Chapter 2: Problem 148
Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor(s) in each case. a. 908 oz to kilograms b. 12.8 L to gallons c. \(125 \mathrm{mL}\) to quarts d. 2.89 gal to milliliters e. 4.48 lb to grams f. 550 mL to quarts
Short Answer
Expert verified
a. 908 oz ≈ 25.74 kg
b. 12.8 L ≈ 3.38 gal
c. 125 mL ≈ 0.132 qt
d. 2.89 gal ≈ 10935.7 mL
e. 4.48 lb ≈ 2032.11 g
f. 550 mL ≈ 0.581 qt
Step by step solution
01
Identify the conversion factor
We need to know the conversion factor between ounces and kilograms: 1 oz = 0.0283495 kg.
02
Apply the conversion factor
Multiply the given value in ounces by the conversion factor: \( 908 \, \mathrm{oz} \times 0.0283495 \, \frac{\mathrm{kg}}{\mathrm{oz}} \).
03
Calculate the result
\( 908 \, \mathrm{oz} \times 0.0283495 \, \frac{\mathrm{kg}}{\mathrm{oz}} = 25.7419 \, \mathrm{kg} \). So, 908 oz is approximately equal to 25.74 kg.
b. Convert 12.8 L to gallons
04
Identify the conversion factor
We need to know the conversion factor between liters and gallons: 1 L = 0.264172 gal.
05
Apply the conversion factor
Multiply the given value in liters by the conversion factor: \( 12.8\, \mathrm{L} \times 0.264172 \, \frac{\mathrm{gal}}{\mathrm{L}} \).
06
Calculate the result
\( 12.8 \, \mathrm{L} \times 0.264172 \, \frac{\mathrm{gal}}{\mathrm{L}} = 3.3814 \, \mathrm{gal} \). So, 12.8 L is approximately equal to 3.38 gal.
c. Convert 125 mL to quarts
07
Identify the conversion factor
We need to know the conversion factor between milliliters and quarts: 1 mL = 0.00105669 qt.
08
Apply the conversion factor
Multiply the given value in milliliters by the conversion factor: \( 125\, \mathrm{mL} \times 0.00105669 \, \frac{\mathrm{qt}}{\mathrm{mL}} \).
09
Calculate the result
\( 125\, \mathrm{mL} \times 0.00105669 \, \frac{\mathrm{qt}}{\mathrm{mL}} = 0.132086 \, \mathrm{qt} \). So, 125 mL is approximately equal to 0.132 qt.
d. Convert 2.89 gal to milliliters
10
Identify the conversion factor
We need to know the conversion factor between gallons and milliliters: 1 gal = 3785.41 mL.
11
Apply the conversion factor
Multiply the given value in gallons by the conversion factor: \( 2.89\, \mathrm{gal} \times 3785.41 \, \frac{\mathrm{mL}}{\mathrm{gal}} \).
12
Calculate the result
\( 2.89\, \mathrm{gal} \times 3785.41 \, \frac{\mathrm{mL}}{\mathrm{gal}} = 10935.7 \, \mathrm{mL} \). So, 2.89 gal is approximately equal to 10935.7 mL.
e. Convert 4.48 lb to grams
13
Identify the conversion factor
We need to know the conversion factor between pounds and grams: 1 lb = 453.592 g.
14
Apply the conversion factor
Multiply the given value in pounds by the conversion factor: \( 4.48\, \mathrm{lb} \times 453.592 \, \frac{\mathrm{g}}{\mathrm{lb}} \).
15
Calculate the result
\( 4.48\, \mathrm{lb} \times 453.592 \, \frac{\mathrm{g}}{\mathrm{lb}} = 2032.11 \, \mathrm{g} \). So, 4.48 lb is approximately equal to 2032.11 g.
f. Convert 550 mL to quarts
16
Identify the conversion factor
We need to know the conversion factor between milliliters and quarts: 1 mL = 0.00105669 qt.
17
Apply the conversion factor
Multiply the given value in milliliters by the conversion factor: \( 550\, \mathrm{mL} \times 0.00105669 \, \frac{\mathrm{qt}}{\mathrm{mL}} \).
