Conversion Factors

so in our exploration of chemistry, eventually going to reach a topic called dimensional analysis, which can be thought of as more complex word problems where our job is to isolate a particular unit. Now a key component of dimensional analysis is the conversion factor. The conversion factor can be thought of as just simply a ratio or fraction that ties together two different units. Not, for example, we can say that a day is composed of 24 hours, So this is saying that one day equals hours. It is a conversion factor because it is tying together day as a unit with ours, which is a different unit. To make it into a conversion factor, we have to change it into a fraction of ratio so we can set it up as one day is. 24 hours or 24 hours is one day. So there were combining these two different types of units and showing their relationship to one another. Besides a conversion factor, we can also have a given amount. Now, a given amount is just a value containing Onley one unit, for example. We spent three hours studying chemistry today and trust me. There will be times when you're spending that many hours orm or in preparation for a quiz or exam. So here are given amount is just three hours. I am not tying those three hours to any other units, so it's just three hours by itself. And it's these combinations up conversion factors and given amounts that will be vital in our understanding of dimensional analysis. But again, before we get to dementia analysis, let's look over some questions where it's just our responsibility to help identify the conversion factors and given amounts within the particular question. So click on the next video. Let's get started.

so clutches ugly but good chocolate chip cookie recipe is always a hit at our office parties. My budget is $80. The recipe makes 18 servings for the party. Each serving requires a chocolate truffle chips at a cost of 50 cents per five. Chocolate truffle chips from the information provided determined a given amount. In all, conversion factors now are given amount. Remember, that's when we have only one unit That's it, are given amount has to be the $80 because they're not saying $80 connected to some other units, it's just dollars by itself. The conversion factors though these air. When we have two units bonded together to different units bonded together, This one is a little bit trickier. If we look at the sentence after the $80 budget, they tell me the recipe makes 18 servings so that there is a conversion factor. The conversion factor is one recipe has 18 servings. Okay, because recipe and serving their two different units, let's look at the next line. Each serving requires ate chocolate truffle chips so servings. Each serving has this many chocolate truffle chips. That's also a conversion factor because it's one serving is eight chocolate truffle chips, which I'll abbreviate as CTC. They tell me that it is 50 cents per five. The word per there definitely is a big help because it tells us that the that amount of 50 cents and five are connected together. So then that would be our last conversion factor. So 50 cents for every five chocolate truffle chips. Eventually, when we move on to dementia analysis later on, we'll see how these units cancel out with one another and help us isolate our final value. But remember, ah, given amount has one unit. Ah, conversion factor is two different units mixed together. Now that we've seen this first example, let's continue onward with practice questions.

So at this point we know that conversion factors tied together two different units, and we're going to say that the most common conversion factors deal with units involved in length, volume and mass. Now we can see that there's a lot of conversion factors being listed here. And remember, Onley, the ones that are in purple boxes are ones that you should commit to memory and memorize. All the other ones are usually given to you in some way or another, either within the question or as a formula sheet. So consult with your professor to make sure which one of these you need to know for the upcoming exam or quiz or homework. Okay, the ones in purple, though you should always at least Novo's all right. So when it comes to a length, the conversion factors and the first one we need to memorize one inch is equal to 2.54 centimeters. Next, we can say that 1 m is equal to 1.94 yards. One yard is equal to 3 ft. One mile is equal to 5280 ft, and then finally, one kilometer is equal 2. miles. So these are our most common types of conversion factors dealing with length. Next, we have volume out of this. The one that you should always remember is one millimeter is equal toe, one centimeters cube. Then we're going to say here that one leader is equal toe. One decile meters cube. One leader is equal to 1.57 quarts, and one gallon is equal to 3. leaders finally mass for mass, we can say one out is equal to 28.35 g. 1 kg is £2.205 and finally we have £1 is equal to 453.59 g. Oftentimes, professors will just round this upto g for the number of pat for equal to £1. So again, as we can see, there's many different conversion factors. These are the most commonly seen ones within chemistry, and out of all of these, the one you should always memorize for sure are the two that are in the purple boxes. The other one's consult with your professor to make sure if you have to memorize them, or will they be given to you on your upcoming quizzes or exams? All right, now that we've seen these common types of conversion factors, let's move on to the next question.

So here in this example question, it says while packing for a trip to Spain, a traveler wishes toe way their luggage to make sure it doesn't exceed kg. Unfortunately, their bathroom scale for some reason, can, on leeway, announces what conversion factors could they use to determine the mass off their luggage. All right, so when this question they're telling us that we don't wanna go over kg. Kilograms is not attached to any other unit. So 23 must represent are given amount. We have 23 kg, and what we need to do here is we need to find a way of dealing with ounces. Okay, so we have to find a way of converting these kilograms in tow ounces because we're dealing with mass values. We know that the conversion factors we're gonna have to utilize have to do with mass in some way. Now, we've kind of done this before when we did metric prefix conversions. We want to get rid of these kilograms. To get rid of these kilograms, we have to place them here on the bottom. And if we go to the conversion factors for mass, we see that kilograms are right here and we wanna get two ounces, right? Well, kilograms are attached to grams by way of metric prefix conversions on. We wanna goto grams because grams are connected to ounces here, we're not going to solve for it here. We're just setting up the conversion factors necessary for us to isolate ounces. We're just getting the hang of this whole idea of conversion factors given amounts and their general positions in dimensional analysis. Don't worry about calculations yet. We're kind of slowly building our way up to questions like that. Alright, so kilograms go here, which will be connected to, um, toe grams over here. Since this is a metric prefix conversion, remember that the coefficient of one is always associate ID or always next to the metric prefix. And remember, from our metric prefix multipliers, 1 kg is 10 to the three. So we started out here by using our conversion factor. So now kilograms are gone. Now we have grams, grams are connected to ounces. So we're gonna bring this conversion factor in right. So we're gonna say here that grands go here ounces go here and the the conversion factor up here says that one ounce is equal to 28 0. g grams would cancel lot and we'll be left with ounces. So for this question, the conversion factors that we have to use is this metric prefix conversion factor of 10 to the 3 g over 1 kg and one ounce over 28. g. Those are the two the two conversion factors would utilize in order to safely convert kilograms into ounces. We see that in everyday processes we can incorporate chemistry and we can incorporate these different types of mathematical operations. Now that we've seen this example, let's move on and continue our discussion on conversion factors and given amounts.