CH. 0: MEASUREMENT AND CALCULATIONS IN...

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CHEMISTRY - ZUMDAHL 2E

CH. 0: MEASUREMENT AND CALCULATIONS IN CHEMISTRY

CONCEPT: SCIENTIFIC NOTATION

We use scientific notation to turn small or large, inconvenient numbers into manageable ones.

6.88 x 10-12

The first number 6.88 is called the __________________________.

It must be greater than or equal to 1 and less than 10.

The second number is known as the ______________________.

It must always be 10 in scientific notation.

In the number 6.88 x 10-12, the number -12 is referred to as the ____________________.

EXAMPLE 1: Convert the following numbers into scientific notation

a. 377,000 b. 0.000101

c. 707.82 d. 161.00 x 107

e. 0.0628 x 10-9



CONCEPT: ERROR

Even though we try to be as accurate as possible, there is always some level of uncertainty called ____________________.

When we investigate the quality of an experimental decision or calculation we take into account two major principles:

• __________________ deals with the reproducibility of our calculations.

• __________________ deals with how close our measured calculation is to the “actual” value.

EXAMPLE 1: Which of the 4 following images is not precise and not accurate?

PRACTICE: A student must measure the weight of a sodium bicarbonate compound, NaHCO3, and obtains the following measurements: 23.12 g, 23.08 g and 23.17g. If the true weight of the compound is 18.01 g what can be said about the student’s results?

a. They are accurate and precise. b. They are accurate, but not precise. c. They are neither accurate or precise. d. They are not accurate, but precise.



CONCEPT: EVALUATING YOUR MEAN VALUE

The ____________________________ measures how close data results are in relation to the mean, or average, value.

• To check if the results are close to the “true” value we can merely look, but sometimes determining their accuracy may require more work.

Σ(x1 − x )2

n−1

x =

x =

n =



CONCEPT: METRIC PREFIXES

pico nano micro milli centi deci 0 deca hecto kilo mega giga tera

(p) (n) (µ) (m) (c) (d) (da) (h) (k) (M) (G) (T)

10-12 10-9 10-6 10-3 10-2 10-1 100 101 102 103 106 109 1012



CONCEPT: SIGNIFICANT FIGURES Significant figures are necessary to communicate the level of accuracy with which values are recorded. It can be easy if you remember these 2 rules.

1. If your number has a decimal point move from ______________________________. o Start counting once you get to your first non-zero number and keep counting until you get to the end.

2. If your number has NO decimal point move from ______________________________.

o Start counting once you get to your first non-zero number and keep counting until you get to the end.

EXAMPLE 1: How many sig figs does each number contain?

(1) 0.0000185 m (2) 749 mol (3) 17.3 x 103 mL (4) 100. min (5) 0.0010050 kg (6) 1560 mol

EXAMPLE 2: Read the length of the metal bar to the correct number of significant figures.

a) 15 cm b) 15.000 cm c) 20 cm d) 15.0 cm e) 15.00 cm



CONCEPT: CALCULATIONS & SIGNIFICANT FIGURES

• Multiplication/Division: Measurement with least _______________________________ determines final answer.

• Addition/Subtraction: Measurement with least _______________________________ determines final answer. EXAMPLE 1: Perform the following calculation to the right number of sig figs:

(3.16) x (0.003027) x (5.7 x 10-3) EXAMPLE 2: Perform the following calculation to the right number of sig figs:

2.628 x 106

6.281 x 104

+ 0.827 x 107

EXAMPLE 3: Perform the following calculation to the right number of sig figs:

(42.00 – 40.915) • (25.739 – 25.729) (11.50 • 1.001) + (0.00710 • 700.)



CONCEPT: TEMPERATURE

Temperature is a measure of thermal energy in a substance, which is __________________ on the amount of matter.

• This is an example of ___________________ property.

• _________________ , _________________ , ______________ , ________________ , ______________ .

Heat is a form of thermal energy, which is __________________ on the amount of matter.

• This is an example of ___________________ property.

• _________________ , _________________ , ______________ .

EXAMPLE 1: Which of the following has the greatest amount of heat?

30 g H2O at 50oC 300 g H2O at 50oC 30 g H2O at 100oC Temperature Conversions

Temperature conversions are easy, as long as you know how to solve for x.

• You only need to know 2 equations to convert from the 3 different units of temperature:

K = 273.15 + oC

oF = 1.8 (oC) + 32

EXAMPLE 2: Convert the following units of temperature

a. -115°C into Fahrenheit b. 73.23 K into Fahrenheit



CONCEPT: MIXTURES

Most matter consists of mixtures of pure substances.

• __________________________ mixtures have no distinguishable parts.

• _____________________________ mixtures have some distinguishable parts.

Changes of Matter

• ______________________ changes are changes in the form of the substance, but not in its chemical composition.

• ______________________ changes create new substances with different properties and different chemical

compositions.

EXAMPLE 1: Which of the following represents a physical change?

a. Alkanes burn spontaneously.

b. The sublimation of CO2.

c. 2 H2 (g) + O2 (g) 2H2O (g)

d. The rusting of a car.