18
Calculate the result
\( 550\, \mathrm{mL} \times 0.00105669 \, \frac{\mathrm{qt}}{\mathrm{mL}} = 0.581686 \, \mathrm{qt} \). So, 550 mL is approximately equal to 0.581 qt.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Conversion Factors
In chemistry and everyday calculations, conversion factors are integral to changing units from one type to another. They serve as bridges that allow us to convert measures like weight, volume, and length from one system to another.
Understanding and properly setting up conversion factors ensure accurate calculations. A conversion factor is a ratio or fraction that represents the relationship between two different units. For example, the conversion factor for converting ounces to kilograms is 1 oz = 0.0283495 kg. To convert ounces to kilograms, you multiply the number of ounces by this conversion factor.
For a successful conversion process, memorize some common conversion factors or know where to find them, and practice the technique of unit cancellation to avoid mistakes. Unit cancellation methodically strikes out units in the conversion factor that are identical to the ones you're converting, leaving you with the desired units.
Understanding and properly setting up conversion factors ensure accurate calculations. A conversion factor is a ratio or fraction that represents the relationship between two different units. For example, the conversion factor for converting ounces to kilograms is 1 oz = 0.0283495 kg. To convert ounces to kilograms, you multiply the number of ounces by this conversion factor.
For a successful conversion process, memorize some common conversion factors or know where to find them, and practice the technique of unit cancellation to avoid mistakes. Unit cancellation methodically strikes out units in the conversion factor that are identical to the ones you're converting, leaving you with the desired units.
Metric System
The metric system is an international decimal system of measurement that is used in nearly all countries worldwide. It is based on multiples of ten and includes units like meters for length, liters for volume, and grams for mass.
In the metric system, units are easily convertible by simply moving the decimal point. Prefixes such as kilo- (1000), centi- (0.01), and milli- (0.001) are used to indicate multiples or subdivisions of units. This system's simplicity makes it easy to calculate different measurements by applying a base ten conversion factor, which is why it's predominantly used in scientific and educational contexts.
Chemistry, in particular, relies heavily on the metric system. Being fluent in this system allows for streamlined calculations and easier understanding of quantities and concentrations.
In the metric system, units are easily convertible by simply moving the decimal point. Prefixes such as kilo- (1000), centi- (0.01), and milli- (0.001) are used to indicate multiples or subdivisions of units. This system's simplicity makes it easy to calculate different measurements by applying a base ten conversion factor, which is why it's predominantly used in scientific and educational contexts.
Chemistry, in particular, relies heavily on the metric system. Being fluent in this system allows for streamlined calculations and easier understanding of quantities and concentrations.
Volume Conversion
Volume conversion is a frequent task in chemistry, where substances are often measured in liters, milliliters, or even cubic meters. When converting between different volume units, especially between the metric system and the U.S. customary system, it's important to use the correct conversion factors. For instance, to convert liters to gallons, the conversion factor is 1 L = 0.264172 gal, and for milliliters to quarts, it's 1 mL = 0.00105669 qt.
Volume conversions often require precision, as volume directly affects the concentration of chemical solutions. Inaccuracies could lead to experiments yielding incorrect results. Application of conversion factors here, as shown in the provided exercise examples, ensures precise transitions from one volume unit to another.
Volume conversions often require precision, as volume directly affects the concentration of chemical solutions. Inaccuracies could lead to experiments yielding incorrect results. Application of conversion factors here, as shown in the provided exercise examples, ensures precise transitions from one volume unit to another.
Mass Conversion
Mass conversion is essential in chemistry for quantifying the amount of a substance. In both laboratory and real-world applications, converting mass between units like grams, kilograms, and pounds is common. For example, the conversion factor between pounds and grams is 1 lb = 453.592 g.
Knowing how to convert mass is critical for preparing solutions, scaling reactions, or assessing quantities for trade and commerce. Careful application of mass conversion principles allows for accurate and repeatable scientific measurements, contributing to consistency in experimental methods. Like in the solution for converting pounds to grams, the mass conversion ensures that calculations adhere to the expected standards of precision within chemistry and other scientific fields.
Knowing how to convert mass is critical for preparing solutions, scaling reactions, or assessing quantities for trade and commerce. Careful application of mass conversion principles allows for accurate and repeatable scientific measurements, contributing to consistency in experimental methods. Like in the solution for converting pounds to grams, the mass conversion ensures that calculations adhere to the expected standards of precision within chemistry and other scientific fields.
