COURSE :Math concepts

DEPARTMENT : Chemistry

PROFESSOR : LARRYBYRD

Lecture 3 : Part_3

View the Power Point Presentation of the Lecture

Welcome to another lesson, todays lesson is the continuation of the math concepts, we are now doing part number three. Converting fractions into percentage, a decimal can be changed into a percentage term by multiplying it by a hundred percent. Notice a decimal and to get a decimal we have to have a fraction first. Remember that a hundred percent has an unlimited number of significant figures, numbers expressed as percentages are commonly used to report which part of a sample is of a certain type. For example if you are a farmer if farmer Brown has a herd of cows that contain a hundred and fifty six males and a hundred and forty four females the number of males can be expressed as a percentage of the group and do remember this very important, percentage of anything is always how many of one specific kind you have as a numerator divided by the total number of members in that group so here is our fraction, numerator denominator and then always times a hundred percent and remember as we said a hundred percent is an unlimited number of significant figures these values will determine how many significant figures we round off to, which also may give us in another way percentage of anything sometimes is simply parts present divided by total parts present. If we are doing our percent males there were a hundred and fifty six males we had a hundred and fifty six plus four hundred and forty four total cows at three hundred cows times a hundred percent, first thing we must divide and get a round off three significant figures zero point five two zero times one hundred percent or multiplying by a hundred percent we get fifty two point zero percent three significant figures three significant figures, three significant figures, three significant figures, remember these do not enter in terms of significant figures. Correct answer, fifty two point zero percentage males in the herd. Notice that we will always set up a fraction then convert it into a decimal and finally convert it into a percentage also called a percent by multiplying by a hundred percent which has an unlimited number of significant figures. When using percentages remember that they are just a standard method, so here we have a standard method all over the world of expressing values as so many parts per hundreds, standard method parts per hundred. Thus the fifty two point zero percent males also mean that farmer Browns herd contains fifty two males per hundred cows. Any percentage value can always be written so any percentage value you are ever given as a fraction with a fraction value written as a numerator without a percent sign so if we have a percentage we will write it, if you want to write it as a fraction use the percent number you know percentage sign and the denominator will be a hundred so know percentage if you are going to write it as a fraction numerator over the denominator which will be a hundred. Thus the fifty two point zero males can be restated in several ways, first we can write the value as a statement on one line as a and b form, the a form fifty two percent males in the group, b part fifty two point zero males per hundred members in the group. Thus the fifty two percent males can be stated as two different fractions, we can write these values in one of two different ways in this case we are going to call them c or d, the first main fraction form will now put the fifty two point zero males in the numerator no percentage per a hundred percent, in other words numerator denominator is a hundred do notice I put three significant figures I put a decimal point here to say then this is three significant figures. This will determine how many significant figures we have in the numerator and in the denominator. Notice this is the main fractional form, however occasionally we might need the inverted form so this is the inverted form of the c part. A hundred total in the group is the same as the numerator divided by the denominator fifty two point zero males in the group. Occasionally we use this if we need it or we can cancel males and so forth, this is the inverted form. If we multiply farmer Browns number of cows, remember we had three hundred and we have counted them and we know exactly there are three hundred and this herd times the c value we will find as we already know that there are a hundred and fifty six males in the herd. For example, three hundred cows total in farmer Browns herd, we have been told it was fifty two percent which is fifty two zero males in the total divided by percentage now gone into males per hundred in the group as we already knew there is a hundred and fifty six males. Do notice total in group, total, cancel. Important note, if you are given a value as a percentage we cannot say this enough remember that it will always be written as a fraction with a given value as a numerator with no percent sign and the denominator will always be a hundred and it may be according to what specific significant figure we need. Usually it is a hundred points. Percentage weight volume solutions, now you are going to find that weight volume solutions are very important in the medical area as well in a lot of chemical areas. For example normal glucose solution, this is the one that is given by IV in case you are ever in the hospital you should memorize it is five point zero zero percentage, weight volume glucose solution. In a hospital they may call it D5W solution, the D is the old name of glucose it used to be called Dextrose. If you look on the back of candy bars and so forth occasionally you will see the word Dextrose, remember that is nothing more than plain old glucose. The five W means five point zero zero percentage the W means weight volume solution of glucose. This solution is composed of solid glucose always weighted out as grams, dissolved and sterile it means absolutely pure it means no micro organisms everything dead, pure pure water and in this class whenever we use the word pure water that really means sterile distilled water the best you can get. Thus the five percent weight volume glucose solution remember the old name Dextrose, D5W, maybe written as follows so this is the way we are going to deal with it modernly. First we will write the value as a statement on one line as a or b forms, first value the easiest way, one line five point zero zero percentage weight volume glucose solution. Or equally correct five point zero zero grams of solid glucose per hundred milliliters of solution remember we could get all of this on one line but the computer was not large enough, notice that per means divide by, three significant figures, three significant figures, three significant figures here. Thus the five percent weight volume glucose solution may be written as the following so now we are going to write it in a fractional form. The