Conversion Factors (Simplified): Study with Video Lessons, Practice Problems & Examples

Dimensional analysis involves using conversion factors, which are ratios that relate different units, to solve complex problems. Key conversion factors to memorize include: 1 inch = 2.54 cm, 1 liter = 1.057 quarts, and 1 pound = 454 grams. A given amount is a value in a single unit, such as 3 hours. Mastering these concepts is essential for effective problem-solving in chemistry, particularly in areas like stoichiometry and unit conversions.

Conversion Factors (Simplified) Concept 1

So in our exploration of chemistry, eventually, we're 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 simply a ratio or fraction that ties together two 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 two 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.

Conversion Factors (Simplified) Example 1

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. 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 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.

Conversion Factors (Simplified) Concept 2

Now remember that a conversion factor deals with two units combined together. And when it comes to our conversion factors, the most common ones involve length, volume, or mass. Now, remember, we see a lot of different conversion factors here, but only the ones that are highlighted in purple you should commit to memory. The others will be given to you within the work problem that you're solving or some type of formula sheet. So let's start out with length. We know here that 1 inch is 2.54 centimeters. So we need to commit that to memory. Next, we can say that 1 yard is equal to 3 feet. One kilometer is 0.6214 miles. One meter is 1.094 yards, and 1 mile is 5,280 feet.

For volume, the first two in purple are the ones you need to memorize, and that's 1 milliliter equals 1 centimeter cubed, and 1 milliliter is equal to 1 cc. Next, we can say that 1 liter is equal to 1.057 quarts, 1 liter is 1 decimeter cubed, 1 fluid ounce is equal to 29.574 milliliters, and 1 gallon is 3.785 liters.

For mass, tablets can come in different types of masses. The most common one is when one tablet is equal to 254 milligrams. Now, if they're talking about a tablet and they don't give you the mass, usually they mean a 250-milligram tablet. But check the question. Sometimes the tablet may be a different mass and they'll tell you that new mass associated with it.

Next, we can say here that 1 pound is equal to approximately 454 grams, 1 ounce is 28.35 grams, and then finally, 1 kilogram is 2.205 pounds. So these are all types of common conversion factors that you'll come into contact with when doing different types of problems. Now remember, only the ones that are highlighted in purple, you should commit to memory.

Conversion Factors (Simplified) Example 2

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 on this side, 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 103. 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 103 grams over 1 kilogram and 1 ounce over 28.35 grams. Those are 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.

A patient has approximately 83 mL of blood pumping by their heart at each beat. By assuming they have a pulse of 75 beats per minute it is calculated that the patient pumps 8.964 x 10⁶ mL in one day. Identify the given amount and all conversion factors.

Here we're told that a patient has approximately 83 milliliters of blood pumping by their heart at each beat. So, by assuming they have a pulse of 75 beats per minute, it is calculated that the patient pumps \(8.964 \times 10^{6}\) milliliters in one day. Identify the given amount and all conversion factors. Alright. So remember, your given amount is just 1 unit by itself. Alright. So here, if we take a look at the information given to us, they're telling us that we have 83 milliliters of blood pumping and that's for each beat. Then, they also tell me that I have 75 beats per minute, and then they tell me that a patient pumps this many milliliters in one day. So here, if we take a look, we can tell that automatically 75 beats per minute is 2 different units mixed together. So that would be a conversion factor. We also have connected this many milliliters of blood associated in one day. So that would be \(8.964 \times 10^{6}\) milliliters per one day. Okay. So, these are our conversion factors. Then what else do we have? They also tell us that we have 83 milliliters of blood. And here's the thing, they say that's per beat. So that's 83 milliliters of blood per 1 beat. So by looking at these options, we see that we have 3 conversion factors given to us. They're not telling us any given amount. There isn't a single unit by itself because here milliliters of blood are combined with beats, beats per minute, and then milliliters in a day. K. Sometimes that happens. Sometimes, we may get to a situation where we're only given conversion factors, and we're going to have to utilize those conversion factors, cancel out units to get to our final answer. This could be one of those cases where in this situation, we have 3 conversion factors, but no given amount.

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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The dispensing of prescription drugs are usually prescribed in units of mg per kg of body weight. A new prescription drug has a recommended dosage of 11 mg/kg. A 75 lb child requires three tablets each weighing 125 mg for their recommended dosage. Identify the given amount and all conversion factors.

In this practice question, it states that dispensing of prescription drugs is usually prescribed in units of milligrams per kilogram of body weight. A new prescription drug has a recommended dosage of 11 milligrams per kilogram. A 75-pound child requires 3 tablets, each weighing 125 milligrams, for their recommended dosage. Identify the given amount in all conversion factors. Alright. So the first conversion factor is pretty blatant here. Here we have milligrams mixed with kilograms, two different units. That automatically tells us there is a conversion factor, which is 11 milligrams per 1 kilogram. Then, what else do we have? We have 75 pounds; they're telling me about 3 tablets; they're telling us each one weighs 125 milligrams. So what they're really saying here is that you have 3 tablets, each one is 125 milligrams. So if you multiply that by 3, that gives us their combined mass which is 375 milligrams. So, 3 tablets, 375 milligrams total for their masses. This is another conversion factor that required us to do a little bit of math. The given amount is a unit that's by itself. In this case, it's the 75-pound child. So the 75-pound child is our given amount where it's just one unit by itself, not connected to another. Right? So, in this case, we have two conversion factors and one given amount.

Here’s what students ask on this topic:

What is a conversion factor in chemistry?

A conversion factor in chemistry is a ratio or fraction that relates two different units, allowing you to convert a quantity expressed in one unit to another unit. For example, the conversion factor between inches and centimeters is 1 inch = 2.54 cm. This means you can convert inches to centimeters by multiplying by 2.54, or convert centimeters to inches by dividing by 2.54. Conversion factors are essential in dimensional analysis, which is used to solve complex problems involving different units.

How do you use conversion factors in dimensional analysis?

In dimensional analysis, conversion factors are used to convert a given amount from one unit to another. You start with the given amount, multiply it by the appropriate conversion factor(s), and ensure that units cancel out correctly. For example, to convert 5 inches to centimeters, you use the conversion factor 1 inch = 2.54 cm: $5 \mathrm{in}\times \frac{2.54 \mathrm{cm}}{1 \mathrm{in}}=12.7 \mathrm{cm}$. The inches cancel out, leaving you with the result in centimeters.

What are some common conversion factors that need to be memorized?

Some common conversion factors that are essential to memorize include: 1 inch = 2.54 cm, 1 liter = 1.057 quarts, 1 pound = 454 grams, 1 milliliter = 1 cm³, and 1 kilometer = 0.6214 miles. These conversion factors are frequently used in chemistry for converting between different units of length, volume, and mass. Memorizing these will help you solve problems more efficiently.

What is the difference between a given amount and a conversion factor?

A given amount is a value expressed in a single unit, such as 3 hours or 5 grams. It does not involve any relationship to another unit. A conversion factor, on the other hand, is a ratio that relates two different units, such as 1 inch = 2.54 cm. Conversion factors are used to convert given amounts from one unit to another in dimensional analysis.

Why is it important to memorize certain conversion factors in chemistry?

Memorizing certain conversion factors is important in chemistry because it allows you to quickly and accurately convert between units without needing to look up the values each time. This is particularly useful in solving problems involving stoichiometry, unit conversions, and other calculations where time and accuracy are crucial. Knowing key conversion factors like 1 inch = 2.54 cm or 1 liter = 1.057 quarts can significantly streamline your problem-solving process.