Chapter 1: Essential IdeasContent check — Chemistry: Atoms First, Chapter 1: Essential Ideas

(a) To three decimal places, what is the volume of a cube (cm³) with an edge length of 0.843 cm?

(b) If the cube in part (a) is copper and has a mass of 5.34 g, what is the density of copper to two decimal places?

Following the water displacement approach, use the simulator to measure the density of the foam sample.

Round the following to the indicated number of significant figures:

(a) 0.424 (to two significant figures)

(b) 0.0038661 (to three significant figures)

(c) 421.25 (to four significant figures)

(d) 28,683.5 (to five significant figures)

(a) Add 2.334 mL and 0.31 mL.

(b) Subtract 55.8752 m from 56.533 m.

(a) Multiply 2.334 cm and 0.320 cm.

(b) Divide 55.8752 m by 56.53 s.

What is the density of a liquid with a mass of 31.1415 g and a volume of 30.13 cm³?

An irregularly shaped piece of a shiny yellowish material is weighed and then submerged in a graduated cylinder, with results as shown.

(a) Use these values to determine the density of this material.

(b) Do you have any reasonable guesses as to the identity of this material? Explain your reasoning.

Convert a volume of 9.345 qt to liters.

What is the volume in liters of 1.000 oz, given that 1 L = 1.0567 qt and 1 qt = 32 oz (exactly)?

A Toyota Prius Hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km (two significant digits).

(a) What (average) fuel economy, in miles per gallon, did the Prius get during this trip?

(b) If gasoline costs $3.90 per gallon, what was the fuel cost for this trip?

Convert 80.92 °C to K and °F.

Convert 50 °F to °C and K.

Explain how you could experimentally determine whether the outside temperature is higher or lower than 0 °C (32 °F) without using a thermometer.

Identify each of the following statements as being most similar to a hypothesis, a law, or a theory. Explain your reasoning.

(a) The pressure of a sample of gas is directly proportional to the temperature of the gas.

(b) Matter consists of tiny particles that can combine in specific ratios to form substances with specific properties.

(c) At a higher temperature, solids (such as salt or sugar) will dissolve better in water.

Identify each of the underlined items as a part of either the macroscopic domain, the microscopic domain, or the symbolic domain of chemistry. For those in the symbolic domain, indicate whether they are symbols for a macroscopic or a microscopic feature.

(a) A certain molecule contains one H atom and one Cl atom.

(b) Copper wire has a density of about 8 g/cm³.

(c) The bottle contains 15 grams of Ni powder.

(d) A sulfur molecule is composed of eight sulfur atoms.

The amount of heat required to melt 2 lbs of ice is twice the amount of heat required to melt 1 lb of ice. Is this observation a macroscopic or microscopic description of chemical behavior? Explain your answer.

What properties distinguish solids from liquids? Liquids from gases? Solids from gases?

How does a homogeneous mixture differ from a pure substance? How are they similar?

How do molecules of elements and molecules of compounds differ? In what ways are they similar?

Many of the items you purchase are mixtures of pure compounds. Select three of these commercial products and prepare a list of the ingredients that are pure compounds.

Classify each of the following as an element, a compound, or a mixture:

(a) iron

(b) oxygen

(c) mercury oxide

(d) pancake syrup

(e) carbon dioxide

(f) a substance composed of molecules each of which contains one hydrogen atom and one chlorine atom

(g) baking soda

(h) baking powder

How are the molecules in oxygen gas, the molecules in hydrogen gas, and water molecules similar? How do they differ?

Prepare a list of the principal chemicals consumed and produced during the operation of an automobile.

When elemental iron corrodes it combines with oxygen in the air to ultimately form red brown iron(III) oxide called rust. (a) If a shiny iron nail with an initial mass of 23.2 g is weighed after being coated in a layer of rust, would you expect the mass to have increased, decreased, or remained the same? Explain. (b) If the mass of the iron nail increases to 24.1 g, what mass of oxygen combined with the iron?

Yeast converts glucose to ethanol and carbon dioxide during anaerobic fermentation as depicted in the simple chemical equation here:

$$\text{glucose}⟶\text{ethanol}+\text{carbon dioxide}$$

(a) If 200.0 g of glucose is fully converted, what will be the total mass of ethanol and carbon dioxide produced?

(b) If the fermentation is carried out in an open container, would you expect the mass of the container and contents after fermentation to be less than, greater than, or the same as the mass of the container and contents before fermentation? Explain.

(c) If 97.7 g of carbon dioxide is produced, what mass of ethanol is produced?

Classify each of the following changes as physical or chemical:

(a) condensation of steam

(b) burning of gasoline

(c) souring of milk

(d) dissolving of sugar in water

(e) melting of gold

The volume of a sample of oxygen gas changed from 10 mL to 11 mL as the temperature changed. Is this a chemical or physical change?

Explain the difference between extensive properties and intensive properties.

The density (d) of a substance is an intensive property that is defined as the ratio of its mass (m) to its volume (V).

$$\text{density}=\frac{\text{mass}}{\text{volume}}\text{d}=\frac{\text{m}}{\text{V}}$$

Considering that mass and volume are both extensive properties, explain why their ratio, density, is intensive.

Is a meter about an inch, a foot, a yard, or a mile?

Indicate the SI base units or derived units that are appropriate for the following measurements:

(a) the mass of the moon

(b) the distance from Dallas to Oklahoma City

(c) the speed of sound

(d) the density of air

(e) the temperature at which alcohol boils

(f) the area of the state of Delaware

(g) the volume of a flu shot or a measles vaccination

Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units.

