Chapter 1: Matter, Measurements, and Calculations
A student is saving money to buy a computer that will cost a total of $1,200. The student has saved $988. What percentage of the purchase price has been saved?
$988. x 100% / $1,200 = 82.3%
Joule
(J), pronounced "jewl", is the metric system unit of energy
Do the following calculations, and round the answer to the correct number of significant figures: (a) (0.0019)(21.39) (b) 8.321 / 4.1 (c) (0.0911)(3.22) / 1.379
(a) 0.040641 = answer will need to be rounded to 2 significant figures to match 0.0019, move the decimal two places to the right and increase the last significant figure by 1 = 4.1 x 10-2 (b) 2.02951219512 = answer will need to be rounded to 2 significant figures to match 4.1 = 2.0 (c) 0.293342 / 1.379 = 0.21272 = answer will need to be rounded to 3 significant figures to match 0.0911 and 3.22, move the decimal 1 place to the right and increase the last significant figure by 1 = 2.13 x 10-1
Do the following additions and subtractions, and round the answers to the correct number of significant figures: (a) 8.01 + 3.2 (b) 3,000 + 20.3 + 0.009 (c) 4.33 - 3.12 (d) 6.023 - 2.42
(a) 11.21 - answer will need to be rounded to have 1 place to the right of the decimal to match 3.2 = 11.2 (b) 3020.309 - answer will have to be rounded to have no place to the right of the decimal to match 3,000 = 3020 (c) 1.21 - answer will be rounded to have two places to the right of the decimal to match both 4.33 and 3.12 = 1.21 (d) 3.603 - answer will be rounded to have two places to the right of the decimal to match 2.42 = 3.60
Perform the following operation, and express the result in the correct scientific notation: (a) (2.4 x 103)(1.5 x 104) (b) 3.5 x 102)(2.0 x 10-3) (c) 6.3 x 105 / 2.1 x 103 (d) 4.4 x 10-2 / 8.8 x 10-3
(a) 3.6 x 107 (b) 7.0 x 10-1 (c) 3.0 x 102 (d) .50 x 101 = 5.0 x 100, or 5.0
Some of the following numbers are written using scientific notation, and some are not. In each case, indicate which numbers are written in scientific notation and rewrite the number using the notation in which it is not written. (a) 5.88 x 102 = YES (b) 0.000439 = NO (c) 3.915 x 10-4 = YES (d) 9870 = NO (e) 36.77 = NO (f) 0.102 = NO
(a) 5.88 x 102 = 588 (b) 0.000439 = 4.39 x 10-4 (c) 3.915 x 10-4 = 0.0003915 (d) 9870 = 9.870 x 103 (e) 36.77 = 3.677 x 101 (f) 0.102 = 1.02 x 10-1
Use scientific notation to express each of the following measurements using the correct number of significant figures: (a) 101 m (b) 1,200 g (c) 0.00230 kg (d) 1296°C (e) 21.65 mL (f) 0.015 km
(a) All the numbers are significant, 3 significant figures, 1.01 x 102 m (b) The trailing zeros are significant, 4 significant figures, 1.200 x 103 g (c) The leading zeros are not significant, 3 significant figures, 2.30 x 10-3 kg (d) All the numbers are significant, 4 significant figures, 1.296 x 103 °C (e) All the numbers are significant, 4 significant figures, 2.165 x 101 mL (f) The leading zeros are not significant, 2 significant figures, 1.5 x 10-2 km
Determine the number of significant figures in each of the following measurements: (a) 24.6°C (b) 0.036 g (c) 15.0 mL (d) 0.0020 m
(a) All the numbers are significant, 3 significant figures, 2.46 x 101 °C (b) The leading zeros are not significant, 2 significant figures, 3.6 x 10-2 g (c) The trailing zero is significant, 3 significant figures, 15.0 x 101 mL (d) The leading zeros are not significant, but the trailing zero is, 2 significant figures, 2.0 x 10-3 m
Classify each of the following changes as physical or chemical: (a) Milk sours = chemical (b) A wet handkerchief dries = physical (c) Fruit ripens = chemical (d) A stick of dynamite explodes = chemical (e) Air is compressed into a steel container = physical (f) Water boils = physical
(a) Changes in taste and odor indicate that new substances formed. (b) The handkerchief doesn't change, and the evaporated water is still water. (c) The changes in color and taste indicate that new substances formed. (d) The gases and smoke released indicate that new substances formed. (e) The air is still air, as indicated by appearance, odor, and so on. (f) On being condensed, the steam forms water, which is the same substance present before the change.
