General orrganic and biological chemistry structures off liffe 5th by karen timberlake02 worked examples

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a Degrees Celsius is a unit of temperature.

b A gram is a unit of mass.

c A liter is a unit of volume.

d An hour is a unit of time.

Study Check 2.1

State the name and type of measurement indicated by an infant that is 32.5 cm long

Answer

A centimeter is a unit of length

On a typical day, a nurse encounters several situations involving measurement State the name and type of

measurement indicated by the units in each of the following:

a A patient has a temperature of 38.5 °C

b A physician orders 1.5 g of Cefuroxime for injection.

c A physician orders 1 L of a sodium chloride solution to be given intravenously.

d A medication is to be given to a patient every 4 h.

Sample Problem 2.1 Units of Measurement

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General, Organic, and Biological Chemistry: Structures of Life, 5/e

Karen C Timberlake

Solution

a The zero in the last decimal place following the 5 is significant The zeros preceding the 2 are not significant.

b Zeros between nonzero digits or at the end of decimal numbers are significant All the zeros in 70.040 g are

significant

c Zeros between nonzero digits are significant Zeros at the end of a large number with no decimal point are

placeholders but not significant The zero between 1 and 2 is significant, but the four zeros following the 2 are

not significant

Study Check 2.2

Identify the significant zeros in each of the following measured numbers:

a 0.04008 m b 6.00 × 103 g

Answer

a The zeros between 4 and 8 are significant The zeros preceding the first nonzero digit 4 are not significant.

b All zeros in the coefficient of a number written in scientific notation are significant.

Identify the significant zeros in each of the following measured numbers:

Sample Problem 2.2 Significant Zeros

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a To round off 35.7823 m to three significant figures, drop 823 and increase the last retained digit by 1 to give 35.8 m.

b To round off 0.002 621 7 L to three significant figures, drop 17 to give 0.002 62 L.

c To round off 3.8268 × 103 g to three significant figures, drop 68 and increase the last retained digit by 1 to give

3.83 × 103 g

Study Check 2.3

Round off each of the numbers in Sample Problem 2.3 to two significant figures

Answer

a 36 m

b 0.0026 L

c 3.8 × 103 g

Round off each of the following numbers to three significant figures:

a 35.7823 m

b 0.002 621 7 L

c 3.8268 × 103 g

Sample Problem 2.3 Rounding Off

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Karen C Timberlake

Solution

Study Check 2.4

Perform the following calculations of measured numbers and give the answers with the correct number of

significant figures:

Answer

Perform the following calculations of measured numbers Round off the calculator display or add zeros to give each answer with the correct number of significant figures

Sample Problem 2.4 Significant Figures in Multiplication and Division

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a.

b.

Study Check 2.5

Perform the following calculations and give the answers with the correct number of decimal places:

a 82.45 mg + 1.245 mg + 0.000 56 mg b. 4.259 L − 3.8 L

Answer

Perform the following calculations and round off the calculator display or add zeros to give each answer with the

correct number of decimal places:

Sample Problem 2.5 Significant Figures in Addition and Subtraction

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Karen C Timberlake

Solution

Study Check 2.6

What is the relationship between millimeters and micrometers?

Answer

1 mm = 1000 μm (mcm)

An endoscopic camera has a width of 1 mm Complete each of the following equalities involving millimeters:

Sample Problem 2.6 Prefixes and Equalities

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The equality for pints and milliliters is 1 pt = 473 mL Answers b and c are correctly written conversion factors for

the equality

Study Check 2.7

What are the two correctly written conversion factors for the equality: 1000 mm = 1 m?

Answer

Identify the correct conversion factor(s) for the equality: 1 pt of blood contains 473 mL of blood

Sample Problem 2.7 Writing Conversion Factors

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Karen C Timberlake

Sample Problem 2.8 Equalities and Conversion Factors Stated in

a Problem

Solution

a There are 40 mg of propranolol in 1 tablet.

Write the equality and conversion factors, and identify each number as exact or give the number of significant

figures for each of the following:

a The medication that Greg takes for his high blood pressure contains 40 mg of propranolol in 1 tablet.

b Cold water fish such as salmon contains 1.9% omega-3 fatty acids by mass.

c The U.S Environmental Protection Agency (EPA) has set the maximum level for mercury in tuna at 0.5 ppm.

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a Problem

Continued

b Cold water fish such as salmon contains 1.9% omega-3 fatty acids by mass.

c The EPA has set the maximum level for mercury in tuna at 0.5 ppm.

