Chemistry
Chemistry
4th Edition
ISBN: 9780078021527
Author: Julia Burdge
Publisher: McGraw-Hill Education
Question
Book Icon
Chapter 1, Problem 66QP
Interpretation Introduction

Interpretation:

The conversions are to be carried out by dimensional analysis for given units of measurement.

Concept introduction:

Dimensional analysis is a way to convert the units of measurement. In order to convert one unit to another, one needs to know the relationship between those units. These relationships are called conversion factors. Dimensional analysis is used to set up and solve a unit conversion problem using conversion factors.

Conversion factor is a fraction obtained from a relationship between the units. It is written as a ratio, and can be inverted to give two conversion factors for every relationship.

1 yd = 36 in, to convert yd to in, the conversion factor is 36 in1 yd.

1 in = 2.54 cm, to convert in to cm, the conversion factor is 2.54 cm1 in.

1 in = 2.54 cm, to convert cm to in, the conversion factor is 1 in2.54 cm.

1 ft=12 in, to convert in to ft, the conversion factor is 1 ft12 in.

1 hr=60 min, to convert hours to minutes, the conversion factor is 60 min1 hr.

1 min=60 s, to convert minute to second, the conversion factor is 60s1min.

1 mile=1609 m, to convert meter to miles, the conversion factor is 1 mile1609 m.

Expert Solution & Answer
Check Mark

Answer to Problem 66QP

Solution:

a)

2.96×103cm

b)

9.8×108 ft/s

c)

8.35×1012 miles

Explanation of Solution

a)32.4 yd to centimeters

The conversion factors are as follows:

1 yd = 36 in

1 in = 2.54 cm

Now, set up the unit conversion calculation using the appropriate conversion factors.

The conversion is as follows:

(32.4 yd × 36 in1 yd×2.54 cm1 in)=2.96×103 cm.

The units in the conversion factor must cancel to give the correct unit for the answer.

Hence,

32.4 yd= 2.96×103 cm.

b) 3.0×1010 cm/s to ft/s

The conversion factors are as follows:

1 in=2.54 cm.

1 ft=12 in.

Now, set up the unit conversion calculation using the appropriate conversion factors.

The conversion is as follows:

(3.0×1010cm/s × 1 in2.54 cm × 1 ft12 in)=9.8×108 ft/s

The units in the conversion factor must cancel to give the correct unit for the answer.

Hence,

3.0×1010 cm/s=9.8×108 ft/s.

c) 1.42 light years to miles

First, convert the speed of light in m/s to mph.

The conversion is as follows:

(3.00×108 m/s × 1 mi1609 m × 60 smin × 60 min1 h)=6.7122×108 mph

The number of hours in a year is calculated as follows:

(365 days)(24 h )=8760 h

The miles in one light year is calculated as follows:

1 light year=(6.7122×108 mph)(8760 h)=5.8799×1012 mi

The final conversion is as follows:

(1.42light year)(5.8799×1012 miles1light year)=8.35×1012 miles

Hence,

1.42 light years=8.35×1012 miles.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Carry out the following conversions: (a) 32.4 yd to centimeters, (b) 3.0 × 1010 cm/s to ft/s, (c) 1.42 light-years to miles (a light-year is an astronomical measure of distance—the distance traveled by light in a year, or365 days; the speed of light is 3.00 × 108m/s).
Carry out the following conversions: (a) 1.42 lightyears to miles (a light-year is an astronomical measure of distance—the distance traveled by light in a year, or 365 days; the speed of light is 3.00x10^8 m/s), (b) 32.4 yd to centimeters, (c) 3.0 3x10^10 cm/s to ft/s.
b) One sphere has a radius of 5.10 cm; another has a radius of 5.00 cm. What is the difference in volume (in cubic centimeters) between the two spheres? Give the answer to the correct number of significant figures. The volume of a sphere is (4/3)TTr³, where TT= 3.1416 and r is the radius.

