1.f^Chapter 1 Ending^22^28^,,^2784^3142%
|(1.1)||Equation for density|
|(1.2)||Converting °F to °C|
|(1.3)||Converting °C to °F|
|(1.4)||Converting °C to K|
The scientific method is a systematic approach to research that begins with the gathering of information through observation and measurements. In the process, hypotheses, laws, and theories are devised and tested.
Chemists study matter and the substances of which it is composed. All substances, in principle, can exist in three states: solid, liquid, and gas. The interconversion between these states can be effected by a change in temperature.
The simplest substances in chemistry are elements. Compounds are formed by the combination of atoms of different elements. Substances have both unique physical properties that can be observed without changing the identity of the substances and unique chemical properties that, when they are demonstrated, do change the identity of the substances.
SI units are used to express physical quantities in all sciences, including chemistry. Numbers expressed in scientific notation have the form N × 10n, where N is between 1 and 10 and n is a positive or negative integer. Scientific notation helps us handle very large and very small quantities. Most measured quantities are inexact to some extent. The number of significant figures indicates the exactness of the measurement.
In the dimensional analysis method of solving problems the units are multiplied together, divided into each other, or canceled like algebraic quantities. Obtaining the correct units for the final answer ensures that the calculation has been carried out properly.
1.1 Define these terms: (a) matter, (b) mass, (c) weight, (d) substance, (e) mixture.
1.2 Which of these statements is scientifically correct?
“The mass of the student is 56 kg.”
“The weight of the student is 56 kg.”
1.3 Give an example of a homogeneous mixture and an example of a heterogeneous mixture.
1.4 What is the difference between a physical property and a chemical property?
1.5 Give an example of an intensive property and an example of an extensive property.
1.6 Define these terms: (a) element, (b) compound.
1.7 Do these statements describe chemical or physical properties? (a) Oxygen gas supports combustion. (b) Fertilizers help to increase agricultural production. (c) Water boils below 100°C on top of a mountain. (d) Lead is denser than aluminum. (e) Uranium is a radioactive element.
1.8 Does each of these describe a physical change or a chemical change? (a) The helium gas inside a balloon tends to leak out after a few hours. (b) A flash-light beam slowly gets dimmer and finally goes out. (c) Frozen orange juice is reconstituted by adding water to it. (d) The growth of plants depends on the sun's energy in a process called photosynthesis. (e) A spoonful of table salt dissolves in a bowl of soup.
1.9 Which of these properties are intensive and which are extensive? (a) length, (b) volume, (c) temperature, (d) mass.
1.10 Which of these properties are intensive and which are extensive? (a) area, (b) color, (c) density.
1.11 Classify each of these substances as an element or a compound: (a) hydrogen, (b) water, (c) gold, (d) sugar.
1.12 Classify each of these as an element or a compound: (a) sodium chloride (table salt), (b) helium, (c) alcohol, (d) platinum.
1.13 Give the SI units for expressing these: (a) length, (b) area, (c) volume, (d) mass, (e) time, (f) force, (g) energy, (h) temperature.
1.14 Write the numbers for these prefixes: (a) mega-, (b) kilo-, (c) deci-, (d) centi-, (e) milli-, (f) micro-, (g) nano-, (h) pico-.
1.15 Define density. What units do chemists normally use for density? Is density an intensive or extensive property?
1.16 Write the equations for converting degrees Celsius to degrees Fahrenheit and degrees Fahrenheit to degrees Celsius.
1.17 A lead sphere has a mass of 1.20 × 104 g, and its volume is 1.05 × 103 cm3. Calculate the density of lead.
1.18 Mercury is the only metal that is a liquid at room temperature. Its density is 13.6 g/mL. How many grams of mercury will occupy a volume of 95.8 mL?
1.19 (a) Normally the human body can endure a temperature of 105°F for only short periods of time without permanent damage to the brain and other vital organs. What is this temperature in degrees Celsius? (b) Ethylene glycol is a liquid organic compound that is used as an antifreeze in car radiators. It freezes at −11.5°C. Calculate its freezing temperature in degrees Fahrenheit. (c) The temperature on the surface of the sun is about 6300°C. What is this temperature in degrees Fahrenheit? (d) The ignition temperature of paper is 451°F. What is the temperature in degrees Celsius?
1.20 (a) Convert the following temperatures to kelvin: (i) 113°C, the melting point of sulfur, (ii) 37°C, the normal body temperature, (iii) 357°C, the boiling point of mercury. (b) Convert the following temperatures to degrees Celsius: (i) 77 K, the boiling point of liquid nitrogen, (ii) 4.2 K, the boiling point of liquid helium, (iii) 601 K, the melting point of lead.