(a) c

(b) d

(c) G

(d) k

(e) m

(f) n

(g) p

(h) T

Visit this density simulation and click the "turn fluid into water" button to adjust the density of liquid in the beaker to 1.00 g/mL.

(a) Use the water displacement approach to measure the mass and volume of the unknown material (select the green block with question marks).

(b) Use the measured mass and volume data from step (a) to calculate the density of the unknown material.

(c) Assuming this material is a widely available copper-containing gemstone, what is its likely identity? Compare the measured density to the values tabulated at this gemstone density guide.

(d) How are mass and density related for blocks of the same volume?

Visit this density simulation and click the “turn fluid into water” button to adjust the density of liquid in the beaker to 1.00 g/mL. Change the block material to foam, and then wait patiently until the foam block stops bobbing up and down in the water.

(a) The foam block should be floating on the surface of the water (that is, only partially submerged). What is the volume of water displaced?
(b) Use the water volume from part (a) and the density of water (1.00 g/mL) to calculate the mass of water displaced.
(c) Remove and weigh the foam block. How does the block’s mass compare to the mass of displaced water from part (b)?

Express each of the following numbers in exponential notation with correct significant figures:

(a) 704

(b) 0.03344

(c) 547.9

(d) 22086

(e) 1000.00

(f) 0.0000000651

(g) 0.007157

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

(a) the number of seconds in an hour

(b) the number of pages in this book

(c) the number of grams in your weight

(d) the number of grams in 3 kilograms

(e) the volume of water you drink in one day

(f) the distance from San Francisco to Kansas City

How many significant figures are contained in each of the following measurements?

(a) 53 cm

(b) 2.05 $\times$ 10⁸ m

(c) 86,002 J

(d) 9.740 $\times$ 10⁴ m/s

(e) 10.0613 m³

(f) 0.17 g/mL

(g) 0.88400 s

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

(a) 0.436

(b) 9.000

(c) 27.2

(d) 135

(e) 1.497 $\times$ 10⁻³

(f) 0.445

Perform the following calculations and report each answer with the correct number of significant figures.

(a) 628 $\times$ 342

(b) (5.63 $\times$ 10²) $\times$ (7.4 $\times$ 10³)

(c) $\frac{28.0}{13.483}$

(d) 8119 $\times$ 0.000023

(e) 14.98 + 27,340 + 84.7593

(f) 42.7 + 0.259

Consider the results of the archery contest shown in this figure.

(a) Which archer is most precise?

(b) Which archer is most accurate?

(c) Who is both least precise and least accurate?

Write conversion factors (as ratios) for the number of:

(a) yards in 1 meter

(b) liters in 1 liquid quart

(c) pounds in 1 kilogram

The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?

How many milliliters of a soft drink are contained in a 12.0-oz can?

The diameter of a red blood cell is about 3 $\times$ 10⁻⁴ in. What is its diameter in centimeters?

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

Many medical laboratory tests are run using 5.0 μL blood serum. What is this volume in milliliters?

Use scientific (exponential) notation to express the following quantities in terms of the SI base units in Table 1.2:

(a) 0.13 g

(b) 232 Gg

(c) 5.23 pm

(d) 86.3 mg

(e) 37.6 cm

(f) 54 μm

(g) 1 Ts

(h) 27 ps

(i) 0.15 mK

Gasoline is sold by the liter in many countries. How many liters are required to fill a 12.0-gal gas tank?

A long ton is defined as exactly 2240 lb. What is this mass in kilograms?

Make the conversion indicated in each of the following:

(a) the length of a soccer field, 120 m (three significant figures), to feet

(b) the height of Mt. Kilimanjaro, at 19,565 ft, the highest mountain in Africa, to kilometers

(c) the area of an 8.5- × 11-inch sheet of paper in cm²

(d) the displacement volume of an automobile engine, 161 in.³, to liters

(e) the estimated mass of the atmosphere, 5.6 × 10¹⁵ tons, to kilograms

(f) the mass of a bushel of rye, 32.0 lb, to kilograms

(g) the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)

A chemist’s 50-Trillion Angstrom Run (see Exercise 1.78) would be an archeologist’s 10,900 cubit run. How long is one cubit in meters and in feet? (1 Å = 1 $\times$ 10⁻⁸ cm)

As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?

A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds?

Solve these problems about lumber dimensions.

(a) To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness $\times$ width $\times$ length dimensions are 1.50 in. $\times$ 3.50 in. $\times$ 8.00 ft in the US. What are the dimensions in cm $\times$ cm $\times$ m?

(b) This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters?

Calculate the density of aluminum if 27.6 cm³ has a mass of 74.6 g.

Calculate these masses.

(a) What is the mass of 6.00 cm³ of mercury, density = 13.5939 g/cm³?

(b) What is the mass of 25.0 mL octane, density = 0.702 g/cm³?

Calculate these volumes.

(a) What is the volume of 25 g iodine, density = 4.93 g/cm³?

(b) What is the volume of 3.28 g gaseous hydrogen, density = 0.089 g/L?

Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin.

Convert the temperature of the coldest area in a freezer, −10 °F, to degrees Celsius and kelvin.

Convert the boiling temperature of liquid ammonia, −28.1 °F, into degrees Celsius and kelvin.

The weather in Europe was unusually warm during the summer of 1995. The TV news reported temperatures as high as 45 °C. What was the temperature on the Fahrenheit scale?