one that is mainly used will be the five point zero zero grams of solid glucose, no longer any percentage per hundred point zero milliliters of solution. Do observe three significant figures one hundred decimal point three significant figures. However we may need the fraction written in its inverted form which we may use, an inverted form a hundred point zero milliliters of solution, now that is glucose solution, is equivalent numerator denominator five point zero zero grams of solid glucose. This is the inverted form, this is the main form. A solution is always composed of a solute and a solvent, when these two are mixed solution, so solute plus solvent solution, solute solvent solution. If a solvent is not given then it is understood that the solvent is pure water the best you can get in the medical area, we want pure water that is sterile distilled. In our above example of percentage weight volume we can also write this simply percentage, no longer with the weight but with the W standing for weight volume capital V. The glucose is a solute and it is measured in grams and weight and the pure water is a solvent thus the glucose solution is composed of solid glucose plus pure water. Another example found in the medical area is known as normal saline or in many cases they just say saline solution. This solution contains solid sodium chloride as a solute mixed with enough pure water to form zero point nine zero zero, three significant figures, weight volume percent sodium chloride solution. The normal saline solution, they can be written as a line, zero point nine zero zero percentage, three significant figures weight volume sodium chloride solution. All on one line expanded out, zero point nine zero zero grams of solid sodium chloride still on one line per hundred point milliliters of solution, three significant figures, three significant figures pointed out here three significant figures. We can also write it in a fraction form which is more useful to us if we are solving problems, the main form is going to be zero point nine zero zero grams remember we have percentage now we have gone to grams of solid sodium chloride per a hundred point milliliters of solution, three significant figures three significant figures or the inverse a hundred point milliliters of solution numerator divided by the denominator zero point nine zero zero grams of solid sodium chloride three significant figures three significant figures, these are the three. Another example of a weight volume percent used in the medical area and this is a very good one to have in your house is used in the home to treat small cuts, it is also used in the hospital to treat skin wounds and bed sores especially bed sores, it is a one point zero zero percentage weight volume iodine solution. Iodine is a very good germ killer, remember that in terms of the water before it comes out to your house water is treated by chlorine to kill germs, well iodine is not quite as good but it is a very good one if you place it on you. Solid iodine, notice the symbol, capital I subscript two is added to a special mixture of skin lotions that allow that stay on your skin very easily. Betadine was the first by a specific company and then its copyright as gone out, Wal Mart has its own brand so this value and this value are absolutely the same, Wal Marts value is one point zero zero weight volume percent iodine solution, same equivalent as the Betadine solution much cheaper. Betadine solution, this solution may be written in the following forms, here is our one line one point zero zero percentage weight volume iodine solution. Written out more, one point zero zero grams of solid iodine, I two capital I, per hundred milliliters of solution three significant figures three significant figures or in the normal useful form as a fraction one point zero zero grams of solid iodine I two per a hundred point zero milliliters solution three significant figures in each case. Or the inverted form, occasionally we need, a hundred point milliliters of solution one point zero zero grams of solid iodine I two. Practice test number three questions, on the back of a tube of Crest toothpaste lets hope you are brushing your teeth, it is labeled as zero point one five zero, three significant figures, weight volume fluoride ions, so next time you are brushing look at your Crest or look at your toothpaste see what it has on it. This really means zero point one five zero percentage, three significant figures, weight volume sodium fluoride solution. The formula for sodium fluoride you must know is NaF write this information as two different fraction forms as we did for normal glucose solution and then in a minute we are going to do if you brush your teeth, notice I say I hope you do so with two point zero zero milliliters of Crest. One morning I was brushing my teeth I decided lets see how much it takes and I found that basically it is about two point zero zero milliliters to brush your teeth and then how many grams of sodium fluoride would you have by brushing your teeth with a toothbrush, will grams of sodium chloride touch your teeth. As we did a minute ago we are going to write this as two different fraction forms as we did for normal glucose so here for sodium chloride it will be zero point one five zero first one line, percentage weight volume sodium fluoride solution are on one line zero point one five zero grams of solid sodium fluoride per one hundred point zero milliliters three significant figures, three significant figures, three significant figures. Then in the fractional form that we may use the normal form no longer in a percentage now we have a fraction so it is zero point one five zero grams of solid sodium chloride per hundred point milliliters of solution, three significant figures, three significant figures, notice where the decimal point is all three of these are significant. These are the three significant, this just holds the place so these are the three significant. Or in the inverted form a hundred point milliliters of solution numerator denominator zero point one five zero grams of solid sodium fluoride, three significant figures, three significant figures, just holds the place. This one is not significant, the zero. If you brush your teeth like we said a moment ago and if we assume it is two point zero zero milliliters of Crest on your toothbrush how many grams of sodium fluoride will touch your teeth. How many grams of NaF, we set it up we have two point zero zero milliliters of Crest solution and we make it a fraction where we can use canceling over one, remember we can divide anything by one and then we are going to multiply that to the normal one we used a minute ago where we have zero point one five zero grams of sodium fluoride numerator per hundred point zero milliliters of Crest solution, we set it up this way and notice milliliters, milliliters cancel. Then we simply multiply two point zero zero times one