1.21 Express these numbers in scientific notation: (a) 0.000000027, (b) 356, (c) 0.096.
1.22 Express these numbers in scientific notation: (a) 0.749, (b) 802.6, (c) 0.000000621.
1.23 Convert these to nonscientific notation: (a) 1.52 × 104, (b) 7.78 × 10−8.
1.24 Convert these to nonscientific notation: (a) 3.256 × 10−5, (b) 6.03 × 106.
1.25 Express the answers to these in scientific notation:
145.75 + (2.3 × 10−1)
79,500 ÷ (2.5 × 102)
(7.0 × 10−3) − (8.0 × 10−4)
(1.0 × 104) × (9.9 × 106)
1.26 Express the answers to these in scientific notation:
0.0095 + (8.5 × 10−3)
653 ÷ (5.75 × 10−8)
850,000 − (9.0 × 105)
(3.6 × 10−4) × (3.6 × 106)
1.27 What is the number of significant figures in each of these measured quantities? (a) 4867 miles, (b) 56 mL, (c) 60,104 tons, (d) 2900 g.
1.28 What is the number of significant figures in each of these measured quantities? (a) 40.2 g/cm3, (b) 0.0000003 cm, (c) 70 min, (d) 4.6 × 1019 atoms.
1.29 Carry out these operations as if they were calculations of experimental results, and express each answer in the correct units and with the correct number of significant figures:
5.6792 m + 0.6 m + 4.33 m
3.70 g − 2.9133 g
4.51 cm × 3.6666 cm
(3 × 104 g + 6.827 g)/(0.043 cm3 − 0.021 cm3)
1.30 Carry out these operations as if they were calculations of experimental results, and express each answer in the correct units and with the correct number of significant figures:
7.310 km ÷ 5.70 km
(3.26 × 10−3 mg) − (7.88 × 10−5 mg)
(4.02 × 106 dm) + (7.74 × 107 dm)
(7.8 m − 0.34 m)/(1.15 s + 0.82 s)
1.31 Carry out these conversions: (a) 22.6 m to decimeters, (b) 25.4 mg to kilograms.
1.32 Carry out these conversions: (a) 242 lb to milligrams, (b) 68.3 cm3 to cubic meters.
1.33 The price of gold on a certain day in 2009 was $932 per troy ounce. How much did 1.00 g of gold cost that day? (1 troy ounce = 31.03 g.)
1.34 Three students (A, B, and C) are asked to determine the volume of a sample of methanol. Each student measures the volume three times with a graduated cylinder. The results in milliliters are A (47.2, 48.2, 47.6); B (46.9, 47.1, 47.2); C (47.8, 47.8, 47.9). The true volume of methanol is 47.0 mL. Which student is the most accurate? Which student is the most precise?
1.35 Three students (X, Y, and Z) are assigned the task of determining the mass of a sample of iron. Each student makes three determinations with a balance. The results in grams are X (61.5, 61.6, 61.4); Y (62.8, 62.2, 62.7); Z (61.9, 62.2, 62.1). The actual mass of the iron is 62.0 g. Which student is the least precise? Which student is the most accurate?
1.36 A slow jogger runs a mile in 13 min. Calculate the speed in (a) in/s, (b) m/min, (c) km/h. (1 mi = 1609 m; 1 in = 2.54 cm.)
1.37 Carry out these conversions: (a) A 6.0-ft person weighs 168 lb. Express this person's height in meters and weight in kilograms. (1 lb = 453.6 g; 1 m = 3.28 ft.) (b) The current speed limit in some states in the United States is 55 miles per hour. What is the speed limit in kilometers per hour? (c) The speed of light is 3.0 × 1010 cm/s. How many miles does light travel in 1 hour? (d) Lead is a toxic substance. The “normal” lead content in human blood is about 0.40 part per million (that is, 0.40 g of lead per million grams of blood). A value of 0.80 part per million (ppm) is considered to be dangerous. How many grams of lead are contained in 6.0 × 103 g of blood (the amount in an average adult) if the lead content is 0.62 ppm?
1.38 Carry out these conversions: (a) 1.42 light-years to miles (a light-year is an astronomical measure of distance—the distance traveled by light in a year, or 365 days), (b) 32.4 yd to centimeters, (c) 3.0 × 1010 cm/s to ft/s, (d) 47.4°F to degrees Celsius, (e) −273.15°C (the lowest temperature) to degrees Fahrenheit, (f) 71.2 cm3 to m3, (g) 7.2 m3 to liters.
