units of miles per gallon so what you notice here is we're going to convert the numerator from Kilometers kilometers to miles and we're going to convert the denominator liter to gallon so let's tackle each of these independently so this is like two conversions that are going to happen here so let's tackle each one separately we want to go from kilometers to miles the first thing that we could do and there's various ways you can do this by the way but based off of what we've covered so far in our lesson the logical thing to do based off of what you've learned so far is go from kilometers to meters and this is easy because you're just using what you know about metric prefixes here all right you know that 1 kilometer is equal to 1,000 M then from meters you can actually go to yards this was one of the unit conversions we showed here all right we know that one meter is equal to 1.95 94 yards so we're going to go ahead and write that conversion to remind ourselves 1 meter is equal to 1.94 94 yards I'm sorry and then last but not least we can actually go from yards to miles this was another conversion we covered where we said that 1 mile mile is equal to 1,760 yard or 5,280 ft here we're concerned about the unit conversion of yards to miles so we're going to write that 1 mile is equal to 1760 yards so now we have devised a plan on how to go from kilometers to miles and let me color this in pink to stay in theme beautiful what about the second part that we need to do because we need to do another conversion we need to go from liters all the way to gallons how are we going to do that well again we're going to use some of the conversions we talked about we can go from liters to quarts for example and we know that one liter is equal to 1.06 quartz and we also have a conversion that we talked about that goes from quartz to gallons one gallon is equal to four quartz beautiful so again we've also devised the plan for this second conversion and now all we have to do for dimensional analysis is put it together so that we can complete the whole conversion and the way that you want to place these conversions that we've talked about right here is in a matter where you're canceling out the units appropriately so for example in our first conversion focusing on kilometers our first conversion is that 1 kilometer equals 1,000 M we're going to put kilometer here in the denominator so that the unit here and here cancel out and we put 1,000 m in the numerator then for our next conversion which is that 1 m equal 1.94 yards we're going to put the the meter in the denominator so again the meters cancel out we'll put 1.94 yards in the numerator and then for that last conversion we want to go from yards to miles we want to make sure yards cancels out so we're going to put 1760 yards in the denominator that way these cancel out and we put one mile in the numerator wonderful and we have gotten Mile in the numerator now so we are good with that first conversion now we want to implement the conversions that are going to allow us to get from liter to gallon so first conversion is to take liters and convert it to quarts here we're going to put leader in the numerator so it cancels out with a lader in the denominator here in the first value we started off with and we'll put one 06 quarts here in the denominator and then the last conversion the last conversion is from quarts to gallons we know that one quart we're going to put that in the numerator so it cancels out is equal to 1 gallon and now the final units that are only left here is this miles right here and this gallon right here in the denominator and so we will get a value with units that are miles over gallons here now for the actual value you can go ahead and plug it into a calculator and what you're going to get is about 35 mil per gallon all right and notice that 35 here two significant figures what we started off 152 significant figures so the results obtained that I'm writing here are done by rounding at the end of the calculation so there it is 35 miles per gallon we were able to convert kilometers per liter to miles per gallon now we can go ahead and move into our objective for density density is a physical property that measures the amount of mass in a given volume of a substance it is calculated by dividing the mass of an object by its volume so here you see the equation that defines density now the SI unit for density is kilogram per cubic meter that makes sense the SI unit for mass we said was kilogram and we talked about how volume is calculated it's meters time meters time meter because the formula for volume is length times width times height and so the SI unit for density is kilogram per cubic meter now this is not to say that other units aren't used so another common unit that is used to describe density is GS per milliliter or G per cubic cm and we're going to discuss when it comes time how we convert between one unit to another if need be again just considers dimensional analysis and we'll get more familiar with that with our practice problem set now density is an important Concept in chemistry because it helps us determine the behavior and characteristics of substances and it can be used to identify and classify materials because substances with different densities often exhibit different physical properties for example oil floats on water because its density is lower than that of water now understanding density allows scientists to predict how substances will interact with each other and with the environment and it's particularly useful in fields like Material Science geology and Engineering where knowledge of density really comes out play in the design and Analysis of various structures and materials now the best way to understand density is to do an example problem so that's exactly what we're going to do this problem says a chemist trying to identify the main component of a compact disc cleaning fluid finds that 20 5 cubic cm of the substance has a mass of 19.625 g at 20° C the following are the names and densities of the compounds that might be the main component which of these compounds is the most likely to be the main component of the compact disc cleaner so in order to identify the unknown substance we're going to have to calculate the density and see which of these materials it aligns with so that