Conversion Factors - Video Tutorials & Practice Problems
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Conversion Factors represent ratios or fractions composed of different units.
Conversion Factor & Given Amount
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Conversion Factors Concept 1
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So in our exploration of chemistry, eventually, we're gonna 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 2 different units. Now, for example, we can say that a day is composed of 24 hours. So this is saying that one day equals 24 hours. It is a conversion factor because it is tying together day as a unit with hours, which is a different unit. To make it into a conversion factor, we have to change it into a fractional ratio. So we can set it up as one day is 24 hours or 24 hours is one day. So there, we're combining these 2 different types of units and showing their relationship to one another. Besides the conversion factor, we can also have a given amount. Now a given amount is just a value containing only one unit. For example, we spent 3 hours studying chemistry today, and trust me there will be times when you're spending that many hours or more in preparation for a quiz or exam. So here, our given amount is just 3 hours. I am not tying those 3 hours to any other units. So it's just 3 hours by itself. And it's these combinations of conversion factors and given amounts that will be vital in our understanding of dimensional analysis. But, again, before we get to dimensional 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 and let's get started.
The given amount contains one unit type and the conversion factor connects two different units together.
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Conversion Factors Example 1
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So Klutch's 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 8 chocolate truffle chips at a cost of 50¢ per 5 chocolate truffle chips. From the information provided, determine the given amount and all conversion factors. Now our given amount, remember, that's when we have only 1 unit. That's it. Our 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 are when we have 2 units bonded together, 2 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 1 recipe has 18 servings. K. Because recipe and servings are 2 different units. Let's look at the next line. Each serving requires 8 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 8 chocolate truffle chips, which I'll abbreviate as CTC. They tell me that it is 50¢ per 5. The word per there definitely is a big help because it tells us that the that amount of 50¢ and 5 are connected together. So then that would be our last conversion factor. So 50¢ for every 5 chocolate truffle chips. Eventually, when we move on to dimensional analysis later on, we'll see how these units cancel out with one another and help us isolate our final value. But remember, a given amount has 1 unit, a conversion factor is 2 different units mixed together. Now that we've seen this first example, let's continue onward with practice questions.
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Conversion Factors Concept 2
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So at this point, we know that conversion factors tie together 2 different units. And we're gonna 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, only 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. K? The ones in purple though, you should always at least know those. Alright. So when it comes to length, the conversion factors, and the first one we need to memorize, 1 inch is equal to 2.54 centimeters. Next, we can say that 1 meter is equal to 1.094 yards, 1 yard is equal to 3 feet. 1 mile is equal to 5,280 feet. And then finally, 1 kilometer is equal to 0.6214 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 1 milliliter is equal to 1 centimeters cubed. Then we're going to say here that 1 liter is equal to 1 decimeters cubed, 1 liter is equal to 1.057 quartz, and 1 gallon is equal to 3 point 785 liters. Finally, mass. For mass, we can say one ounce is equal to 28.35 grams, 1 kilogram is 2.205 pounds, And finally, we have 1 pound is equal to 4 53.59 grams. Oftentimes, professors will just round this up to 454 grams for the number of for equal to 1 pound. 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 2 that are in the purple boxes. The other ones, 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. Alright. Now that we've seen these common types of conversion factors, let's move on to the next question.
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Conversion Factors Example 2
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So here in this example question, it says while packing for a trip to Spain, a traveler wishes to weigh their luggage to make sure it doesn't exceed 23 kilograms. Unfortunately, their bathroom scale, for some reason, can only weigh in ounces. What conversion factors could they use to determine the mass of their luggage? Alright. So in this question, they're telling us that we don't want to go over 23 kilograms. Kilograms is not attached to any other unit, so 23 must represent our given amount. We have 23 kilograms, 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 into 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'd 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 want to get to ounces. Right? Well, kilograms are attached to grams by way of metric prefix conversions, and we want to go to grams because grams are connected to ounces. Here, we're not gonna 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, to grams over here. Since this is a metric prefix conversion, remember that the coefficient of 1 is always associated or always next to the metric prefix. And remember, from our metric prefix multipliers, 1 kilo is 10 to the 3. 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 grams go here, ounces go here, and the conversion factor up here says that 1 ounce is equal to 28.35 grams. Grams would cancel out and we'd be left with ounces. So for this question, the conversion factors that we'd have to use is this metric prefix conversion factor of 10 to the 3 grams over 1 kilogram and 1 ounce over 28.35 grams. Those are the 2 the 2 conversion factors we'd 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.
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For 7 hours, an intravenous bag delivers medication to a patient at a rate of 2.75 drops a second with a mass of 42 mg per drop. Identify the given amount and all conversion factors.
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During World War II in the US, nickel metal was in short supply and needed for the war effort. So from 1942 to 1945 the government replaced the nickel in the five-cent coin with silver until it was 35 grams of silver per 100 grams. Today the mass of the coin is 5.0 grams with a value of approximately $28.40 per ounce. Identify the given amount and all the conversion factors from the presented information.
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The F-51 jet engine consumes gasoline at a rate of 31.810 L per hour with a density of 0.819 g/cm3 for the gasoline. The engine is ran continuous for 1.35 days. Identify the given amount and provide ALL the necessary conversion factors.