1.39 Aluminum is a lightweight metal (density = 2.70 g/cm3) used in aircraft construction, high-voltage transmission lines, and foils. What is its density in kg/m3?
1.40 The density of ammonia gas under certain conditions is 0.625 g/L. Calculate its density in g/cm3.
1.41 Which of these describe physical and which describe chemical properties? (a) Iron has a tendency to rust. (b) Rainwater in industrialized regions tends to be acidic. (c) Hemoglobin molecules have a red color. (d) When a glass of water is left out in the sun, the water gradually disappears. (e) Carbon dioxide in air is converted to more complex molecules by plants during photosynthesis.
1.42 In 2004 about 87.0 billion pounds of sulfuric acid were produced in the United States. Convert this quantity to tons.
1.43 Suppose that a new temperature scale has been devised on which the melting point of ethanol (−117.3°C) and the boiling point of ethanol (78.3°C) are taken as 0°S and 100°S, respectively, where S is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at 25°C?
1.44 In the determination of the density of a rectangular metal bar, a student made the following measurements: length, 8.53 cm; width, 2.4 cm; height, 1.0 cm; mass, 52.7064 g. Calculate the density of the metal to the correct number of significant figures.
1.45 Calculate the mass of each of these: (a) a sphere of gold of radius 10.0 cm [the volume of a sphere of radius r is ; the density of gold = 19.3 g/cm3], (b) a cube of platinum of edge length 0.040 mm (the density of platinum = 21.4 g/cm3), (c) 50.0 mL of ethanol (the density of ethanol = 0.798 g/mL).
1.46 A cylindrical glass tube 12.7 cm in length is filled with mercury. The mass of mercury needed to fill the tube is found to be 105.5 g. Calculate the inner diameter of the tube. (The density of mercury = 13.6 g/mL.)
1.47 This procedure was carried out to determine the volume of a flask. The flask was weighed dry and then filled with water. If the masses of the empty flask and the filled flask were 56.12 g and 87.39 g, respectively, and the density of water is 0.9976 g/cm3, calculate the volume of the flask in cubic centimeters.
1.48 A silver (Ag) object weighing 194.3 g is placed in a graduated cylinder containing 242.0 mL of water. The volume of water now reads 260.5 mL. From these data calculate the density of silver.
1.49 The experiment described in Problem 1.48 is a crude but convenient way to determine the density of some solids. Describe a similar experiment that would enable you to measure the density of ice. Specifically, what would be the requirements for the liquid used in your experiment?
1.50 The speed of sound in air at room temperature is about 343 m/s. Calculate this speed in miles per hour (mph).
1.51 The medicinal thermometer commonly used in homes can be read to ±0.1°F, whereas those in the doctor's office may be accurate to ±0.1°C. In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of 38.9°C.
1.52 A thermometer gives a reading of 24.2°C ± 0.1°C. Calculate the temperature in degrees Fahrenheit. What is the uncertainty?
1.53 Vanillin (used to flavor vanilla ice cream and other foods) is the substance whose aroma the human nose detects in the smallest amount. The threshold limit is 2.0 × 10−11 g per liter of air. If the current price of 50 g of vanillin is $112, determine the cost to supply enough vanillin so that the aroma could be detectable in a large aircraft hangar of volume 5.0 × 107 ft3.
1.54 A resting adult requires about 240 mL of pure oxygen/min and breathes about 12 times every minute. If inhaled air contains 20 percent oxygen by volume and exhaled air 16 percent, what is the volume of air per breath? (Assume that the volume of inhaled air is equal to that of exhaled air.)
1.55 The total volume of seawater is 1.5 × 1021 L. Assume that seawater contains 3.1 percent sodium chloride by mass and that its density is 1.03 g/mL. Calculate the total mass of sodium chloride in kilograms and in tons. (1 ton = 2000 lb; 1 lb = 453.6 g.)
1.56 Magnesium (Mg) is a valuable metal used in alloys, in batteries, and in chemical synthesis. It is obtained mostly from seawater, which contains about 1.3 g of Mg for every kilogram of seawater. Calculate the volume of seawater (in liters) needed to extract 8.0 × 104 tons of Mg, which is roughly the annual production in the United States. (Density of seawater = 1.03 g/mL.)
1.57 A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density = 0.9986 g/cm3). The readings are 860.2 g and 820.2 g, respectively. Given that the density of platinum is 21.45 g/cm3, what should her conclusion be based on these measurements? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyancy of air.)
1.58 At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?
1.59 The surface area and average depth of the Pacific Ocean are 1.8 × 108 km2 and 3.9 × 103 m, respectively. Calculate the volume of water in the ocean in liters.