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Karen C Timberlake

a Problem

Continued

Study Check 2.8

Levsin (hyoscyamine), used to treat stomach and bladder problems, is available as drops with 0.125 mg Levsin per

1 mL of solution Write the equality and its corresponding conversion factors, and identify each number as exact

or give the number of significant figures

Answer

0.125 mg of Levsin = 1 mL of solution

The 0.125 mg is measured: It has three SFs The 1 mL is exact

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Step 1 State the given and needed quantities

Step 2 Write a plan to convert the given unit to the needed unit The conversion factor relates the given unit in

the U.S system of measurement and the needed unit in the metric system

Step 3 State the equalities and conversion factors

Greg’s doctor has ordered a PET scan of his heart In radiological imaging such as PET or CT scans, dosages of

pharmaceuticals are based on body mass If Greg weighs 144 lb, what is his body mass in kilograms?

Sample Problem 2.9 Problem Solving Using Conversion Factors

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Karen C Timberlake

Step 4 Set up the problem to cancel units and calculate the answer Write the given, 144 lb, and multiply by the

conversion factor that has the unit lb in the denominator (bottom number) to cancel out the given unit (lb) in the numerator

Look at how the units cancel The given unit lb cancels out and the needed unit kg is in the numerator The

unit you want in the final answer is the one that remains after all the other units have canceled out This is

a helpful way to check that you set up a problem properly

Continued

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The calculator display gives the numerical answer, which is adjusted to give a final answer with the proper number of significant figures (SFs)

The value of 65.5 combined with the unit, kg, gives the final answer of 65.5 kg With few exceptions, answers to numerical problems contain a number and a unit

Study Check 2.9

A total of 2500 mL of a boric acid antiseptic solution is prepared from boric acid concentrate How many quarts of

boric acid has been prepared?

Answer

2.6 qt

Continued

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Karen C Timberlake

Solution

Study Check 2.10

A newborn has a length of 450 mm In the following setup that calculates the baby’s length in inches, fill in the

missing parts of the conversion factors, show the canceled units, and give the correct answer:

Answer

A doctor’s order for 0.50 g of Keflex is available as 250-mg tablets How many tablets of Keflex are needed? In the following setup, fill in the missing parts of the conversion factors, show the canceled units, and give the correct answer:

Sample Problem 2.10 Using Two or More Conversion Factors

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Step 2 Write a plan to convert the given unit to the needed unit

Synthroid is used as a replacement or supplemental therapy for diminished thyroid function A doctor’s order

prescribes a dosage of 0.150 mg of Synthroid If tablets in stock contain 75 mcg of Synthroid, how many tablets

are required to provide the prescribed medication?

Sample Problem 2.11 Problem Solving Using Two Conversion Factors

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Karen C Timberlake

Step 4 Set up the problem to cancel units and calculate the answer The problem can be set up using the metric

factor to cancel milligrams, and then the clinical factor to obtain the number of tablets as the final unit

A bottle contains 120 mL of cough syrup If one teaspoon (5 mL) is given four times a day, how many days will

elapse before a refill is needed?

Answer

6 days

Sample Problem 2.11 Problem Solving Using Two Conversion Factors

Continued

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Step 2 Write a plan to convert the given unit to the needed unit

A person who exercises regularly has 16% body fat by mass If this person weighs 155 lb, what is the mass, in

kilograms, of body fat?

Sample Problem 2.12 Using a Percentage as a Conversion Factor

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Karen C Timberlake

Step 4 Set up the problem to cancel units and calculate the answer We set up the problem using conversion factors

to cancel each unit, starting with lb of body weight, until we obtain the final unit, kg of body fat, in the numerator

Sample Problem 2.12 Using a Percentage as a Conversion Factor

Continued

Uncooked lean ground beef can contain up to 22% fat by mass How many grams of fat would be contained in 0.25 lb

of the ground beef?

Answer

25 g of fat

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Step 2 Write a plan to calculate the needed quantity

Step 3 Write the equalities and their conversion factors including density

Ken, a 195-lb male patient, has a blood volume of 7.5 qt If the density of blood is 1.06 g/mL, what is the mass, in

grams, of Ken’s blood?

Sample Problem 2.13 Problem Solving with Density

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Karen C Timberlake

During surgery, a patient receives 3.0 pt of blood How many kilograms of blood (density = 1.06 g/mL) were needed

for the transfusion?

Answer

1.5 kg of blood

Sample Problem 2.13 Problem Solving with Density

Continued

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