Determine which of the following numbers are written correctly using scientific notation. For those that are not, rewrite correctly. (a) 6.25 x 104 (b) 0.0098 (c) 0.0041 x 10-3 (d) 7.85 x 102
(a) Incorrect - the decimal is not in standard position. Move the decimal one place to the left and increase the exponent by 1 to account for moving the decimal: 6.25 x 105 (b) Incorrect - The decimal is not in standard position, and no exponent is used. Move the decimal three places to the right and use -3 for the exponent to account for moving the decimal: 9.8 x 10-3 (c) Incorrect - The decimal is not in the standard position. Move the decimal three places to the right and reduce the exponent by 3 to account for moving the decimal: 4.1 x 103 (d) Correct
Classify the molecules as those of an element or compound. (a) 1 / 1 / 2 = compound (b) 2 = element (c) 4 = element (d) 1 / 4 = compound
(a) Polyatomic and Heteroatomic (b) Diatomic and Homoatomic (c) Polyatomic and Homoatomic (d) Polyatomic and Heteroatomic
Use the terms diatomic, triatomic, polyatomic, homoatomic, or heteroatomic to classify the following molecules correctly: (a) Water molecules have been found to contain two hydrogen atoms and one oxygen atom = H2O = triatomic and heteroatomic molecules (b) Molecules of the ozone contain three oxygen atoms = O3 = triatomic and homoatomic molecules (c) Natural gas is made up primarily of methane molecules, which contain one atom of carbon and four atoms of hydrogen = CH4 = polyatomic and heteroatomic molecules
(a) Triatomic and heteroatomic: the three atoms of two kinds (oxygen and hydrogen) make it both triatomic (three atoms) and heteroatomic (two or more kinds of atoms). (b) Triatomic and homoatomic: the three atoms make it triatomic, and all three atoms are the same (oxygen) which makes it homoatomic. (c) Polyatomic and heteroatomic: a total of five atoms make it polyatomic, and the two different kinds of atoms (carbon and hydrogen) make it heteroatomic.
Calorie
(cal) is a slightly larger unit of heat energy. One calorie is the amount of heat energy required to increase the temperature of 1 g of water by 1°C The calorie and joule are related as follows: 1 cal = 4.184 J
Do the following calculation and express the answer using the correct number of significant figures. (342) x (0.0012) ÷ 100.0 (a) 0.00410 (b) 0.0041 (c) 4.10 x 10ˉ3 (d) 0.004104
0.0041
Which of the following set-ups will allow you to calculate the cost of fruit in dollars per gram, if the price is given as 0.79 dollars per pound? (a) 0.79 dollars/lb. x 2.20 lb./1000g (b) 0.79 dollars/lb. x 457 g/1 dollar (c) lb./0.79 dollars x 1 lb./457 g (d) lb./0.79 dollars x 1 kg/2.20 lb.
0.79 dollars/lb. x 2.20 lb./1000g
The javelin thrown by male competitors in track and field meets must have a minimum mass of 0.800 kg. A javelin is weighed and found to have a mass of 0.819 kg. Express the mass of the weighed javelin in grams.
1 kg = 1,000 g 0.819 kg x 1,000 g = 819 g
A sheet of paper is 0.0 106 cm or 0.0042 in. thick. Write both numbers using scientific notation.
1.06 x 10-2 cm or 4.2 x 10-3 in.
Do the following calculation and express the answer using the correct number of significant figures. (1.21 x 10-3 + 1.3 x 10,-3) x 6.453 x 102 = (a) 1.619 (b) 2 (c) 1.6 (d) 1.62
1.6
Do the following calculation, and express the answer using correct scientific notation. (2.97 x 102) x (6.09 x 10-7) (a) 5.53 x 103 (b) 1.81 x 10ˉ4 (c) 4.88 x 108 (d) 2.05 x 10ˉ9
1.81 x 10ˉ4
A furnace delivers 8.0 x 104 BTU per hour. How many kilocalories per hour is this? (hint: 1 cal = 0.00397 BTU) (a) 3.2 x 10-5 kcal (b) 3.2 x 102 kcal (c) 2.0 X 104 kcal (d) 2.5 x 102 kcal
2.0 X 104 kcal
Based on data obtained in an experiment, to determine the density of a metal, the following calculation is carried out. Express the answer to the correct number of significant figures. 57.67 g - 3.047 g / 25.65 mL - 0.15 mL = 2.1422745098 mL (a) 2.1 g/mL (b) 2.14 g/ml (c) 2.142 g/mL (d) 2.1423 g/mL
2.142 g/mL
Perform the following multiplications and express each answer using scientific notation. a) (2.2 x 102)(3.1 x 10-3) b) (4.9 x 10-3)(1.8 x 10-2) c) (9.1 x 104)(1.2 x 101) d) (8.3 x 104)(4.1 x 103) e) (7.3 x 104)(6.6 x 10-7)
2.2 x 3.1 x 10(2 + -3) = 6.82 x 10-1 = 6.8 x 10-1 4.9 x 1.8 x 10(-3 + -2) = 8.82 x 10-5 = 8.8 x 10-5 9.1 x 1.2 x 10(4 + 1) = 10.92 x 105 = 1.1 x 106 8.3 x 4.1 x 10(4 + 3) = 34.03 x 107 = 3.4 x 108 7.3 x 6.6 x 10(4 + -7) = 48.18 x 10-3 = 4.8 x 10-2
Calculate the volume of an aluminum sample that has a mass of 98.5 g
2.7 g = 98.5 g / ? cm3 = 36.48 cm3 = 3.6 x 101 cm3
Aluminum metal has a density of 2.7 g / cm3. Calculate the mass of an aluminum sample with the volume of 60.0 cm3.
2.7 g = ? / 60.0 cm3 = 162 g = 1.6 x 102 g
On a cold winter day the weather report gives the temperature as -5.0° F. What would this temperature be if reported on the Kevin scale? (a) 252 K (b) 258 K (c) 268 K (d) -20.6 K
252 K
Which of the following numbers is correctly expressed using scientific notation? (a) 3489 (b) 5.248 x 104 (c) 45.78 X 106 (d) .0987 x 103
5.248 x 104
Do the following calculation, and express the answer using correct scientific notation. (6.00 x 1023) x (3.00) / (284) (a) 6.34 x 1021 (b) 1.58 x 10ˉ22 (c) 6.34 x 10ˉ2 (d) 15.8
6.34 x 1021
In 2.0 g of hydrogen gas, there are approximately 6.02 x 1023 hydrogen molecules. Write this number without using scientific notation.
602 000 000 000 000 000 000 000 hydrogen molecules
In a chemistry class of 83 students, 90.4% voted not to take the final exam. How many students wanted to take the exam?
83 x 90.4% / 100% = 75.0 students did NOT want to take the exam. Therefore 8 students wanted to take the exam.
Measurement Units
All measurements are based in standard units that have been agreed on and adopted. The earliest measurements were based on human body dimensions, but the changeable nature of such basic units made the adoption of a worldwide standard desirable.
Large and Small Numbers
Because of difficulties in working with very large and very small numbers in calculations, a system of scientific notation has been devised to represent such numbers. In scientific notation, numbers are represented by products of nonexponential numbers and a 10 raised to some power. The nonexponential number is always written with a decimal in the standard position (to the right of the first non-aero digit in the number). Numbers written in scientific notation can be manipulated in calculation by following a few rules.
°C = 5/9 (°F - 32)
Boiling Point = 100 °C Difference = 100 °C Freezing Point = 0 °C Absolute Zero = -273 °C
°F = 9/5 (°C) + 32
Boiling Point = 212 °F Difference = 180 °F Freezing Point = 32 °F Absolute Zero = -459 °F
K = °C + 273
Boiling Point = 373 K Difference = 100 Kelvins Freezing Point = 273 K Absolute Zero = 0 K
Properties and Changes
Chemical properties cannot be determined without attempting to change one kinds of matter into another. Physical properties can be determined without attempting such composition change. Any change in matter that is accompanied by a composition change is a chemical change. Physical changes take place without the occurrence of any composition change.
Under the appropriate conditions, hydrogen peroxide can be changed to water and oxygen gas. Use the terms homoatomic and heteroatomic to classify molecules of hydrogen peroxide. Explain your reasoning.
Heteroatomic. A single molecule decomposes to make two different molecules and the name, hydrogen peroxide, includes the names of two kinds of elements.
Methane gas, a component of natural gas, is burned in pure oxygen. The only products of the process are water and carbon dioxide. Use the terms homoatomic and heteroatomic to classify molecules of methane.
Heteroatomic. The molecules of the products, carbon dioxide and water, contain carbon and oxygen and hydrogen and oxygen, respectively. The oxygen atoms came from the air, so the carbon atoms and hydrogen atoms in the products must have come from the methane.
Significant Figures
In measured quantities, the significant figures are the numbers representing the part of the measurement that is certain, plus one number representing an estimate. The maximum number of significant figures possible in a measurement is determined by the design of the measuring device. The result of calculations made using numbers from measurements can be expressed with the proper number of significant figures by following simple rules.
Classifying Matter
It often simplifies things to classify the items being studied. Some useful categories into which matter can be classified are heterogeneous, homogeneous, solution, pure substance, element, and compound. All matter is either heterogeneous or homogeneous. Heterogeneous matter is a mixture in which the properties and appearance are not uniform. Homogeneous matter is either a mixture of two or more pure substances (and the mixture is called a solution), or it is a pure substance. If it is a pure substance, it is either an element (containing atoms of only one kind) or a compound (containing two or more kinds of atoms).
1.19 Classify each pure substance represented below by a capital letter as an element or a compound. Indicate when such a classification cannot be made and explain your answer. a) Two elements when mixed combine to form only substance L. b) An element and a compound when mixed form substances M and Q. c) Substance X is not changed by heating it.
L is a compound. It is formed by combining two elements. M and Q cannot be determined. The substance formed from the element must be a compound; the other could be either an element of a compound. X cannot be determined. The absence of a change is not conclusive
Early scientists incorrectly classified calcium oxide (lime) as an element for a number of years. Discuss one or more reasons why you think they might have done this.
Lime was thought to be an element because it was the product of decomposing limestone (calcium carbonate); and because of the difficulty in decomposing lime to the elements calcium and oxygen.
What is Matter?
Matter, the substance of everything, is defined as anything that has mass and occupies space. Mass is the measurement of the amount of matter present in an object. Weight is the measurement of the gravitational force pulling on the object.
Which of the following is an example of a homogeneous mixture? (a) NaOH solution (b) Mortar (mixture of water, sand, and cement) (c) Vinegar and oil salad dressing (d) More than one response is correct
NaOH solution
Which of the following is an example of a homogenous mixture? (a) NaOH solution (b) Mortar (mixture of water, sand and cement) (c) Vinegar and oil salad dressing (d) more than one response is correct
NaOH solution
A Model of Matter
Scientific models are explanations of observed behavior. The results of many observations led scientists to a model for matter in which all matter is composed of tiny particles. In many substances, these particles are called molecules, and they represent the smallest piece of such substances that is capable of stable existence. Molecules, in turn are made up of atoms, which represent the limit of chemical subdivision for matter. The terms diatomic, triatomic, polyatomic, homoatomic, and heteroatomic are commonly used to describe the atomic composition of molecules.
In the distant past, 1 in. was defined as the length resulting from laying a specific number of grain kernels such as corn in a row. Discuss the disadvantages of such a system.
Since the size of individual kernels varies and the tightness of packing is not consistent, the unit obtained is not constant in all situations.
The area of a circle is given by the formula A = πr2, where r is the radius and π = 3.14. Calculate the area of the circle that has a radius of 3.5 cm.
Substitute the given radius (3.5 cm) and the π (3.14) values into the equation: A = πr2 = (3.14)(3.5 cm)2 = (3.14)(12.25 cm2) = 38 cm2
A sample of liquid alcohol is frozen to a solid, then allowed to melt back to a liquid. Have the alcohol molecules been changed by the process? Explain your answer.
The alcohol is reversibly changed from a liquid to a solid and back again. It is the same material regardless of state. Changes in phase are physical changes.
In each of the following, identify the measured numbers and exact numbers. Perform the indicated calculation. Write your answer using the correct number of significant figures. a) An individual has a job of counting the number of people who enter a store between 1 p.m. and 2 p.m. each day for 5 days. The counts were 19, 24, 17, 31, and 40. What was the average number of people entering the store per day for the 5-day period? b) The starting five members of a women's basketball team have the following heights: 61", 5'8", 5'6", 5'1", and 4'11". What is the average height per person of the starting five?
The average is the total divided by the number of objects. a) Both the number of days and the number of people are exact. Total people=19+24+17+31+40=131 b) The number of people is exact (5). The heights are estimated to the nearest inch. Convert height to inches: 6'11" = 73 in.; 5'8" = 68 in.; 5'6" = 66 in.; 5'1" = 61 in.; and 4'11" = 59 in. Total height=73+68+66+61+59=327 in. Total height has 3 sig. fig and the average can have 3 sig. fig.
What Kelvin thermometer reading would correspond to the 77°F reading described above?
The change is from °C to K, so K = °C + 273 = 25°C + 273 = 298 K
A temperature reading of 77°F is measured with a Fahrenheit thermometer. What reading would this temperature give if a Celsius thermometer was used?
The change is from °F to °C, so °C = 5/9 (°F - 32) = 5/9 (77° - 32) = 5/9 (45°F) = 25°C Thus, the reading on a Celsius thermometer would be 25°C
Density
The density of a substance is the number obtained by dividing the mass of a sample by the volume of the same sample. Measured values of density provide two factors that can be used with the factor-unit method to calculate the mass of a substance if the volume in known, or the volume of the mass is known.
Using Units in Calculations
The factor-unit method for doing calculations is based on a specific set of steps. One crucial step involves the use of factors that are obtained from fixed numerical relationships between quantities. The units of the factor must always cancel the units of the unknown quantity and generate the units of the unknown desired quantity.
A small box of irregular pieces of metal was found in a storage room. It was known that the metal was either nickel or chromium. A 35.66 g sample of the metal was weighed and put into a graduated cylinder that contained 21.2 mL of water. The water level after the metal was added was 25.2 mL. Was the metal nickel (density = 8.9 g/cm3) or chromium (density = 7.2 g/cm3)?
The identity can be determined by calculating the density of the sample from the data and comparing the density with the known densities of the two possible metals. The volume of the sample is equal to the difference between the cylinder readings with the sample present and with the sample absent. Volume = 25.2 mL - 21.2 mL = 4.0 mL Remember, 1 mL = 1 cm3, so the sample volume = 4.0 cm3 The density of the sample is equal to the sample mass divided by the sample volume. Density = mass / volume = 35.66 g / 4.0 cm3 = 8.9 g/cm3 A comparison with the known densities of nickel and chromium allows the metal to be identified as nickel.
Metric System
The metric system of measurement is used by most scientists worldwide and all major nation except the United States. It is a decimal system in which larger and smaller units of quantity are related by factors of 10. Prefixes are used to designate relationships between basic unit and larger or smaller units of quantity.
Suppose an element and a compound combine to form only one product. Classify the product as an element or a compound.
The product would have to be a compound because it would be polyatomic (more than one atom because two substances were used) and heteroatomic (different atoms from the two different substances).
A heavy steel ball is suspended by a thin wire. The ball is hit from the side with a hammer, but hardly moves. Describe what you think would happen if this identical experiment were carried out on the moon.
The same. It depends only on the mass of the ball and hammer.
A pipet was used to put a 10.00 mL sample of a liquid into an empty container. The empty container weighted 51.22 g and the container with the liquid sample weighed 64.93 g. Calculate the density of the liquid in g / mL using the formula: Density = Mass / Volume
The sample mass is equal to the difference between the mass of the container with the sample inside and the mass of the empty container. Mass = 64.93 g - 51.22 g = 13.71 g The density of the sample is equal to the sample mass divided by the sample volume. Density = mass / volume = 13.71 g / 10.00 mL = 1.371 g/mL
A rectangular aquarium has sides with lengths of 30.0 cm and 20.0 cm, and a height of 15.0 cm. Calculate the volume of the aquarium, and express the answer on milliliters (mL) and liters (L).
The volume of a rectangular object is equal to the product of the three sides: V = (length)(width)(height) V = (30.0 cm)(20.0 cm)(15.0 cm) 9,000 cm3 or (9.00 x 103 mL) 1 mL = 1 cm3, so the volume is 9.00 x 103 mL 1 L = 1,000 mL, so 9,000 ml = 9 L
Calculating Percentages
The word percentage means per one hundred, and a percent is literally the number of specific items contained in a group of 100 items. Few items always occur in groups of exactly 100, so a calculation can be done that determines how many specific items would be in a group if the group actually did contain exactly 100 items.
A standard system of units was developed in France about the time of the French Revolution and was soon adopted by scientists throughout the world.
This system, called the metric system, has since been adopted and is used by almost all nations of the world.
A world class sprinter can run 100 m in 10.0 s. This corresponds to a speed of 10.0 m/s. Convert this speed to mph.
Two factors result from the relationship meters / miles. The factors are: 1 km / 1,000 m and 0.621 m / 1 km Two factors result from the relationship seconds / hours. The factors are: 60 s / 1 min. and 60 min. / 1 h (10.0 m/s)(1 km / 1,000 m)(0.621 mi / 1 km)(60 s / 1 min)(60 min / 1 h) The meters, kilometers, seconds, and minute units cancel out: rounding to 3 significant figures gives 22.4 mph.
Creatinine is a substance found in the blood. An analysis of a blood serum sample detected 1.1 mg of Creatinine. Express this amount in grams by using the factor-unit method. Remember the prefix milli means 1/1,000 so, 1 g = 1,000 mg
Two factors resulting from the relationship 1 g = 1,000 mg. The factors are: 1 g / 1,000 mg and 1,000 mg / 1 g The first factor is used because it cancels the mg unit and generates the g unit: Step 1 1.1 mg Step 2 1.1 mg = ? g Step 3 (1.1 mg) 1 g / 1,000 mg = ? g The mg units cancel out Step 4 (1.1)(1 g) / (1,000) = 0.0011 g = 1.1 x 10-3 g The number of significant figures matches the number 1.1 because the 1 and 1,000 are exact numbers.
Calculate the volume and density of a rectangular block of aluminum metal (Al) with the edges 5.50 cm, 12.0 cm, and 4.00 cm. The block weighs 929.5 g.
Volume = L x W x H = 5.50 cm x 12.0 cm x 4.00 cm = 264 cm3 Density = mass/volume = 929.5 g/264 cm3 = 3.52 g/cm3
Tell how you would try to prove to a doubter that air is matter.
Weigh precisely a deflated balloon and then weigh it again after inflating.
Mass
a measurement of the amount of matter in an object
A measurement consists of two parts:
a number and an identifying unit. A number expressed without a unit is generally useless.
Express each number below using scientific notation, then carry out the multiplication. Express each answer using scientific notation. a) (835)(0.0045) b) (300)(245) c) (68.3)(421) d) (32.9)(0.115)
a) (8.35 x 102)(4.5 x 10-3) = 3.8 b) (3.00 x 102)(2.45 x 102) = 7.35 x 104 c) (6.83 x 101)(4.21 x 102) = 2.88 x 104 d) (3.29 x 101)(1.15 x 10-1) = 3.78
Which of the following quantities are expressed in metric units? a) The amount of antibiotic in a capsule: 125 mg b) The amount of gasoline in a tank: 15 gal c) The diameter of a contact lens: 6 mm d) The amount of heat used to warm some water: 50 BTU e) The distance of a foot race: 100 m f) The diameter of a circular table: 6 ft
a) 125 mg c) 6 mm e) 100 m
Determine the number of significant figures in each of the following: a) 0.010 b) 14.84 c) 3.11 x 103 d) 157.2 e) 10.05 f) 162.15
a) 2 b) 4 c) 3 d) 4 e) 4 f) 5
Write each of the following numbers using scientific notation. a) Two thousand b) 5162 c) 0.00493 d) 91.88 e) 2.7 million f) 500
a) 2 x 103 b) 5.162 x 103 c) 4.93 x 10-3 d) 9.188 x 101 e) 2.7 x 106 f) 5.00 x 102
Perform the following calculations and use the correct number of significant figures in your answers. Assume all numbers are the results of measurements. a) 2.1+5.07+0.119 b) 0.051+8.11+0.02 c) 4.337-3.211 d) (2.93x10-1)+(6.2x10-2) e) 471.19-365.09 f) 17.76-0.0497
a) 7.289 (round to tenths) = 7.3 b) 8.181 (round to hundredths) = 8.18 c) 1.126 (keep 3 decimal places) d) 0.293 + 0.062 = 0.0355 (keep 3 decimal places) e) 106.10 (keep 2 decimal places) f) 17.7103 (round to hundredths) = 17.71
Do the following, using the appropriate values from Table 1.3. a) Calculate the area in square meters of a circular skating rink that has a 12.5 m radius. For a circle, the area (A) is related to the radius by A =π r2, where π = 3.14. b) Calculate the floor area and volume of a rectangular room that is 5.0 m long, 2.8 m wide, and 2.1 m high. Express your answer in square meters and cubic meters (meters cubed). c) A model sailboat has a triangular sail that is 25 cm high (h) and has a base (b) of 15 cm. Calculate the area (A) of the sail in square centimeters. A = 0.5 (b)(h)
a) A = 3.14 x (12.5 m)2 = 491 m2 b) A = length x width = (5.0 m) x (2.8 m) = 14 m2 V = length x width x height = (5.0 m) x (2.8 m) x (2.1 m) = 29 m3 c) A = 0.5(15 cm)(25 cm) = 1.9 x 102 cm2
Write the following measured quantities as you would record them, using the correct number of significant figures based on the device used to make the measurements. a) A length of two and one-half cm measured with a measuring telescope with smallest scale markings of 0.1 mm. b) An initial reading of exactly 0 for a buret with scale markings of 0.1 mL. c) A length of four and one-half cm measured with a ruler that has a smallest marking of 0.1 cm d) An atmospheric pressure of exactly 690 torr measured with a barometer that has smallest markings of 1 torr.
a) A marking of 0.1 mm would be 0.01 cm. The reading should be 2.500 cm. b) 0.00 mL c) 4.50 cm d) 690.0 torr
Which of the following numbers are written using scientific notation correctly? For those that are not, explain what is wrong. a) 3.6 x 1025 b) 3.9-2 c) 295 x 103 d) 0.05 x 10-3 e) 10-4 f) 13.1 x 106
a) Correct b) The coefficient has the exponent on it rather than on the "10." 3.9 x 10-2 would be the correct scientific notation. c) Wrong coefficient, 2.95 x 105 would be correct. d) Wrong coefficient, 5 x 10-5 would be correct. e) No coefficient, 1 x 10-4 would be correct. f) Wrong coefficient, 1.31 x 101 would be correct.
Classify the following properties as physical or chemical. Explain your reasoning in each case. a) Iron melts at 1535°C; b) Alcohol is very flammable; c) The metal used in artificial hip joint implants is not corroded by body fluids; d) A 1 in. cube of aluminum weighs less than a 1 in. cube of lead; e) An antacid neutralizes stomach acid.
a) Physical - Melting is determined by heating the iron until it liquefies. b) Chemical - Flammability is the ability to burn in air. c) Chemical - Corrosion is the combination of a metal with air. d) Physical - Weighing an object does not cause a chemical change, so the weight and the volume are physical properties. e) Chemical - The fact that the acid has been neutralized implies it is no longer an acid. Thus its composition has been changed.
Classify each of the following as a physical or chemical change and give at least one observation, fact, or reason to support your answer. a) an inflated balloon gets larger when heated; b) a baking cake burns; c) a bottle of milk sours; d) a stretched rubber band breaks.
a) Physical - The gas expands when heated but will contract when cooled. b) Chemical - The color, taste and texture all change irreversibly. c) Chemical - The taste and aroma change irreversibly. d) Physical - Broken or not, the material is still the same.
Indicate to what decimal position readings should be estimated and recorded (nearest 0.1, 0.01, etc.) for measurements made with the following devices. a) a buret with smallest scale marking of 0.1 mL. b) a graduated cylinder with smallest scale marking of 1 mL c) a thermometer with smallest scale marking of 0.1°C d) a barometer with smallest scale marking of 1 torr
a) The marking is 0.1 mL. The reading is made to the nearest 0.01 mL. b) The marking is 1 mL. The reading is made to the nearest 0.1 mL. c) The marking is 0.1 °C. The reading is made to the nearest 0.01 °C. d) The marking is 1 torr. The reading is made to the nearest 0.1 torr.
A sample of solid elemental phosphorus, that is deep red in color, is burned. While the phosphorus is burning, a white smoke, that is actually a finely divided white solid, is produced and is collected. a) Have the molecules of the phosphorus been changed by the process of burning? Explain your answer. b) Is the collected white solid a different substance than the phosphorus? Explain your answer. c) In terms of the number of kinds of atoms contained, how do you think the size of the molecules of the white solid compares to the size of the molecules of phosphorus? Explain your answer. d) Classify molecules of the collected white solid using the terms homoatomic and heteroatomic. Explain your reasoning.
a) Yes. White solid particles have different properties than the red solid. b) Yes. White solid particles have different properties than the red solid. c) The molecules of the white solid contain both oxygen atoms and phosphorus atoms. The elemental phosphorus contains only phosphorus atoms. The white solid has more kinds of atoms and should be larger. d) Heteroatomic. They contain two kinds of atoms.
Classify each of the following as homogeneous or heterogeneous. a) muddy flood water b) gelatin dessert c) normal urine d) smog-filled air e) an apple f) mouthwash g) petroleum jelly
a) heterogeneous b) homogeneous c) homogeneous d) heterogeneous e) heterogeneous f) homogeneous g) homogeneous
The attractive force of gravity for objects near the earth's surface increases as you get closer to the center of the earth. Suppose you are transported from a deep mine to the top of a tall mountain. a. How would your mass be changed by the move? b. How would your weight be changed by the move?
a. Mass is independent of gravity so your mass would not change. b. Weight depends on gravity, which decreases with distance from the earth's center; your weight would be less on the mountaintop.
Matter
anything that has mass and occupies space
Elements
are a pure substance consisting of only one kind of atom in the form of homoatomic molecules or individual atoms
Physical Changes
are changes matter undergoes without changing the composition of the substance
Chemical Changes
are changes that matter undergoes that involve changes in the composition of the substance
Scientific Models
are explanations for observed behavior in nature • All matter is made up of particles that are too small to see. The early framers of this model called the small particles molecules. It is now known that molecules are the constituent particles of many, but not all, substances.
Factors used in the factor-unit method
are fractions obtained from numerical relationships between quantities.
Solutions
are homogeneous mixtures of two or more substances
Polyatomic Molecules
are molecules that contain more than three atoms
Homoatomic Molecules
are molecules that contain only one kind of atom
Triatomic Molecules
are molecules that contain three atoms
Diatomic Molecules
are molecules that contain two atoms
Heteroatomic Molecules
are molecules that contain two or more kinds of atoms
Exact Numbers
are numbers that have no uncertainty; numbers from defined relationships, counting numbers, and numbers that are part of simple fractions.
Compounds
are pure substances consisting of two or more kinds of atoms in the form of heteroatomic molecules or individual atoms
Significant Figures
are the numbers in a measurement that represents the certainty of the measurement, plus one number representing an estimate • The maximum number of significant figures possible in a measurement is determined by the design of the measuring device and cannot be changed by expressing the measurement in different units. • Zeros located to the left of nonzero numbers are never considered to be significant. • Zeros located between nonzero numbers or trailing zeros located at the end of numbers will be considered significant.
Chemical Properties
are the properties matter demonstrates when attempts are made to change it into other kinds of matter or new substances
The limit of chemical subdivision of an element is the: (a) atom (b) molecule (c) proton (d) compound
atom
Classify as a pure substance or a solution each of the materials in the question above that you classified as homogenous.
b) solution c) solution d) solution f) solution g) solution
As two clear liquid solutions are thoroughly mixed, a red solid forms. This change is most likely (a) physical (b) chemical (c) neither chemical nor physical (d) both chemical and physical
chemical
The fact that gold does not corrode is a (a) physical property (b) personal property (c) real property (d) chemical property
chemical property
Table salt, NaCl is best classified as a(n) (a) compound (b) element (c) homogenous mixture (d) heterogenous mixrure
compound
Homoatomic pure substances are known as (a) protons (b) elements (c) compound (d) molecules
elements
Do the following calculation. How many significant figures are justified for the answer? 6.02 + 5.119 + 0.04218 (a) three (b) four (c) five (d) seven
four
A molecule represented by O-O-O must be classified as (a) homoatomic and polyatomic (b) homoatomic and monoatomic (c) heteroatomic and polyatomic (d) heteroatomic and momoatomic
homoatomic and polyatomic
Standard Position for a Decimal
in scientific notation, the position to the right of the first non-zero digit in the non-exponential number
Metric System
is a decimal system in which larger and smaller units of a quantity are related by factors of 10
Mixture
is a physical blend of matter that can theoretically be physically separated into two or more components
Basic Unit of Measurement
is a specific unit from which other units for the same quantity are obtained by multiplication or division
Factor-Unit Method
is a systematic approach to solving numerical problems and consists of the following steps: Step 1 - Write down the known or given quantity. Include both the numerical value and the unit of the quantity. Step 2 - Leave some working space and set the known quantity equal to the units of the unknown quantity. Step 3 - Multiply the known quantity by one or more factors, such that the units of the factor cancels the units of the unknown quantity and generate the units of the unknown quantity. Step 4 - After you get the desired units, do the necessary arithmetic to produce the final answer.
Derived Unit of Measurement
is a unit obtained by multiplication or division of one or more basic units
Scientific Notation
is a way of representing numbers consisting of a product between a non-exponential number and 10 raised to a whole-number exponent that may be positive or negative
Heterogeneous Matter
is matter in which the properties and appearance are not uniform throughout the sample
Pure Substance
is matter that has a constant composition and fixed set of physical and chemical properties
Homogeneous Matter
is matter that has a uniform appearance and the same properties throughout the sample
Density
is the number given when the mass of a sample of a substance is divided by the volume of the sample.
Molecule
is the smallest particle of a pure substance that has the properties of that substance and is capable of a stable independent existence. Alternatively, a molecule is the limit of physical subdivision for a pure substance
Percent
means per one hundred % = part / total x 100 or Part / Percent % Total / 100 %
John Dalton (1766-1844) is generally credited with developing the first atomic theory containing ideas that are still used today. The main points of his theory, which he proposed in 1808, can be summarized in the following five statements:
o All matter is made up of tiny particles called atoms. o Substances called elements are made up of atoms that are all identical. o Substances called compounds are combinations of atoms or two or more elements. o Every molecule of a specific compound always contains the same number of atoms of each kind of element found in the compound. o In chemical reaction, atoms are rearranged, separated, or combined, but are never created or destroyed.
To follow these rules, it is often necessary to reduce the number of significant figures by rounding answers. The following rules are for rounding:
o If the first of the non-significant figures to be dropped from an answer is 5 or greater, all the non-significant figures are dropped, and the last significant figure is increased by 1. o If the first of the non-significant figures to be dropped from an answer is less than 5, all the non-significant figures are dropped, and the last significant figure is left unchanged.
Thermometers can have temperature scales that represent different units:
o K = Kelvins o F = Fahrenheit o C = Celsius
Multiplication and division of numbers written in scientific notation can be done quite simply by using some characteristics of exponentials
o Multiplication = add the exponents o Division = Subtract the exponents
Most measurements that are made are not final answers. They are usually used to make calculations involving multiplication, division, addition, or subtraction. The answer obtained from such a calculation cannot have more certainty than the least certain measurement used in the calculation. It should be written to reflect an uncertainty equal to that of most uncertain measurement. This is accomplished by the following rules:
o The answer obtained by multiplication or division must contain the same number of significant figures as the quantity with the fewest significant figures used in the calculation. o The answer obtained by addition or subtraction must contain the same number of places to the right of the decimal as the quantity in the calculation with the fewest number of places to the right of the decimal.
The rule that specifies counting trailing zeros as significant is generally followed by scientists, but some quantities are expressed with trailing zeros that are not significant. The rule for determining the significance of zeros are summarized as follows:
o Zeros not proceeded by non-zero numbers are not significant figures. These zeros are sometimes called leading zeros. o Zeros between non-zero numbers are significant figures. These zeros are sometimes called buried or confined zeros. o Zeros located at the end of a number are significant zeros. These zeros are sometimes called trailing zeros.
Physical Properties
properties of matter that can be observed or measured without trying to change the composition of the matter being studied - no original substances are destroyed and no new substances appear.
Weight
the measurement of the gravitational force acting on an object
How is the weight of an object influenced when the gravitational force on the object is increased? (a) the weight decreases (b) the weight increases (c) the weight is unchanged (d) the weight is equal to the mass
the weight increases
Which of the following terms correctly applies to a molecule of CO2? (a) triatomic, heteroatomic (b) polyatomic, diatomic (c) triatomic, homoatomic (d) diatomic, heteroatomic
triatomic, heteroatomic
Density = Mass / Volume
• The mass of a sample is obtained by weighing the sample. • The volume of a sample can be calculated if the sample is a regular solid. If the sample is a liquid, or an irregular solid, the volume can be measured by using volumetric apparatus. • Densities of solids are often given in units of g / cm3, and those of liquids in units of g / mL. • 1 cm3 = 1 mL, so the numerical value is the same regardless of which of the two volume units is used.
