Intro Math
Use Dimensional Analysis to solve the following problems. Show all work. Every number must have a unit. Round to the correct number of significant digits. Circle the answer.
Table of Conversion Factors
Length1 nautical mile = 6076.11549 feet
1 standard mile = 5280 feet
1 inch = 2.54 cm
1 league = 5280 yards
1 cable = 120 fathoms
1 fathom = 6 feet
1 degree = 69.047 miles
1 hand = 4 inches
1 foot = 12 inches
1 meter = 39.36 inches / Volume
4 gills = 1 pint
2 pints = 1 quart
1 liter = 1.0567 quarts
1 bushel = 4 pecks = 32 quarts
1 gallon = 4 quarts / Mass
1 pound = 453.6 grams
1000milligrams=1 grams
1 kg = 1000 grams
Time
1 year = 365.24 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Moles
1 mole = 6.02x1023 atoms
1 mole = 22.41 liters
1)A student is 17.5 years old. Convert her age to seconds. 5.52 x 108 seconds
2)A student lives 1.00 miles from school. Convert this distance to centimeters. 1.61 x 105 cm
3)A person’s weight is 154 pounds. Convert this to milligrams. 6.99 x 107 mg
4)An aspirin tablet contains 325 mg of acetaminophen. How many grains is this equivalent to? (1 gram = 15.432 grains) 5.02 grains
5)Each liter, L, of air has a mass of 1.80 grams. 2.5 x103 kg of air would equal how many L?1.4 x 106 L
6)16.0 grams of food contain 130. calories. How many grams is equivalent to 2150 calories?2.65 x102g
7)The cost of 1.00 Liter of gas is 98.4 cents. How many dollars will 12.00 gallons cost?44.69 dollars
8)Light travels 186,282 miles / second. How far is a light year in meters? (1 light year is the distance light travels in one year.)9.46 x 1015meters/year
9)1 mole of Si atoms contains 6.02 x1023 atoms. This many Si atoms has a mass of 28.1 g. How many atoms of Si are contained in a computer chip with a mass of 38.02 x 10-3 g?8.15 x 1020atoms
10)Your cruise ship is leaving for a 610.-league adventure. How many nautical miles is this?1590 nautical miles
11)The ship hits a giant squid and sinks. Later the ship is discovered at 38 fathoms depth under water. Convert to meters. 70. meters
12)Fortunately you survived! You are stranded on a deserted island that is located 12.5 degrees north of the equator. How many kilometers is this from the equator?1390 km
13)You ration yourself to 32 gills of fresh water a day. How many liters is this?3.8 L
14)To reach the top of a palm tree for a coconut you will have to climb 7.4 meters.How many hands is this? 73 hands
15)The island is rich with hot chile peppers. You can collect 1.6 pecks a day. How many liters could you collect in 1 week? 85Liters/ week
16)Later, a tidal wave washes over the island and you find Leonardo DiCaprio lying on the beach. You tell him your story and he is willing to pay you 150,000 “clams” for the movie rights. How many dollars is this? (1.7 clams = 5 cents.) Should you sell?$4400
17)Bonus:A car’s engine is rated at 3.60 Liters (volume in the cylinders). How many cubic inches is this? 1 L is a cube that is 10 cm on a side. 1 inch = 2.54 cm.
18)2000 mg = ______g
19)5 L = ______mL
20)16 m = ______mm
21)104 km = ______m
22)198 g = ______dag
23)2500 m = ______Hm
24)480 cm = _____ m
25)75 mL = _____ L
26)65 g = _____ mg
27)50 cm = _____ m
28)6.3 cm = _____ mm
29)8 Hm = _____ cm
30)120 mg = _____ g
31)24900 kg = ____ dag
32)123 cm = ______mm
33)723 mg = ______g
34)3770 ml = ______L
35)37 g = ______kg
36)12.3in = ______cm
37)32.9cm = ______in
38)3.2m = ______in
39)237°C =______K
40)12°C =______K
41)327K= ______°C
42)165K =______°C
43)35mL=______dL
44)950g=______kg
45)275mm=_____cm
46)1,000.L=______kL
47)1,000mL=______l
48)4.5x103mg=_____g
49)25cm=_____mm
50)0.005kg=_____dag
51)0.075m=_____cm
52)15.32g=_____mg
53)3.0hrs=_____s
54)0.035mg=_____cg
55)5.50kg=_____lbs
56)2.5yds=______in
57)1.3yrs=______hr
58)3.0moles=______molecules
59)2.5x1024molecules=______moles
60)5.00moles=_____liters
61)100.L=_____moles
62)50.L=____molecules
63)5.00x1024molecules=_____L
64)7.51x103mL=______L
Calculate the number of moles in the following.
65)0.039g of palladium 3.7 x 10-4
66)8200g of iron 150
Calculate the mass in grams of each of the following amounts.
67)1.002mol of chromium 52.10
68)550mol of aluminum 15000
Calculate the number of atoms in each of the following amounts.
69)17.0mol of germanium 1.02 x 1025
70)0.6144mol of copper 3.700 x 1023
Calculate the number of moles in each of the following quantities.
71)6.022 x 1024 atoms of cobalt 10.00
72)1.06 x 1023 atoms of tungsten 0.176
Calculate the number of atoms in each of the following masses.
73)0.0082g of gold 2.5 x 1019
74)812g of molybdenum 5.10 x 1023
Calculate the mass of each of the following.
75)8.22 x 1023 atoms of rubidium 117
76)9.96 x 1026 atoms of tellurium 211000
77)How many atoms are in 5.80moles Sulfur? 3.49x1024
78)How many grams in 1.5 moles Nickel? 88
79)How many moles are in 108g boron? 9.99
80)How many atoms are in 19.62g helium? 2.95x1024
81)How many grams are in 11.3moles sodium? 260
82)How many grams in 9.0x1023atoms Selenium? 120
83)How many moles in 2.4x1024atoms Phosphorus? 4.0
84)How many moles are in 96g calcium? 2.4
85)How many grams are in 12.25 moles lithium? 85.0
86)How many grams in 4.2x1025atoms gold? 1.4x104
87)How many atoms are in 7.93grams Aluminum? 1.77x1023
88)How many moles in 1.17x1024atoms Cobalt? 1.94
89)How many moles in 3.6x1023atoms Carbon? 0.60
90)How many atoms are in 17.30moles Potassium? 1.042x1025
91)How many moles are in 64 grams Copper?1.0
92)How many atoms are in 6.85grams Zinc? 6.31x1022
93)How many grams in 4.72x1025atoms Magnesium? 1910
94)How many grams in 3.13x1022atoms Manganese? 2.86
95)How many atoms are in 8.230 moles Titanium? 4.956x1024
96)How many atoms are in 4.92grams Silicon? 1.05x1023
97)The density of silver is 10.5 g/cm3. Find the mass that occupies 965 cm3. 1.01x104g Ag
98)A 2.75 kg sample of a substance occupies a volume of 250.0 cm3. Find its density in g/cm3 (convert kgg). 11.0g/cm3
99)Oxygen gas has a density of 0.00134g/mL. Find the volume of 250.0g O2. 1.87x105mL O2
100)Find the volume that 35.2 g of carbon tetrachloride (CCl4) will occupy if it has a density of 1.60 g/mL. 22.0 mLCCl4
101)The density of ethanol is 0.789 g/mL at 20oC. Find the mass of a sample that occupies 150.0 mL at this temperature. 118g ethanol
Find the volume of 30.0 g of each of the following acids:
102)hydrochloric acid, HCl, density = 1.164 g/mL 25.8mL HCl
103)sulfuric acid, H2SO4, density = 1.834 g/mL 16.4mL H2SO4
104)nitric acid, HNO3, density = 1.251 g/mL 24.0mL HNO3
105)A rectangular block of lead measures 2.00cm x 3.00cm x 4.50cm. If the density is 11.34 g/cm3, calculate the mass of the block. 306g Pb
106)A cube of gold has a side length of 1.55 cm. If the sample is found to have a mass of 71.9 g, find the density of Au. 19.3g/cm3Au
107)An irregularly-shaped sample of aluminum has a mass of 43.6g. Water displacement is used to find its volume. The initial volume is 25.5 mL. After the sample is added, the water level rose to 41.7 mL. Find the density of the Al sample in g/cm3. (Remember:1 mL = 1 cm3) 2.69g/cm3Al
108)A gas has a mass of 3175g and takes up enough space to fill a room that is 200.cm x 200.cm x 500.cm. What is the gas’s density? What gas is it?
Gas / air / helium / hydrogen / nitrogen / oxygen / carbon dioxideDensity
(g/cm3) / 0.0013 / 0.0001588 / 0.00009 / 0.001251 / 0.0013 / 0.00195