1.60 Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value:
where the vertical lines indicate absolute value. Calculate the percent error for these measurements: (a) The density of alcohol (ethanol) is found to be 0.802 g/mL. (True value: 0.798 g/mL.) (b) The mass of gold in an earring is analyzed to be 0.837 g. (True value: 0.864 g.)
1.61 Osmium (Os) is the densest element known (density = 22.57 g/cm3). Calculate the mass in pounds and kilograms of an Os sphere 15 cm in diameter (about the size of a grapefruit). See Problem 1.45 for volume of a sphere.
1.62 A 1.0-mL volume of seawater contains about 4.0 × 10−12 g of gold. The total volume of ocean water is 1.5 × 1021 L. Calculate the total amount of gold in grams that is present in seawater and its worth in dollars, assuming that the price of gold is $930 an ounce. With so much gold out there, why hasn't someone become rich by mining gold from the ocean?
1.63 The thin outer layer of Earth, called the crust, contains only 0.50 percent of Earth's total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon (Si) is the second most abundant element in Earth's crust (27.2 percent by mass). Calculate the mass of silicon in kilograms in Earth's crust. (The mass of Earth is 5.9 × 1021 tons. 1 ton = 2000 lb; 1 lb = 453.6 g.)
1.64 The diameter of a copper (Cu) atom is roughly 1.3 × 10−10 m. How many times can you divide evenly a piece of 10-cm copper wire until it is reduced to two separate copper atoms? (Assume there are appropriate tools for this procedure and that copper atoms are lined up in a straight line, in contact with each other.) Round off your answer to an integer.
1.65 One gallon of gasoline burned in an automobile's engine produces on the average 9.5 kg of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States, and each car covers a distance of 5000 mi at a consumption rate of 20 mi per gallon.
1.66 A sheet of aluminum (Al) foil has a total area of 1.000 ft2 and a mass of 3.636 g. What is the thickness of the foil in millimeters? (Density of Al = 2.699 g/cm3.)
1.67 Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine or 1 g of chlorine per million g of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains 6.0 percent chlorine by mass and there are 2 × 104 gallons of water in the pool. (1 gallon = 3.79 L; density of liquids = 1.0 g/mL.)
1.68 Fluoridation is the process of adding fluorine compounds to drinking water to help fight tooth decay. A concentration of 1 ppm of fluorine is sufficient for the purpose. (1 ppm means 1 g of fluorine per 1 million g of water.) The compound normally chosen for fluoridation is sodium fluoride, which is also added to some toothpastes. Calculate the quantity of sodium fluoride in kilograms needed per year for a city of 50,000 people if the daily consumption of water per person is 150 gallons. What percent of the sodium fluoride is “wasted” if each person uses only 6.0 L of water a day for drinking and cooking? (Sodium fluoride is 45.0 percent fluorine by mass. 1 gallon = 3.79 L; 1 year = 365 days; density of water = 1.0 g/mL.)
1.69 In water conservation, chemists spread a thin film of certain inert material over the surface of water to cut down the rate of evaporation of water in reservoirs. This technique was pioneered by Benjamin Franklin three centuries ago. Franklin found that 0.10 mL of oil could spread over the surface of water of about 40 m2 in area. Assuming that the oil forms a monolayer, that is, a layer that is only one molecule thick, estimate the length of each oil molecule in nanometers. (1 nm = 1 × 10−9 m.)
1.70 Pheromones are compounds secreted by females of many insect species to attract mates. Typically, 1.0 × 10−8 g of a pheromone is sufficient to reach all targeted males within a radius of 0.50 mi. Calculate the density of the pheromone (in grams per liter) in a cylindrical air space having a radius of 0.50 mi and a height of 40 ft.
1.71 Three different 25.0 g samples of solid pellets are added to 20.0 mL of water in three different cylinders. The results are illustrated here. Given the densities of the three materials used, identify each sample of solid pellets: solid A (2.9 g/cm3), solid B (8.3 g/cm3), and solid C (3.3 g/cm3).
1.72 Dinosaurs dominated life on Earth for millions of years and then disappeared very suddenly. In the experimentation and data-collecting stage, paleontologists studied fossils and skeletons found in rocks in various layers of Earth's crust. Their findings enabled them to map out which species existed on Earth during specific geologic periods. They also revealed no dinosaur skeletons in rocks formed immediately after the Cretaceous period, which dates back some 65 million years. It is therefore assumed that the dinosaurs became extinct about 65 million years ago.