we can determine the main component this can be done just using the formula for density which is mass over volume we're given both those values the mass is 19.625 G and the volume is 25 cubic cm if we plug this into a calculator we'll get 0.785 G per cubic cm now notice this is really good the units that we calculate from the values that were given match the units that our table are in so we don't have to do any conversions to be able to start comparing this value with the values in the table so just by doing a comparison we notice that this number aligns with the density of isopropyl alcohol this density corresponds exactly to that of isopropyl alcohol and that means this is the most likely component of the cleaner now we can move on to talking about temperature an integral Concept in our explanation of thermodynamics is going to be temperature but what exactly is temperature in everyday language we often use it the term temperature to convey the sensation of hotness or coldness however in the realm of thermodynamics this is going to be a topic we cover in a lot of details here in general chemistry 1 it possesses a more precise and profound significance so at the molecular level temperature correlates with the average kinetic energy of the constituent particles of a substance and on a macroscopic scale the temperature differential between two objects directs the flow of heat heat will spontaneously move from regions of higher temperature to those of lower temperature but how does this knowledge actually translate to like the Practical function of thermometers well thermometers have been used to identify the temperature of substances since the 18th century and some well-known uh systems include Fahrenheit Celsius and Kelvin scales now both Celsius and Fahrenheit are based on the phase changes of water which makes them convenient for everyday use the Celsius scale defines the freezing and boiling point of water as 0° C and 100° C respectively while the Fahrenheit scale defines the freezing and boiling points of water to be 32° F and 212° F respectively the Kelvin scale this is most commonly used for scientific measurement and it's one of the seven SI base units it defines as the zero reference point to be absolute zero this is the theoretical temperature at which there is no thermal energy and it sets the freezing point of water at 273 Kelvin now it's going to be really important to be able to convert between the different units so if you know Fahrenheit you can convert to Celsius using this equation 5 over9 multiplied Fahrenheit minus 32 will give you celsius if you have Celsius and you want to get to Fahrenheit you can do 9 over5 multiplied Celsius + 32 and the way to get Kelvin is just to take the Celsius and add 273 to it we're going to cover uh temperature in more details of course when we cover therm chemistry but these equations are important to know in uh preliminarily anyways so with that being said that's all we're going to talk about temperature here we're going to go ahead and move into our last and final objective which is classification of matter matter is defined as anything occupying space and having Mass matter exists in three states solid liquid and gas technically four if you count plasma but that's not going to be a topic of Interest here in general chemistry 1 now we can visualize these states of matter here solid it holds shape and has fixed volume liquid takes the shape of the container but it has a fixed volume and gas takes the shape and the volume of the container now matter is complex and it has many levels of organization at the highest level matter is categorized into two broad types heterogeneous mixtures and homogeneous mixtures heterogeneous mixtures are those in which the different components can be visually distinguished and so they are not uniformly distributed throughout the mixture examples include things like salad Sandy water or oil and vinegar dressing in contrast homogeneous mixtures are uniform in composition and the different components can't be easily separated by physical means these mixtures are also known as Solutions so you can think of like salt dissolved in water or air moving deeply uh homogeneous mixtures are further classified as pure substances um pure substances are forms of matter that have a constant composition and properties throughout they can be elements or compounds elements or substances that cannot be broken down into simpler substances by chemical means and they're made of only one type of atom like just gold or just oxygen compounds on the other hand consist of two or more elements that are chemically bonded together like water H2O or carbon dioxide CO2 CO2 at the atomic level elements are made up of atoms and atoms are the smallest unit of an element that can retain its chemical properties atoms themselves consist of a nucleus surrounded by electrons the nucleus contains protons and neutrons and they are collectively known as nucleons electrons are negatively charged particles that orbit the nucleus and they're involved in chemical reactions and bonding this is going to be the focus of next chapter actually so we're going to talk a lot more about atoms but just to drill down to the subatomic level to really give you a feeling of how matter is so complex and it has so many levels of organization protons and neutrons are actually composed of even smaller particles called quarks and quarks are fundamental constituents of matters and they come in different types up and down quirks and they combine in specific ways to form the particles in the atomic nucleus so these protons and neutrons they're made out of quirks they're also made out of gluons which kind of keep the quarks glued together to form these protons and neutrons um we're not going to get too much into that besides that but subatomic structures of atoms are something that we're going to talk about in the next chapter so definitely stay tuned and I hope that this flow chart actually provides a clear visualization of the complexity of matter with that being said we've covered everything that we needed to in this first chapter titled chemical foundations I really hope this was helpful to you let me know if you have any questions comments concerns down below other than that good luck happy studying and have a beautiful beautiful day