Conversion Factors: Videos & Practice Problems

Dimensional analysis is a method in chemistry for solving complex problems by isolating specific units through the use of conversion factors. A conversion factor is a ratio that equates two different units, such as 1 day to 24 hours. This method also utilizes given amounts, which are values with only one unit, like spending three hours studying. Common conversion factors in chemistry often involve units of length, volume, and mass. Essential conversion factors to remember include:

• 1 inch equals 2.54 centimeters for length,
• 1 milliliter equals 1 cubic centimeter for volume, and
• 1 ounce equals 28.35 grams for mass.

It's important to know which conversion factors need to be memorized and which will be provided, as this varies by instructor and assessment. Understanding these concepts is crucial for accurately converting and comparing different units in chemical calculations.

Conversion Factors

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 the mental analysis is the conversion factor. The conversion factor can be thought of as just simply a ratio or fraction that ties together to 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 1 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 only 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 or more in preparation for a quiz or exam. So here our given amount is just three hours. I am not tying those 3 hours to any other units, so it's just three hours by itself.

And if 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. Let's get started.

Conversion Factors Example

So clutch is ugly, but good. Chocolate chip cookie recipe is always a hit at our office parties. My budget is $80.00. The recipe makes 18 servings for the party. Each serving requires 8 chocolate truffle chips at a cost of $0.50 per five chocolate truffle chips.

From the information provided, determine the given amount in all conversion factors. Now our given amount. Remember, that's when we have only one unit. That's it. Our given amount has to be the $80.00 because they're not saying $80.00 connected to some other units. It's just dollars by itself.

The conversion factors though, These are when we have two units bonded together, two different units bonded together. This one is a little bit trickier. If we look at the sentence after the $80.00 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 two 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 $0.50 per five the word per. There definitely is a big help because it tells us that that that amount of $0.50 and fiber connected together.

So then that would be our last conversion factor, so $0.50 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 one unit. A conversion factor is two different units mixed together.

Now that we've seen this first example, let's continue onward with practice questions.

Common Conversion Factors

So at this point, we know that conversion factors tie together two different units, and we're going to say that the most common conversion factors deal with units involved in IT 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.

OK, the ones in purple, though, you should always at least know those. All right. So when it comes to length, the conversion factors and the first one we need to memorize, 1 inch = 2.54 centimeters. Next, we can say that 1 m = 1.094 yards, 1 yard = 3 feet, 1 mile = 5280 feet, and then finally 1 kilometer = 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 = 1 centimeters3. Then we're going to say here that 1 liter = 1 decimeters3, 1 liter = 1.057 quarts, and 1 gallon = 3.785 liters. Finally, mass for mass, we can say 1 oz = 28.35 grams, 1 kilogram = 2.205 lbs, and finally we have 1.00 lb = 453.59 grams. Oftentimes professors will just round this up to 454 grams for the number of for equal to 1 lb.

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 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. All right. Now that we've seen these common types of conversion factors, let's move on to the next question.

Weight Conversion Example

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?

All right, so in this question they're telling us that we don't want to go over 23kg. Kilograms is not attached to any other unit. SO23 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 Oz. So we have to find a way of converting these kilograms into Oz. Because we're dealing with mass values, we know that the conversion factors are going to 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 Oz, 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 going to solve for it here. We're just setting up the conversion factors necessary for us to isolate Oz. 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. All right. So kilograms go here, which will be connected to grams over here.

Since this is a metric prefix conversion, remember that the coefficient of one is always associated or always next to the metric prefix. And remember from our metric prefix multipliers 1K 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 going to bring this conversion factor in. So we're going to say here now, Grams go here, Oz go here, and the conversion factor up here says that one oz is equal to 28.35g grams would cancel out and we'd be left with oz.

So for this question, the conversion factors that we'd have to use is this metric prefix conversion factor of 10³g / 1 kilogram and one ounce over 28.35 grams. Those are the two the two conversion factories we'd utilize in order to safely convert kilograms into Oz. 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.

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.

• A.
• B.
• C.
• D.
• E.

Answer: (B)

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.

• A.
• B.
• C.
• D.
• E.

Answer: (D)

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.

• A.
• B.
• C.
• D.
• E.

Answer: (D)

Here’s what students ask on this topic:

What are conversion factors?

Conversion factors are numerical tools that allow you to change one unit of measure into another. They are used to convert quantities expressed in one set of units to equivalent values in another set of units. Conversion factors are based on the relationship between different units of measurement, which can be constants like those between inches and centimeters, or more complex ones like those between miles per gallon and liters per 100 kilometers.

To use a conversion factor, you multiply the quantity you want to convert by the factor that relates the units you have to the units you need. For example, to convert inches to centimeters, you would use the conversion factor of 2.54 cm/inch. If you have 10 inches and want to know how many centimeters that is, you multiply 10 inches by 2.54 cm/inch to get 25.4 centimeters. Conversion factors are essential in science, engineering, and daily life whenever different units of measurement are used.

How to do conversion factors in chemistry?

Conversion factors in chemistry are used to change one unit of measure into another. To create a conversion factor, you need to know the relationship between the two units you are converting. For instance, if you're converting from grams to moles, you'd use the substance's molar mass as the conversion factor.

Here's a step-by-step guide:

1. Identify the units you are converting from and to.
2. Write down the known conversion relationship (e.g., 1 mole of a substance = its molar mass in grams).
3. Set up the conversion factor so that the unit you want to get rid of (cancel out) is in the denominator, and the unit you want to convert to is in the numerator.
4. Multiply your original quantity by the conversion factor.
5. Ensure that the units you wanted to cancel out do so, leaving you with the desired unit.
6. Calculate the result to complete the conversion.

For example, if you have 10 grams of a substance with a molar mass of 2 grams/mole, the conversion factor is 1 mole/2 grams. Multiply 10 grams by this conversion factor to get 5 moles (10 grams × 1 mole/2 grams = 5 moles).

How can conversion factors be used?

Conversion factors are used to change one unit of measurement into another. They are essential in various fields, including science, engineering, mathematics, and everyday life, to ensure that measurements are accurate and consistent.

To use a conversion factor, you first identify the unit you want to convert from and the unit you want to convert to. The conversion factor is a ratio that represents how many of one unit equals another. For instance, if you want to convert inches to centimeters, you would use the conversion factor:

$1\text{inch =}2.54\text{centimeters}$

Here's how you apply it:

1. Write down the measurement you want to convert.
2. Multiply that measurement by the conversion factor.
3. The result will be the equivalent measurement in the new unit.

For example, to convert 10 inches to centimeters, you multiply:

$10\text{inches by}2.54\text{cm/inch to get}25.4\text{centimeters}$

Always ensure that the units you want to cancel out are diagonal from each other when you set up the multiplication. This way, they effectively cancel out, leaving you with the desired unit.