Chapter 1 Solutions

Chemistry

Ch. 1.3 - What is the density of an object that has a volume...Ch. 1.3 - A sample of water is heated from room temperature...Ch. 1.3 - Prob. 4CPCh. 1.4 - Prob. 1PPACh. 1.4 - Prob. 1PPBCh. 1.4 - Practice Problem CONCEPTUALIZE The diagram on the...Ch. 1.4 - Prob. 1CPCh. 1.4 - Prob. 2CPCh. 1.5 - Practice Problem ATTEMPT Determine the number of...Ch. 1.5 - Practice ProblemBUILD For each of the following...Ch. 1.5 - Prob. 1PPCCh. 1.5 - 1.5.1 What volume of water does the graduated...Ch. 1.5 - Which of the following is the sum of the following...Ch. 1.5 - The true dependence of y on x is represented by...Ch. 1.5 - What is the result of the following calculation to...Ch. 1.6 - Practice ProblemATTEMPT Perform the following...Ch. 1.6 - Practice ProblemBUILD Perform the following...Ch. 1.6 - Practice Problem CONCEPTUALIZE A citrus dealer in...Ch. 1.6 - The density of lithium metal is 535 kg/m 3 . What...Ch. 1.6 - 1.6.2 Convert to liters. Ch. 1.6 - 1.6.3 What is the volume of a 5.75-g object that...Ch. 1.6 - How many cubic centimeters are there in a cubic...Ch. 1.7 - Practice Problem ATTEMPT An empty container with...Ch. 1.7 - Practice Problem BUILD Another empty container...Ch. 1.7 - Practice ProblemCONCEPTUALIZE Several pieces of...Ch. 1.8 - Practice ProblemATTEMPT The American Heart...Ch. 1.8 - Practice ProblemBUILD An object has a mass of...Ch. 1.8 - Practice ProblemCONCEPTUALIZE The diagram contains...Ch. 1.9 - Practice ProblemATTEMPT The density of silver is...Ch. 1.9 - Practice ProblemBUILD The density of mercury is 13...Ch. 1.9 - Practice ProblemCONCEPTUALIZE Each diagram [ ( i )...Ch. 1 - 1.1 Given that the density of gold is , calculate...Ch. 1 - Prob. 2KSPCh. 1 - Determine the density of the following object in...Ch. 1 - A 28-kg child can consume a maximum of 23...Ch. 1 - Define the terms chemistry and matter.Ch. 1 - 1.2 Explain what is meant by the scientific...Ch. 1 - what is the difference between a hypothesis and a...Ch. 1 - Classify each of the following statements as a...Ch. 1 - Classify each of the following statements as a...Ch. 1 - Identify the elements present in the following...Ch. 1 - Identify the elements present in the following...Ch. 1 - Give an example for each of the following terms:...Ch. 1 - 1.9 Give an example of a homogeneous mixture and...Ch. 1 - Give an example of an element and a compound. How...Ch. 1 - What is the number of known elements?Ch. 1 - Give the names of the elements represented by the...Ch. 1 - 1.13 Give the chemical symbols for the following...Ch. 1 - Classify each of the following substances as an...Ch. 1 - Classify each of the following as an element, a...Ch. 1 - Identify each of the diagrams shown here as a...Ch. 1 - Identify each of the diagrams shown here as an...Ch. 1 - Name the SI base units that are important in...Ch. 1 - 1.19 Write the numbers represented by the...Ch. 1 - 1.20 What units do chemists normally use for the...Ch. 1 - 1.21 What is the difference between mass and...Ch. 1 - 1.22 Describe the three temperature scales used in...Ch. 1 - Bromine is a reddish-brown liquid. Calculate its...Ch. 1 - 1.24 The density of ethanol, a colorless liquid...Ch. 1 - Prob. 25QPCh. 1 - Prob. 26QPCh. 1 - 1.27 The density of water at is . What is the...Ch. 1 - The density of platinum (Pt) is 21 .5 g/cm 3 at...Ch. 1 - Convert the following temperatures to kelvin: (a)...Ch. 1 - Convert the following temperatures to degrees...Ch. 1 - 1.31 Which of the following illustrations best...Ch. 1 - The diagram shows balls of aluminum foil dropped...Ch. 1 - What is the difference between qualitative data...Ch. 1 - Using examples, explain the difference between a...Ch. 1 - How does an intensive property differ from an...Ch. 1 - Determine which of the following properties are...Ch. 1 - Classify the following as qualitative or...Ch. 1 - 1.38 Determine whether the following statements...Ch. 1 - Determine whether each of the following describes...Ch. 1 - 1.40 A student pours 44.3 g of water at into a...Ch. 1 - Prob. 41QPCh. 1 - Comment on whether each of the following...Ch. 1 - What is the advantage of using scientific notation...Ch. 1 - Define significant figure. Discuss