Essential Ideas

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

 _{\(\begin{aligned}{\rm{density = }}\frac{{{\rm{mass}}}}{{{\rm{volume}}}}\\{\rm{d = }}\frac{{\rm{m}}}{{\rm{v}}}\end{aligned}\)}

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

Is one liter about an ounce, a pint, a quart, or a gallon?

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:

1. The length of a marathon race (26 miles 385 yards)
2. The mass of an automobile
3. The volume of a swimming pool
4. The speed of an airplane
5. The density of gold
6. The area of a football field
7. The maximum temperature at the South Pole on April 1, 1913 

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

1. The mass of the moon
2. The distance from Dallas to Oklahoma City
3. The speed of sound
4. The density of air
5. The temperature at which alcohol boils
6. The area of the state of Delaware
7. The volume of a flu shot or a measles vaccination

Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities.

a. 10³

b. 10^-2

c. 0.1

d. 10^-3

e. 1,000,000

f. 0.000001

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

1. c
2. d
3. G
4. k
5. m
6. n
7. p
8. T

A large piece of jewelry has a mass of 132.6g. A graduated cylinder initially contains 48.6 mL water. When the jewellery is submerged in the graduated cylinder, the total volume increases to 61.2 mL.

a) Determine the density of this piece of jewelry.

b) Assuming that the jewellery is made from only one substance, what substance is it likely to be? Explain.

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty: (a) the number of eggs in a basket (b) the mass of a dozen eggs (c) the number of gallons of gasoline necessary to fill an automobile gas tank (d) the number of cm in 2 m (e) the mass of a textbook (f) the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h.

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

(a) 53 cm 

(b) 2.05 × 10⁸ m 

(c) 86,002 J 

(d) 9.740 × 10⁴ m/s 

(e) 10.0613 m³ 

(f) 0.17 g/mL 

(g) 0.88400 s

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each. 

(a) 0.0055 g active ingredients 

(b) 12 tablets 

(c) 3% hydrogen peroxide 

(d) 5.5 ounces 

(e) 473 mL 

(f) 1.75% bismuth 

(g) 0.001% phosphoric acid 

(h) 99.80% inert ingredients

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 × 10^-3

(f) 0.445

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

(a) 517 

(b) 86.3 

(c) 6.382 ×10³ 

(d) 5.0008 

(e) 22.497 

(f) 0.885

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

A barrel of oil is exactly 42 gal. How many liters of oil are in a barrel?

Calculate these volumes. 

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

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

Matter is everywhere around us. Make a list by name of fifteen different kinds of matter that you encounter every day. Your list should include (and label at least one example of each) the following: a solid, a liquid, a gas, an element, a compound, a homogenous mixture, a heterogeneous mixture, and a pure substance.

Calculate these volumes. (a) What is the volume of 11.3gmgraphite, density2.25g/cm³? 

(b) What is the volume of 39.657gm bromine, density 2.928g/cm³?

Convert the temperature of scalding water, \(54{\rm{ }}^\circ C,\) into degrees Fahrenheit and kelvin.

Convert the temperature of the coldest area in a freezer, \( - 10{\rm{ }}^\circ F,\)to degrees Celsius and kelvin.

Convert the boiling temperature of liquid ammonia, \( - 28.1^\circ F,\) into degrees Celsius and kelvin.

The label on a pressurized can of spray disinfectant warns against heating the can above \(130^\circ F\)). What are the corresponding temperatures on the Celsius and kelvin temperature scales? 

The weather in Europe was unusually warm during the summer of \(1995\). The TV news reported temperatures as high as \(45{\rm{ }}^\circ C\). What was the temperature on the Fahrenheit scale?

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

(a) 628 × 342 

(b) (5.63 ×10²) × (7.4 ×10³) 

(c) 28.0/ 13.483 

(d) 8119 × 0.000023 

(e) 14.98 + 27,340 + 84.7593 

(f) 42.7 + 0.259

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

(a) 62.8 × 34 

(b) 0.147 + 0.0066 + 0.012 

(c) 38 × 95 × 1.792 

(d) 15 – 0.15 – 0.6155 

(e) 8.78 × (0.0500/ 0.478)

(f) 140 + 7.68 + 0.014 

(g) 28.7 – 0.0483 

(h) (88.5 − 87.57)/ 45.13

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) kilometers in 1 mile 

(b) liters in 1 cubic foot 

(c) grams in 1 ounce

The diameter of a red blood cell is about 3 × 10^-4 in. What is its diameter in centimeters?