GENERAL CHEMISTRY 1: MEASUREMENT

0:06 welcome again chemistry students this video we're going to discuss some topics in measurement that you will be needing for your general chemistry one so these topics will include physical quantities accuracy and precision significant figures scientific notation measurement of density and conversion so to start with let's define measurement what is measurement measurement is obtaining any numerical values or data from experiments so this is done by using some measuring devices such as ruler in measuring a small length a meter stick we also have weighing scales to determine mass and many others some examples of measurements

0:51 are five kilogram so we we have magnitudes when we are doing measurement we assign value and we choose a unit length we have 100 centimeter and third time we have 500 seconds so what are we measuring we are measuring fundamental quantities which are divided into two groups we have the fundamental and the derived quantities for fundamental we have seven fundamental quantities these are the following one is mass must may be expressed in many different units but the fundamental of all this is kilogram another is length the fundamental unit is mass

1:37 time we have second temperature may be expressed in three scales we have degrees celsius degrees fahrenheit and kelvin but among the three the fundamental is kelvin luminous intensity candela as the fundamental unit symbol is cd electric current ampere or a and amount of substance mole for the the right quantities we have some examples volume density weight energy pressure mass work and many others since we only have seven fundamental quantities all the rest of the quantities that you will encounter will definitely fall under the right quantities the units that you see here are based on the international

2:24 system of measurement this is the system of units modified in decimal fashion by a series of prefixes let us sub some examples of let me correct that that's that's uh derived quantities so one is volume volume will be determined as the product of length width and height so notice these three are three similar units they are three lengths so volume is a combination of three fundamental quantities so that's how we define the right quantities the right quantity is quantities that are combinations of two or more

3:09 similar or different fundamental quantities like in the case of volume we we combine three fundamental quantities which are three lengths another example is density density is expressed in gram per cubic centimeter so for the formula you will see the equation mass over volume so mass is a fundamental quantity volume is a combination of three fundamental quantities so density is a combination of four fundamental quantities let's have another velocity velocity is meter per second

3:55 this is determined as the ratio of distance over time so distance is length time is another fundamental so velocity is a combination of two fundamental quantities and the rest you will see that there they are combinations of fundamental quantities so they are what we call again derived physical quantities let's move on to some common prefixes used in measurement so we have kilo kilo denotes a thousand times greater than a unit or a preceding unit in exponent it's a one or simply ten exponent three hecto is one thousand times greater

4:40 deca is 10 times deci is 10 times smaller than a preceding unit in equation in exponent exponential form is 10 raised to negative 1 centimeters 100 times smaller melee is one thousand times smaller and micro one million times smaller examples okay we have here the equivalent kilogram to gram so as i said earlier we have kilo as uh 1000 times greater so in one kilogram we expect a thousand times gram 1000 times gram same with the centimeter centimeter meter meter is

5:25 greater greater by how many times 100 times so 100 centimeter equals one meter so in one meter we have 100 centimeters or if it's the reverse um one meter equals 0.01 centimeter so you can always have the opposite so if it's one meter it should be 100 centimeters or 1 centimeter equals 0.01 meter so that's it another is liter liter 2 milliliter melee is 1000 times greater so you have a the equivalent 1 liter equals 1000 times of milliliter

6:13 so that's how you make use of prefixes in measurement let's now move on to the difference between accuracy and precision of course when doing measurement we we aim for accuracy but when do we say that our measurement is accurate the term accuracy refers to the closeness of a single measurement to the true value precision on the other hand refers to the closeness of several measurements not to the true value necessarily from the true value but from the or to the common value let's take uh have let's have this as an example let's make use of a ruler notice here three measurements

6:59 measurements a b and c so we have different measurements of length we have a 1.55 inches b we have 1.97 inches c we have 1.97 inches so when do we say that the measurement is accurate we have to compare the individual measurements uh with the true value what is the true value let's say the true value is 1.9 so which among these three measurement is considered or are considered most accurate so we have here a 1.55 that is not too close to 1.9 as a true value

7:44 b we have 1.9 very very close to the true value in fact exactly is the true value so we can say that measurement b is accurate or most accurate we have c 1.97 inches so this is um close but b measurement b is still closest to the true value so among these three measurements we can conclude that measurement b is most accurate measurement a is least accurate for the position of the measurement we have to determine the common value to determine the common value we get the average of the three measurements so getting the average of the three measurement we add 1.55

8:31 1.9 and 1.97 inches and divide the sum by three so you will get the average 1.81 inches and then you compare the closest of the three measurements to the average or common value the average is what we consider the common value are 1.85 1.9 and 1.87 close to the same value or common value 1.89 not all because 1.55 is not too close to 1.81 so we cannot exactly say that the measurements are precise one of them is um most accurate which is measurement

9:17 b but in terms of precision we cannot say that they are precise because not all of them are close to the common value of the average to determine the the the accuracy uh you can also check the percent error the smaller the error in the measurement the more accurate is your measurement so percent errors error is determined as the difference of experimental value and true value divided by the true value times 100 so in the case for example of measurement b to determine the error experimental value 1.9 minus x true value 1.9 divided by true value 1.9

10:03 so experimental 1.9 minus 1.9 divided by 1.9 times 100 you will get zero so that zero indicates that the measurement is too accurate very accurate because it's exactly as the true value on the other hand for example you determine the present error for measurement c so experimental value 1.7 minus true value 1.9 divided by 1.9 times 100 you will get less than 5 percent error when the error is less than 5 percent we can say that the measurement is accurate so the smaller the percent

10:49 error the more accurate is your measurement let's now move on to significance of figures what are significant figures significant figures are digits or numbers in a measurement that are known precisely plus one last digit that is estimated if we are after accuracy why do we have the term estimated in the definition of significant figures let's take a look again at this ruler so let's say we are doing some measurements let's say we do again measurement a so as in the previous slide the first measurement done give us 1.55 inches why is it 1.55 inches

11:36 if it is exactly along this line exactly between 1 and 2 of course the measurement is 1.5 but notice the line does not fall exactly at the line or on the line between 1 and 2. it is between 1.5 and 1.6 exactly in the middle of 1.5 and 1.6 so we can say that 1 and 5 are accurate but the third digit 5 is just estimated so that's what we mean by estimation the last digit is the best estimate that you can do but is considered still as

12:22 significant let's take a look at another example uh 1.9 why is it 1.9 because the measurement is exactly at that mark 1.9 so the uh last digit here is nine so nine is considered estimated one is most accurate is uh precise nine is estimated but the two values or digits are considered significant for the third measurement the third measurement you will notice the measurement does not fall exactly between 1.9 to 2 but it is closest to two but not exactly

13:07 marking the two inches mark so for the digits one is precise nine is also precise but it exceeded nine so it may be uh six seven eight or nine so it may be 1.96 1.97 1.98 or 1.99 so the third digit is considered estimated but still considered significant so that's what we mean by precision and estimated in terms of significant figures okay yeah the seven digit is uh already

13:54 estimated so in terms of significance of digits um we consider the following flow chart so you will see here the breakdown of digits as non-zero and zero so to recall the guidelines guideline one states that all non-zero digits in a measurement or in a number are considered significant for example we have the number 987 million 865 231 since all the digits are non-zero all the digits are considered significant so in this measurement we

14:39 have nine significant figures for the zero digits in measurement it depends on the position of the zeros we have three types of zeros in measurement we have the leading zeros confined zeros and trailing zeros let's take a look at this examples so for example number one we have 0.00231 how many significant figures we have three significant figures these zeros are called leading zeros zeros to the left of uh non-zero digits as well as that zero uh to the left of the decimal point are not significant so in this case you will only take into

15:26 account the nonzero digits because guideline number one again states that all nonzero digits are significant another example we have 987 million 231 so we have here another type of zeros we have confined zero zeros in between non-zero digits these zeros are always significant so this number will give us a total of nine significant figures combined zeros zeros between nonzero digits are always significant and for the last set we have trailing zeros so we have here 987 thousand these three zeros following uh nine seven the nine eight seven digits are

16:11 what we call trailing zeros and these zeros are not significant unless you put a bar over the zeros to consider them significant for but in this case the zeros are trailing and are not significant and therefore this number has three significant figures so what about if you have the last number zero point zero zero two three one zero zero zeros why is it that there are six significant figures so let me have two types of zeros here the leading zeros and the trailing zeros but as another uh guideline zeros to the left of a non-zero and a decimal point are not significant zeros to the right of a non-zero and a decimal point

16:57 are significant so in this case you have the first three zeros as not significant and the next three zeros to the right of a decimal and then a zero that are significant so this gives us a total of six significant figures so that's those are the guidelines in determining numbers of significant figures in measurement okay can you tell the number of significant figures in this measurement so in 24 ml we have two nonzero digits according to guideline number one all nonzero digits are significant therefore this measurement has two significant figures number two we have three thousand one

17:43 gram zeros are between nonzero digits and therefore significance so this has four significant figures number three we have zero point zero three two zero the first two zeros are not significant the other zero to the right of a decimal and a non-zero is significant therefore it has one two three significant figures four we have five uh 160 gram the zero is a trailing zero therefore it is not significant so this number has only two significant figures and the last one when the number is expressed in scientific notation or exponential form

18:28 you only take a look at the base here so six point four t has how many significant figures three the zero is to the right of a non-zero and a decimal point and therefore significant so this has three significant figures you are disregarding the uh power of 10 when counting for the number of significant figures only in the base that you are counting the number of significant figures moving on uh how do we apply the rules in significant figures in doing calculations so in addition and subtraction we have we follow the same guidelines or the same rules for example we are doing this addition

19:16 89.332 plus 1.1 so notice both have decimal places in the first number we have one two three decimal places or decimal digits we have one in 1.1 so in expressing the final answer you get the number of list significant least decimal place so you get the one digit after the decimal point as reference for your final answer so if you get a sum of 90.432 for example that's uh that's the sum of the two here so you have to round it off in such that you will reduce it with one decimal place

20:04 by doing the proper rounding off since the next digit to four is three you just drop it and retain four so the final answer should be 90.4 in doing subtraction you follow the same guideline or rule so we have two point zero nine seven in this case minus point twelve the initial answer is one point nine seven seven you round out of two two point zero nine seven has three decimal digits or places point twelve plus two so you get the smaller digits after the decimal point and express the final answer in the same number of decimal digits so the final answer should be rounded off to 1.98 since the digit after the first seven is

20:49 eight you have to add one to the last digit remaining so the final answer should be 1.98 what what about in doing multiplication and division we also follow the same rules or guidelines so for example we multiply two point eight and four point five zero three nine the initial answer is to twelve point zero six one zero nine two in expressing the final answers you consider the number of significant figures so you count the number of significant figures in your factors we have 2.8 here it has two significant figures 4.5039 has one how many significant figures a total of five so compare the number of significant

21:35 figures this is two versus five so you get the least number of significant figures and round off the final answer to two significant figures since the two significant figures remaining are two one and two and the next digit two six to two is six so you have to add one to two so that will become 13 so the final answer is 13 with two significant figures the same as 2.8 in doing division let's say 6.85 divided by 112. the initial answer is 0.0611388739 so you get the smaller number of significant figures we have 6.85

22:23 is 3 versus five here so you get the smaller number of significant figures and express the final answer in the same number of significant figures three the initial answer has two four six eight nine significant figures so to retain only three you draw numbers starting with three here so what remains should be uh six one one the first two zeros are not significant these three non-zero digits are significant since the following digit 2 1 is 3 you retain 1 so the final answer is 0.0611 so that's how you apply the rules and significant figures when doing

23:08 calculations let's move on to scientific notation scientific notation is the convenient way of expressing extremely large or small numbers for example you have this extremely large number 987 million six hundred fifty four thousand two hundred thirty one so this number is um quite long so to express this in a shorter manner we use the scientific notation how do you do that for whole numbers the the [Music] decimal point is imaginary to the right of the last digit so in this case this is the this is where you assume the decimal point so to

23:54 express this to scientific notation to reduce the the numbers you move the decimal point to the left 1 2 3 4 5 six seven and eight the base should have one non-zero digit followed by the decimal point and the rest of the significant figures let's say you are task two you're asked to leave two significant figures so the first two digits will be left in the number since the next digit to the last remaining digit is seven you have to increase eight by one so that will be rounded off to 9. so that is rounded off to 9. so the base should be 1

24:40 9.9 and then you use the power of 10 the exponent depends on the number of times you move the decimal point so in this case you moved it how many times eight times so the exponent is eight so that's how you express some large numbers in scientific notation for small numbers such as this we have zero point or this is six we have tenths hundredths thousandths ten thousands hundred thousands millions so this is ten millions so the number is read at six ten millions so how do you express that in scientific notation this is

25:26 extremely small this is way far from one so if in the first example you move the decimal point to the left to obtain a nonzero this time you move the decimal point which is visible to the right so you move that how many times three six you have to obtain another zero before the decimal point you are moving the decimal point up to after six so you will have the non-zero digit 6 followed by the decimal point that you mod if you need to express the base or the number of significant figures in in 2 then you have the freedom to add zero to add significant digits or figure so in this

26:13 case the only digit available is six if you are asked to uh express it into significant figures just add one so the answer is the expression is 6.0 times 10 raised to negative 7 is obtained because you move the decimal point seven times to the right to obtain a nonzero so that will give you an exponent of negative seven next let's have the density density is a distinct property of all types of matter density is the ratio of mass to volume this is the mass of an object divided by its volume and equation we have density equals mass divided by volume

26:58 so in symbols we have d equals mass over volume its si unit is kilogram per cubic meter so these are some examples of densities of some substances so so as i said uh density is a distinct characteristic of matter it's one of the intrinsic physical properties so for air we have 0.001 the unit for these densities are is gram per cubic centimeter so ethanol we have 0.79 gram per cubic centimeter water is 1.00 gram per cubic centimeters and the rest follows let's

27:45 have an example gold is a precious metal that is chemically unreactive and is usually used in jewelry a piece of gold weighs 301 gram and has a volume of 15.6 cubic centimeter so calculate the density of gold so to determine the density of gold we make use of the equation density equals mass over volume we substitute the given the given mass is three point uh 301 so you substitute that here as the given mass divided by the given volume of 15.6 so that's 15.6 here is the denominator cubic centimeter so for the answer just divide the two

28:32 and express the unit as the ratio gram per cubic centimeter so we have the answer 19.6 since this this is division let's take a look at the number of significant figures this has three significant figures because three is between the non-zero versus three significant figures all nonzero so therefore significant so you are not comparing different significant figures so you express the final answer in the same significant figures 3 so 19.3 is the final answer gram per cubic centimeter so for this another example a piece of platinum of metal with the density of 21.5 gram per cubic centimeter has a volume of 4.49

29:22 um cubic centimeter what is its mass so for this you can consider the equation density over volume and then you derive mass so for for the derivation you cross multiply density and volume to get the equation mass equals density times volume and then you multiply the the you first substitute the given mass and substitute the given rather substitute the given density and volume and then you multiply

30:09 you cancel the volume so you will be left with the unit gram and then express the final answer with the same uh number of significant figures that is um smaller so between the two the smaller significant figures is will will be the basis for in expressing your final answer so the final answer is given 6.5 let's go to conversion conversion is the process of changing a unit of measurement from one form to another for example can you change five grams to gram yes you cannot change 5 gram to

30:54 a newton or 5 kilogram to meter so if you are changing a unit it has to be the same of the same quantity so if it's length the unit you're changing it to should be another unit of length so this is a unit of mass you're changing it to another unit of mass so kilogram can be changed to gram length we have centimeter to meter time second to millisecond in doping conversion we apply the most common technique called the dimensional analysis or factor label method this is a procedure used to convert units in solving chemistry

31:40 problems so as a general equation we have the given quantity what do you do with a given quantity you multiply that by a certain conversion factor which is from an equivalent relationship between two quantities so the product will give you the desired quantity so there we have the given unit times the conversion factor the given unit is uh in the numerator you can have that cancel with the unit of the denominator of the conversion factor so cancellation is always done between numerator of one factor and denominator of another factor in a conversion so that will uh

32:28 make you arrive at the desired unit let's have an example one dollar is equal to 100 pennies so how many pennies are equivalent to 2.46 dollars so what is the given here the given is 2.46 dollars what is the given equivalent relationship we have one dollar is equal to 100 pennies so the conversion factor will be derived from this equivalent so that will give us two possible conversion factors one dollar over 100 pennies or 100 pennies over one dollar so in doing the calculation we start

33:14 with the given as we have seen in the previous slide we start with the given the given is 2.46 dollars you multiply that by the conversion factor taken by the given equivalent relationship you use the the ratio 100 over one in order for you to cancel dollars numerator divided by denominator so cancel dollar and you will be left with the desired unit and then you do the operation 2.46 times 100 that will give you a product of 246 and copy the unit pennies another example

34:04 what is the equivalent of 57.8 meter 2 centimeter the equivalent relationship given here is 100 i don't know 100 centimeter equals 1 meter but in this case one centimeter is equal to point zero zero one meter is the given so from here we can obtain two possible conversion factors so you just use between do between the two possible conversion factors that will enable you to do cancellation to arrive at the desired quantity so for the um solution

34:49 so this is what we're looking for this is what we are given 57.8 meter multiply that by the conversion factor taken from this equivalent so you choose this because you can cancel meter here and meter in the denominator to leave to have to arrive at the required unit centimeter so in doing the operation you do division 57.8 divided by 1 times 10 raised to negative 2 or simply 0.01 that will give you an initial answer of 5780 centimeter that in exponential or in

35:35 scientific notation 5.78 times 10 raised to 3 centimeter so that's how you do conversion let's do this a person's average daily index of glucose a form of sugar is 0.0833 pound pound is lb in symbol what is this mass in milligrams given the equivalent one pound equals four 156 point 453.6 grams so to solve you use the the equation again given times the conversion factor

36:22 equals the desired quantity so you start with a given multiply that by the conversion factor taken from the given conversion factor or equivalent converted to conversion factor it's just the conversion factor that will allow you to do the cancellation so you cancel um the similar units between numerator and denominator and then you do the operation to arrive at the answer so that's how you will convert the given to the required quantity in doing conversion so that will be all for this um topic i hope you were able to refresh these topics in preparation for

37:08 your next lessons in general chemistry thank you for watching i hope to [Music] to have you again on next videos for your general chemistry so thank you