the importance...Ch. 1 - Distinguish between the terms accuracy and...Ch. 1 - 1.46 Express the following numbers in scientific...Ch. 1 - Express the following as decimals: (a) 1.52 × 10 −...Ch. 1 - Express the answers to the following calculations...Ch. 1 - 1.49 Express the answers to the following...Ch. 1 - 1.50 Determine the number of significant figures...Ch. 1 - Determine the number of significant figures in...Ch. 1 - Prob. 52QPCh. 1 - Carry out the following operations as if they were...Ch. 1 - Three students ( A, B, and C ) are asked to...Ch. 1 - Three apprentice tailors ( X, Y, and Z ) are...Ch. 1 - Carry out the following conversions: (a) 22.6 m to...Ch. 1 - Carry out the following conversions: (a) 242 lb to...Ch. 1 - The average speed of helium at 25°C is 1255 m/s ....Ch. 1 - Prob. 59QPCh. 1 - Prob. 60QPCh. 1 - Prob. 61QPCh. 1 - 1.62 A 6.0-ft person weighs 168 lb. Express this...Ch. 1 - The highest speed limit in the United States is 85...Ch. 1 - For a fighter jet to take off from the deck of an...Ch. 1 - Prob. 65QPCh. 1 - Prob. 66QPCh. 1 - Carry out the following conversions: (a) 185 nm to...Ch. 1 - 1.68 Aluminum is a lightweight metal used in...Ch. 1 - Prob. 69QPCh. 1 - (a) Carbon monoxide ( CO ) is a poisonous gas...Ch. 1 - Prob. 71QPCh. 1 - A human brain weighs about 1 kg and contains about...Ch. 1 - Using the appropriate number of significant...Ch. 1 - 1.74 A piece of metal with a mass of 13.2 g was...Ch. 1 - 1.75 Which of the following statements describe...Ch. 1 - 1.76 In determining the density of a rectangular...Ch. 1 - Calculate the mass of each of the following: (a) a...Ch. 1 - 1.78 A cylindrical glass tube 12.7 cm in length is...Ch. 1 - The following procedure was used to determine the...Ch. 1 - 1.80 The speed of sound in air at room temperature...Ch. 1 - A piece of silver ( Ag ) metal weighing 194.3 g is...Ch. 1 - The experiment described in Problem 1.81 is a...Ch. 1 - A lead sphere has a mass of 1 .20 × 10 4 g . and...Ch. 1 - Lithium is the least dense metal known ( density =...Ch. 1 - At what temperature does the numerical reading on...Ch. 1 - Prob. 86APCh. 1 - Prob. 87APCh. 1 - A sheet of aluminum ( A1 ) foil hat a total area...Ch. 1 - Prob. 89APCh. 1 - 1.90 The surface area and average depth of the...Ch. 1 - The unit "troy ounce" is often used for precious...Ch. 1 - Prob. 92APCh. 1 - Calculate the percent error for the following...Ch. 1 - In water conservation, chemists spread a thin film...Ch. 1 - 1.95 You are given a liquid. Briefly describe the...Ch. 1 - A gas company in Massachusetts charges $1 .30 for...Ch. 1 - Prob. 97APCh. 1 - 1.98 A bank teller is asked to assemble sets of...Ch. 1 - The men's world record for running a mile outdoors...Ch. 1 - 1.100 Venus, the second closest planet to the sun....Ch. 1 - Comment on whether each of the following is a...Ch. 1 - It has been estimated that 8.0 × 10 4 tons of gold...Ch. 1 - Prob. 103APCh. 1 - 1.104 Measurements show that 1.0 g of iron ...Ch. 1 - 1.105 The thin outer layer of Earth, called the...Ch. 1 - 1.106 The radius of a copper atom is roughly ....Ch. 1 - A graduated cylinder is filled to the 40.00-mL...Ch. 1 - A chemist mixes two liquids A and B to form a...Ch. 1 - A chemist in the nineteenth century prepared an...Ch. 1 - Chlorine is used to disinfect swimming pools. The...Ch. 1 - Prob. 111APCh. 1 - Prob. 112APCh. 1 - Chalcopyrite, the principal one of copper ( Cu ) ,...Ch. 1 - 1.114 Vanillin (used to flavor vanilla ice cream...Ch. 1 - One gallon of gasoline in an automobile’s engine...Ch. 1 - 1.116 Magnesium (Mg) is a valuable metal used in...Ch. 1 - Prob. 117APCh. 1 - The natural abundances of elements in the human...Ch. 1 - A resting adult requires about 240 mL of pure...Ch. 1 - 1.120 (a) Referring to Problem 1.119. calculate...Ch. 1 - The medicinal thermometer commonly used in homes...Ch. 1 - TUMS is a popular remedy for acid indigestion. A...Ch. 1 - Prob. 123APCh. 1 - English writer and essayist Lady Mary Wortley...Ch. 1 - English writer and essayist Lady Mary Wortley...Ch. 1 - English writer and essayist Lady Mary Wortley...Ch. 1 - English writer and essayist Lady Mary Wortley...
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning