CHAPTER 2 HW PRACTICE SOLUTIONS

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1 CHAPTER 2 HW PRACTICE SOLUTIONS SIGNIFICANT FIGURES 1.) How many significant figures are shown in each of the following numbers? a SF c SF e SF b SF d. 91,000,000 2 SF f SF 2.) How many significant figures are shown in each of the following numbers? a SF c. 12,007 5 SF e. 5 1 SF b SF d SF f SF 3.) Report each of the following values to four significant figures (i.e. in some cases round the values). a c. 36,054,210 36,050,000 b d ) Report each of the following values to three significant figures. a. 15,569,300 15,600,000 c b. 25,105 25,100 d SIGNIFICANT FIGURES IN CALCULATIONS 5.) Perform the following calculations, keeping in mind significant figures and units. a L L = 3.13 L c C C = 22.0 C _ 22.0 b. (5.376 m) (20.66 m) = m 2 d. 10,600 cm 2 / 49 cm = 220 cm 6.) Perform the following calculations, keeping in mind significant figures and units. a. 325 mg 12.0 mg = 313 mg c g / ml = 3100 g/ml b. (3.4 cm) (5.06 cm) = 17 cm 2 d. 26,000 m + 1,720 m = 28,000 m Problem a) , ,720 27,720 Page 1

2 7.) The mass of a container is g. The mass of the same container with salt inside is g. What is the mass of the salt in the container? Answer must have the same # precision as the numbers (4 past decimal) g 8.) A measuring cup contains ml of water. A syringe removes 3.07 ml of water from the measuring cup. What is the remaining volume of water in the cup? g g g Answer must have the same # precision as the least precise (1 past decimal) ml ml ml ml 9.) A perfect cube of plastic measures 8.05 cm on each side. What is the volume of the cube of plastic? Volume = (8.05 cm) (8.05 cm) (8.05 cm) = 522 cm 3 10.) Perform the following calculations, keeping in mind significant figures and units (if given). a.!"# ("%.') = 99,600 = b. #.#)#!".%% + %.', #.!#% = )".'% Round after the add/subtracting: 37.0 = ) Perform the following calculations, keeping in mind significant figures and units (if given). a. -!. (-.#/".) = 0.92 g 2 /day b /"5 67,#.#0 67 = ml/kg /0.' 8. Round after the subtracting: 1.58 = SCIENTIFIC NOTATION 12.) How many significant figures are shown in each of the following numbers? a SF b SF c SF 13.) Convert the following numbers from standard notation into scientific notation. Maintain the same number of significant figures. a c b. 6,070, d Page 2

3 14.) Convert the following numbers from standard notation into scientific notation. Maintain the same number of significant figures. a. 678,000, c b. 2, d ) Convert the following numbers from scientific notation into standard notation. Maintain the same number of significant figures. a c b d ) Convert the following numbers from scientific notation into standard notation. Maintain the same number of significant figures. a ,800,000 c ,999.9 b d ) Report each of the following values to four significant figures. a c. 42, b or d or UNITS 18.) Describe how the terms length, mass, temperature, and volume can apply to a glass of water. a. Length: The height or diameter of the glass can be described by a length (use a ruler). b. Mass: The glass of water s mass (~ weight ) can be described by putting it on a balance. c. Temperature: The temperature of the water (or glass) can be described by using a thermometer. d. Volume: The volume can describe how much three-dimensional space the water occupies. 19.) Which is a larger quantity in each pair? a. 50 cl or 50 L b. 6 km or 6 m c. 7.5 mg or 7.5 g d. 21 ml or 21 kl 20.) Which quantity in roughly the width of a Sharpie pen? a. 1.0 mm b. 1.2 cm c g d m Page 3

4 DIMENSIONAL ANALYSIS For the problems in this section, use the equation sheet given in lecture. Some conversions need to be obtained from memory. Show your work using the dimensional analysis method, including units on all intermediate steps. 21.) Perform the following conversions. a. How many meters are in mm? mm -### 66 = 21.9 m b. How many liters are in 5.90 gallons of water? 5.90 gal!.5) = 22.3 L 22.) Perform the following conversions. a. How many grams are equal to kg? kg -### = 813,600 g or g b. How many miles tall is the tallest building in Chicago, the Willis Tower (formerly the Sears Tower), which rises to 1451 feet? 1451 ft - 6:9; = miles 0")# <= 23.) Perform the following multi-step conversions. a. How many millimeters are in 30.8 cm? cm -## >6 -### 66-6 = 308 mm b. How many seconds are in 2.5 hours? /# 6:? 2.5 hr /# 4;> - 6:? = s (which is 9000 s to 2SF) Page 4

5 24.) Perform the following multi-step conversions. a. How many kiloliters are in quarts of oil? qt #05 B= - 87 = kl -### 7 (5 SF) (4 SF) (exact) b. How many feet are in 7.77 km? - 6: 7.77 km -./#' 86 0")# <= - 6: = 25,500 ft 25.) Your chemistry textbook has a mass of 5.79 lbs. What is the mass of your textbook in grams? 5.79 lbs %0!./. - 9C = g or 2,630 g 26.) How much does a carat diamond weigh in grams? A carat is exactly equal to 200 mg carat "## 6. - >2A2= -. -### 6. = g 27.) A pair of shoes costs $55.50 (tax included) in Canada on December 19, Given the exchange rate at the time ($1 US = $1.33 Canadian dollars) how many US dollars does the pair of shoes cost? $- EF 1G992A4 $55.50 Canadian dollars $-.!! H2?21:2? 1G992A4 = $ 41.7 US dollars 28.) The moon is 239,000 miles away from the surface of the Earth. How many seconds would it take light from a flashlight to reach the moon, if the light is traveling m/s? -./#' ,000 miles - 6: -### ".'') I -# J 6 = 1.28 s Note: see your instructor if you are not getting this answer; the problem may be how you are typing the exponent into your calculator. Page 5

6 DENSITY CONCEPTS 29.) Is each statement true or false? a. A cubic centimeter is exactly equal to 1 milliliter. True b. Density is constant for a substance and doesn t depend on how much there is. True c. An object with a density greater than 1 g/ml will float on water. False (will sink) d. The density of aluminum is 2.7 g/ml. This means that 2.7 g of aluminum occupies 1 ml volume. True 30.) A piece of plastic is placed into a cylinder containing layers of liquids A, B and C. The plastic rests between liquids B and C as shown in the diagram. Are the following statements true or false? a. The plastic is less dense than liquid A. False b. The plastic is denser than liquid B. True c. The plastic is less dense than liquid C. True d. If a larger piece of plastic were used, it s possible it might sink to the bottom of liquid C. False (density is a constant) 31.) A graduated cylinder contains gasoline (d = 0.70 g/cm 3 ) and water (d = g/cm 3 ), as shown below. An object is placed into the graduated cylinder. At what position (A-E) will the object come to rest if: a. The object s density is 0.30 g/cm 3 Position A b. The object s density is 0.85 g/cm 3 Position C c. The object s density is g/cm 3 Position D Gasoline d = 0.70 Water d = position A position B position C position D position E 32.) A balance containing block A and block B on different sides comes to rest as shown in the figure below. Based on the figure, which block is denser? Briefly explain your answer. A B The blocks have the same apparent volume, but block B is heavier (has more mass). If V is the same, when mass increases, density increases. Therefore, block B is denser. Page 6

7 DENSITY CALCULATIONS 33.) An empty beaker contains 69.5 ml of glass and has a mass of g. What is the density of the glass? d = -5!.)/0. /'.0 67 = 2.50 g/ml 34.) A flat, rectangular sheet of copper has dimensions of 5.20 cm, cm, and cm. It has a mass of kg. What is the density of the copper (in g/cm 3 )? V = (5.20 cm)(6.054 cm)( cm) = 18.1 cm 3 m = kg -### = 163 g -/!. d = = 9.01 g/cm3 -).- >6K OR do it all in one step: d = #.-/! 8.( LMMM N L ON ) = 8.99 g/cm3 (0."# >6)(/.#0% >6)(#.05/" >6) Note: I am OK that you get slightly different numbers based on how you approached this problem (with rounding). Technically you shouldn t round until the end if you are not mixing operations, (8.99 number is more correct), but I am more lenient with multi-step problems. 35.) Find the density of a 225 mg sample of gas that occupies 2.50 cm mg -. -### 6. = g d = #.""0. = g/cm3 ".0# >6K 36.) Find the density of a 125 ml block of wood that has a mass of 0.14 pounds lb %0!./. - 9C = 64 g d = /%. = 0.51 g/ml -" ) Find the mass of copper that has a volume of 5.78 cm 3. (The density of copper is 8.96 g/cm 3.) 5.78 cm 3 ).'/. - >6 K = 51.8 g 38.) Find the volume of 2.06 g of bronze. (The density of bronze is 7.70 g/ml.) 2.06 g - 67 = ml 5.5#. 39.) How many milligrams of iron are in a pure iron nail with a volume of 0.88 ml? (The density of iron is 7.87 g/cm 3.) 0.88 ml 5.) ### = 6,900 mg Page 7

8 40.) How many liters of Styrofoam (density = g/ml) have a mass of 25,000 g? 25,000 g - 67 #.#0" ### 67 = 480 L 41.) A sample of steel with a mass of 52.4 g is placed into a graduated cylinder containing 75.0 ml of water. The water level rises to 81.7 ml. Calculate the density of the steel. m = 52.4 g 75.0 ml 81.7 ml V steel = 81.7 ml 75.0 ml = 6.7 ml d = 0".%. = 7.8 g/ml / ) Cork has a density of 0.24 g/ml. If you have an oddly shaped piece of cork, why can you not use the water displacement method (similar to the previous problem) to find the volume of the cork? To use the water displacement method, the object has to sink, or be fully submerged by the water to accurately represent its total volume. The cork has too low a density, and it would float on water. 43.) The density of pure silver is 10.5 g/ml. If 5.25 g of pure silver is added to a graduated cylinder containing 11.2 ml of water, to what volume level will the water in the cylinder rise? 5.25 g - 67 = ml -#.0. V f = 11.2 ml ml = 11.7 ml 44.) Three uniformly sized balls of nickel are placed into a graduated cylinder containing 3.50 ml of water. The water level rises to 7.62 ml. Find the mass of EACH nickel ball. The density of nickel is 8.91 g/cm 3. V balls = 7.62 ml 3.50 ml = 4.12 ml 4.12 ml ).' = 36.7 g (all three) Each ball = 36.7 g / 3 = 12.2 g Page 8

9 LABORATORY MEASUREMENTS 45.) What are the lengths of each of these blocks? Use significant figures and units cm cm Block Block Block Length: 3.20 cm, 3.19 cm, 3.21 cm (any of these are acceptable: 2 past decimal) Block Length: 2.00 cm, 2.01 cm, 2.02 cm 46.) Make the following measurements using the appropriate number of significant figures and units. Then categorize each type of measurement. (cm) o C Measurement: 5.3 cm (or 5.4 cm) C 12.8 ml (or 12.7, 12.9 ml) Length, mass, volume, or temperature? Length Temperature Volume Page 9