Among the many hypotheses put forward to account for their disappearance were disruptions of the food chain and a dramatic change in climate caused by violent volcanic eruptions. However, there was no convincing evidence for any one hypothesis until 1977. It was then that a group of paleontologists working in Italy obtained some very puzzling data at a site near Gubbio. The chemical analysis of a layer of clay deposited above sediments formed during the Cretaceous period (and therefore a layer that records events occurring after the Cretaceous period) showed a surprisingly high content of the element iridium. Iridium is very rare in Earth's crust but is comparatively abundant in asteroids.
This investigation led to the hypothesis that the extinction of dinosaurs occurred as follows. To account for the quantity of iridium found, scientists suggested that a large asteroid several miles in diameter hit Earth about the time the dinosaurs disappeared. The impact of the asteroid on Earth's surface must have been so tremendous that it literally vaporized a large quantity of surrounding rocks, soils, and other objects. The resulting dust and debris floated through the air and blocked the sunlight for months or perhaps years. Without ample sunlight most plants could not grow, and the fossil record confirms that many types of plants did indeed die out at this time. Consequently, of course, many plant-eating animals gradually perished, and then, in turn, meat-eating animals began to starve. Limitation of food sources obviously affects large animals needing great amounts of food more quickly and more severely than small animals. Therefore, the huge dinosaurs vanished because of lack of food.
How does the study of dinosaur extinction illustrate the scientific method?
Suggest two ways to test the hypothesis.
In your opinion, is it justifiable to refer to the asteroid explanation as the theory of dinosaur extinction?
Available evidence suggests that about 20 percent of the asteroid's mass turned to dust and spread uniformly over Earth after eventually settling out of the upper atmosphere. This dust amounted to about 0.02 g/cm2 of Earth's surface. The asteroid very likely had a density of about 2 g/cm3. Calculate the mass (in kilograms and tons) of the asteroid and its radius in meters, assuming that it was a sphere. (The area of Earth is 5.1 × 1014 m2; 1 lb = 453.6 g.) (Source: Consider a Spherical Cow—A Course in Environmental Problem Solving by J. Harte, University Science Books, Mill Valley, CA, 1988. Used with permission.)
1.73 You are given a liquid. Briefly describe steps you would take to show whether it is a pure substance or a homogeneous mixture.
1.74 A bank teller is asked to assemble “one-dollar” sets of coins for his clients. Each set is made of three quarters, one nickel, and two dimes. The masses of the coins are: quarter: 5.645 g; nickel: 4.967 g; dime: 2.316 g. What is the maximum number of sets that can be assembled from 33.871 kg of quarters, 10.432 kg of nickels, and 7.990 kg of dimes? What is the total mass (in g) of this collection of coins?
1.75 A graduated cylinder is filled to the 40.00-mL mark with a mineral oil. The masses of the cylinder before and after the addition of the mineral oil are 124.966 g and 159.446 g, respectively. In a separate experiment, a metal ball bearing of mass 18.713 g is placed in the cylinder and the cylinder is again filled to the 40.00-mL mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g. Calculate the density and radius of the ball bearing. [The volume of a sphere of radius r is (4/3)πr3.]
1.76 Bronze is an alloy made of copper (Cu) and tin (Sn). Calculate the mass of a bronze cylinder of radius 6.44 cm and length 44.37 cm. The composition of the bronze is 79.42 percent Cu and 20.58 percent Sn and the densities of Cu and Sn are 8.94 g/cm3 and 7.31 g/cm3, respectively. What assumption should you make in this calculation?
1.77 A chemist in the nineteenth century prepared an unknown substance. In general, do you think it would be more difficult to prove that it is an element or a compound? Explain.
1.78 Tums is a popular remedy for acid indigestion. A typical Tums tablet contains calcium carbonate plus some inert substances. When ingested, it reacts with the gastric juice (hydrochloric acid) in the stomach to give off carbon dioxide gas. When a 1.328-g tablet reacted with 40.00 mL of hydrochloric acid (density: 1.140 g/mL), carbon dioxide gas was given off and the resulting solution weighed 46.699 g. Calculate the number of liters of carbon dioxide gas released if its density is 1.81 g/L.
1.79 A 250-mL glass bottle was filled with 242 mL of water at 20°C and tightly capped. It was then left outdoors overnight, where the average temperature was −5°C. Predict what would happen. The density of water at 20°C is 0.998 g/cm3 and that of ice at −5°C is 0.916 g/cm3.
(a) 621.5°F, (b) 78.3°C, (c)−196°C.
(a) Two, (b) four, (c) three, (d) two. (e) three or two.
(a) 26.76 L, (b) 4.4 g, (c) 1.6 × 107 dm2, (d) 0.0756 g/mL, (e) 6.69 × 104 m.
1.08 × 105 m3.