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

In the study of chemistry, dimensional analysis plays a crucial role in solving complex word problems by isolating specific units. A fundamental aspect of dimensional analysis is the conversion factor, which is a ratio or fraction that connects two different units. For instance, the relationship between days and hours can be expressed as a conversion factor: one day equals 24 hours. This can be represented as a fractional ratio, either as:

\[ \frac{1 \text{ day}}{24 \text{ hours}} \quad \text{or} \quad \frac{24 \text{ hours}}{1 \text{ day}} \]

This demonstrates how different units relate to one another. In addition to conversion factors, we also encounter given amounts, which are values expressed in a single unit. For example, if you study for 3 hours, the given amount is simply 3 hours, without any connection to other units.

Understanding how to identify and utilize conversion factors and given amounts is essential for mastering dimensional analysis. This skill will be particularly useful as you tackle more complex problems in chemistry. As you prepare for quizzes and exams, practice identifying these components in various questions to strengthen your analytical skills.

Conversion Factors Example

In this scenario, we are working with a budget of $80 to prepare Klutch's chocolate chip cookies for an office party. The recipe yields 18 servings, and each serving requires 8 chocolate truffle chips. The cost of the chocolate truffle chips is 50¢ for every 5 chips. To analyze this situation, we need to identify the given amount and the conversion factors.

The given amount in this context is the $80 budget, as it stands alone without any associated units. This is crucial because it represents the total amount available for spending.

Next, we identify the conversion factors, which involve two different units:

• One recipe yields 18 servings. This means that for every recipe made, there are 18 servings available.
• Each serving requires 8 chocolate truffle chips (CTC). This indicates that for every serving, 8 chips are needed.
• The cost of the chocolate truffle chips is 50¢ for every 5 chips. This establishes a relationship between the cost and the quantity of chips.

These conversion factors will be essential for performing dimensional analysis, allowing us to cancel out units and isolate the final value needed for our calculations. Understanding the distinction between a given amount (which has only one unit) and conversion factors (which involve two different units) is key to solving problems effectively.

Common Conversion Factors

Conversion factors are essential tools that connect different units of measurement, particularly in the realms of length, volume, and mass. Understanding these factors is crucial for solving problems in chemistry and other scientific disciplines. While there are numerous conversion factors, it is important to focus on those that are most commonly used and to commit certain key factors to memory.

For length, the following conversion factors are vital:

• 1 inch = 2.54 centimeters
• 1 meter = 1.094 yards
• 1 yard = 3 feet
• 1 mile = 5,280 feet
• 1 kilometer = 0.6214 miles

In terms of volume, the key conversion factors include:

• 1 milliliter = 1 cubic centimeter (cm³)
• 1 liter = 1 cubic decimeter (dm³)
• 1 liter = 1.057 quarts
• 1 gallon = 3.785 liters

For mass, the important conversion factors are:

• 1 ounce = 28.35 grams
• 1 kilogram = 2.205 pounds
• 1 pound = 453.59 grams (often rounded to 454 grams)

Among these, the conversion factors highlighted in purple are particularly important to memorize. For any additional factors, it is advisable to consult with your professor to determine which ones you need to know for exams or quizzes. Mastering these conversion factors will enhance your ability to perform calculations and solve problems effectively in chemistry.

Weight Conversion Example

When preparing for a trip, it's essential to ensure that your luggage does not exceed the weight limit, in this case, 23 kilograms. To convert this mass into ounces, you need to utilize specific conversion factors that relate kilograms to ounces through grams.

First, recognize that 23 kilograms is your starting point. To convert kilograms to ounces, you will need to go through grams as an intermediary unit. The conversion factors you will use are:

1. The relationship between kilograms and grams, which is defined by the metric prefix: 1 \text{ kg} = 10^3 \text{ g}. This means that 1 kilogram is equal to 1,000 grams.

2. The relationship between grams and ounces, which is given by: 1 \text{ oz} = 28.35 \text{ g}. This indicates that one ounce is equivalent to approximately 28.35 grams.

To set up the conversion, you would arrange the factors to cancel out the units appropriately. Start by placing kilograms in the denominator to eliminate them:

23 \text{ kg} \times \frac{10^3 \text{ g}}{1 \text{ kg}} \times \frac{1 \text{ oz}}{28.35 \text{ g}}

In this setup, the kilograms will cancel out, leaving you with grams, which will then cancel with the grams in the second conversion factor, ultimately resulting in ounces. This method of dimensional analysis allows you to convert between different units of mass effectively.

By understanding and applying these conversion factors, you can ensure that your luggage meets the weight requirements for your trip, demonstrating the practical application of mathematical operations in everyday scenarios.

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.