point one five zero, one times a hundred, numerator times a numerator, denominator times a denominator and then we are going to express it as three point zero zero times ten to minus three grams of sodium fluoride. Now we could have written it as zero point zero zero zero zero zero, these are the only three significant figures. This holds a place, this holds a place, this holds a place, then we start three zero zero and inside of notation as we found a minute ago that it becomes three point zero zero times ten to the minus three grams of sodium fluoride. So lets not leave it in this form, always write in scientific notation, we could also give it in milligrams because in a lot of cases in the medical area you see milligrams so we are going to have three point zero zero times ten to the minus three grams of sodium chloride here it is in scientific notation over one again to where we have a numerator denominator or you can multiply a numerator times a numerator, denominator times a denominator and we find that it is one times ten to the third power milligrams in other words there are a thousand milligrams per one gram of sodium fluoride. We set it up where grams of sodium fluoride cancel and we find then in that toothpaste that you brushed on two milliliters you actually exposed your teeth to three point zero zero milligrams of sodium fluoride. The other type of percentage solution is known as a percentage volume volume. Now it is not quite as useful as the other however in the medical field there are several of these, in this solution the solute is a liquid and the solvent usually water is as we know a liquid, notice that both are measured in milliliters since they are liquids, two examples of this type of solution are often found in your bathroom. We have hydrogen peroxide there, it is a low level germ killer and remember it is not as good as that iodine solution not as good as the Betadine and rubbing alcohol if you put that on a child they will jump up and down and they will never tell you again if they got hurt, they say do not put this rubbing alcohol on but use the iodine solution which does not burn. These solutions are good germ killers, the rubbing alcohol quite often is used to rub the skin before they give you a shot or do an IV. The first solution is really a three point zero zero volume volume hydrogen peroxide solution so if you read the label you will see it says three percent usually it will say volume volume. This bottle contains the liquid hydrogen peroxide in milliliters mixed with pure water remember that is sterile distilled water in milliliters. The best rubbing alcohol solution is really a seventy point zero zero percentage, four significant figures of isopropyl alcohol mixed with water. Now you have got to be careful because now some companies are selling the fifty percent and that is not as good a germ killer, you need the seventy percent to wipe the skin off to make sure you have killed all of the germs fifty percent may or may not kill all of the germs. Practice test number four, question, express the percentage of hydrogen peroxide as a fraction in parts per a hundred milliliters notice three significant figures. Number two, express the percentage of isopropyl alcohol and that is rubbing alcohol as a value in parts per hundred and also as an inverted fraction of milliliters of total solution per hundred milliliters of isopropyl alcohol. Number one, express the percentage of hydrogen peroxide as a fraction in parts per hundred milliliters very easy, all we do since it was a three percent we drop the percentage and write three point zero zero milliliters since we are measuring the hydrogen peroxide in milliliters per hundred milliliters of solution. Observe three significant figures three significant figures, notice where this decimal point is to indicate three significant figures three significant figures. Number two, express the percentage of isopropyl alcohol remember that is rubbing alcohol as a value in parts per hundred as an inverted fraction form so we are going to do it two ways. Here we are going to start out in the normal way, seventy point zero zero, four significant figures there should have been one more zero here, a hundred point zero to give us four significant figures milliliters of isopropyl alcohol per hundred point zero milliliters of solution, the inverted form should have been a hundred point zero milliliters to be consistent with what we have here milliliters of solution seventy point zero zero milliliters of isopropyl alcohol. Question number one, now we are on practice test number five, if we mix five point eight five grams of solid sodium of table salt and we are assuming this is ultra pure table salt, best you can get with pure water that means sterile distilled water to form six hundred and fifty point zero milliliters of solution, three significant figures, five point eight five, four significant figures, six hundred and fifty point zero grams milliliters. What is the percentage of sodium chloride in this solution so we are going to do a percentage solution. If we mix five point eight five grams of solid sodium chloride best we can get with enough pure water to form six hundred and fifty milliliters of solution what is the percentage of sodium chloride. First way in doing this question is set up your equation percentage of anything. Now always on you paper do not leave this out, do not start jumping down here start with percentage of anything is parts present divided by total parts present times a hundred percent. Always show everyone what you are going to start with, now you can substitute the percentage of sodium chloride now the anything is sodium chloride we find five point eight five grams of salt here we have total volume so grams total volume six hundred and fifty point zero milliliters times a hundred percent remember there are unlimited number of significant figures here, three four so this is going to determine how many we have in our final answer. We work it out and we find the percentage of sodium chloride so like we did a minute ago this is normal saline solution zero point nine zero zero percentage weight volume. Sodium chloride solution, three significant figures, there is out answer three significant four cannot use it got to have three. Notice that the solution we have just prepared has zero point nine zero zero grams of sodium chloride per hundred milliliters, there is our decimal point three significant three significant milliliters of total solution. This solution as we found before is called a normal saline solution this is widely used in hospitals for electrolyte balance so if a person has lost blood volume or is low on sodium chloride content because of sweating or so forth or high fever this is the type of solution they give them, zero point nine zero zero weight volume percent also known as saline solution, normal saline solution. Thank you for watching part number three.