CONCEPT: CONVERSIONS

Length 1 km = 0.6214 miles 1 m = 1.094 yards 1 in = 2.54 cm 1 mile = 5280 ft

Volume 1 gallon = 3.785 L 1 L = dm3 1 mL = 1 cm3 1 L = 1.057 qt

Mass 1 kg = 2.205 lbs 1 lb = 454 g 1 oz = 28.35 g

EXAMPLE 1: Every Saturday morning Gregor has to travel from Main Campus to his parents’ home. If his car gets 58.5 km/L how many L will his car need to travel the 19.3 miles? EXAMPLE 2: A backyard swimming pool holds 315 cubic yards (yd3) of water. What is the mass of the water in pounds? PRACTICE: An intravenous bag delivers medication to a patient at a rate of 2.75 drops a second. If a drop weighs 42 mg, how many grams of solution are delivered in 7.0 hours?



CONCEPT: DIMENSIONAL ANALYSIS We use dimensional analysis as a fail proof process to convert from one unit to another.

- Design the problems to ______________ with your known, and to _____________ with the unit of your unknown. - Be sure ALL of your units cancel out! Just follow the units.

EXAMPLE 1: Natty Light contains 4.2% alcohol. Steve from Kappa Epsilon Gamma, KEG for short, wants to get tanked tonight, and he is aiming to down at least 175 ml of alcohol in one night. If each can of Natty light contains 355 mL of beer, how many cans of Natty Light must Steve consume at minimum to reach his goal? EXAMPLE 2: A Volkswagen diesel engine consumes diesel at a rate of 25.83 L per hour. If the density of the diesel is 0.850

g/mL, what is the mass (in mg) of diesel needed to drive for a continuous 8.5 hours?

PRACTICE: An acetaminophen suspension for toddlers contains 95 mg/0.85 mL suspension. The recommended dose is 22 mg/kg body weight. How many liters of this suspension should be given to a toddler weighing 30.5 lbs?



CONCEPT: DENSITY

We use density to understand the relationship between ______________ and ______________.

• We can use it within dimensional analysis to go from one unit to the other or vice versa.

Density =

EXAMPLE 1: If the density of an unknown metal is 21.4 g/cm3, express its density in lb/ft3. Remember that 1 in = 2.54 cm.

EXAMPLE 2: A piece of unknown metal weighs approximately 0.45 lbs. When a scientist places it in a glass beaker the water level increases from 1.85 L to 2.13 L. What is the density of the palladium metal in g/mL?

PRACTICE: The U.S. Environmental Protection Agency sets the maximum safe level of lead in blood at 24 µg per dL of blood. The average person has 60 mL of blood per kilogram of body weight. For a 63.7-kg (140.459 lb) person, what is the total maximum safe content of lead in blood?



8. The barium content of a metal ore was analyzed several times by a percent composition process.

Method

Barium (weight %)

1

0.012

0.016

0.010

0.012

a) Calculate the mean, median and mode. b) Calculate the standard deviation.



13. Determine which of the following represents a physical change and a chemical change.

a)

b)

c)



14. Answer each of the following questions based on the images provided below.

a) Which of the following images represents an elemental gas? b) Which of the following images represents a heterogeneous mixture? c) Which of the following images represents a liquid?



15. Which of the following represents a physical property? a) Mercury is a liquid at room temperature.

b) Alkanes burn spontaneously.

c) CO2 (s) CO2 (g)

d) 2 H2 (g) + O2 (g) 2 H2O (g)

e) The rusting of a car.



18. A cigarette lighter contains the substance butane, C4H10, with the given properties. a) The lighter contains 10 g of butane b) the density of butane is 0.57 g/cm3 c) The freezing point of the butane is -138oC d) Butane is combustible in air. Which of the following features is a chemical change? Which of the following properties are intensive properties?



19. Which of the following properties about an unknown metal represent chemical properties? I. It has a bluish-green color. II. Upon exposure to air the metal experiences corrosion. III. It has a density of 4.36 g/cm3. IV. It has a boiling point of 522oC. V. It conducts electricity.

a. IV b. V c. I, II, III d. II e. IV and V



25. An empty flask has a volume of 250 mL. When water is placed inside the flask (d = 0.9983 g/mL) the volume is 124.3 mL. What is the mass (in grams) of the water inside the flask?



26. If a statue at an art gallery is covered in 279 kg of copper. If the copper on the statue has a thickness of 0.0055 cm,

what surface area is covered (in square meters)? Copper has a density of 8.96 g/cm3.



30. A Volkswagen diesel engine consumes diesel at a rate of 20.17 L per hour. If the density of the diesel is 0.850

g/mL. What is the mass (in mg) of diesel needed to drive for a continuous 4.3 hours?



32. If the charge and mass of one proton is 1.60218 x 10-19 C and 1.673 x 10-30 g respectively, what is the charge of

378 kg of protons.



32. A cylindrical tube has a length that is 15.2 cm and is filled with bromine liquid. If the mass of the bromine is 112.3 g and has a density of 25.3 g/mL. What is the inner diameter of the glass tube? ( V = π• r2 •h )



33. A large body of water contaminated with lead has an average depth of 750 m, a total area of 1.25 x 105 km2, and

an average of 5.8 x 10-12 g/L of dissolved lead. How many milligrams of lead are in this large body of water?



34. Calculate the mass (in grams) of a golden sphere with a diameter of 30.0 mm. The density of gold is 19.3 g/cm3.

(Vsphere = π ! r3).



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