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Density and Significant Figures in Calculations. Practice Problems. 1) A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?. Given: Volume = 15.0 mL Mass = 40.5 g Density = Density = 40.5 g = 2.70 g/mL 15.0 mL.

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## Density and Significant Figures in Calculations

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**Density and Significant Figures in Calculations**Practice Problems**1) A block of aluminum occupies a volume of 15.0 mL and**weighs 40.5 g. What is its density? Given: Volume = 15.0 mL Mass = 40.5 g Density = Density = 40.5 g = 2.70 g/mL 15.0 mL**2) Mercury metal is poured into a graduated cylinder that**holds exactly 22.5 mL. The mercury used to fill the cylinder weighs 306.0 g. From this information, calculate the density of mercury. Given: Volume = 22.5 mL Mass = 306.0 g Density = Density = 306.0 g = 13.6 g/mL 22.5 mL**3) What is the weight of the ethyl alcohol that exactly**fills a 200.0 mL container? The density of ethyl alcohol is 0.789 g/mL. Given: Volume = 200.0 mL Density = 0.789 g/mL Density = D V = M or M = D V Mass =(0.789 g/mL)(200.0mL) = 157.8 g 158 g**4) A rectangular block of copper metal weighs 1896 g. The**dimensions of the block are 8.4 cm by 5.5 cm by 4.6 cm. From this data, what is the density of copper? Given: Mass = 1896 g Volume = 8.4cm x 5.5cm x 4.6cm = 212.52cm3 = 210 cm3 Density = Density = 1896 g = 9.028571429 g/cm3 210 cm3 = 9.0 g/cm3**5) A flask that weighs 345.8 g is filled with 225 mL of**carbon tetrachloride. The weight of the flask and carbon tetrachloride is found to be 703.55 g. From this information, calculate the density of carbon tetrachloride. Given: Mass flask/carbon tetrachloride = 703.55 g Mass flask= 345.8g Mass carbon tetrachloride = 703.6g - 345.8g = 357.8g Volume = 225 mL Density = Density = 357.8 g = 1.5902222222 g/mL 225 mL= 1.59 g/mL**6) Calculate the density of sulfuric acid if 35.4 mL of the**acid weighs 65.14 g. Given: Volume = 35.4 mL Mass = 65.14 g Density = Density = 65.14 g = 1.840112994 g/mL 35.4 mL= 1.84 g/mL**7) Find the mass of 250.0 mL of benzene. The density of**benzene is 0.8765 g/mL. Given: Volume = 250.0 mL Density = 0.8765 g/mL Density = D V = M or M = D V Mass = (0.8765g/mL)(250.0mL) = 219.125g =219.1g**8) A block of lead has dimensions of 4.50 cm by 5.20 cm by**6.00 cm. The block weighs 1587 g. From this information, calculate the density of lead. Given: Mass = 1587 g Volume = 4.50cm x 5.20cm x 6.00cm = 140.4cm3 = 140. cm3 Density = Density = 1587 g = 11.33571429 g/cm3 140. cm3 = 11.3 g/cm3**9) 28.5 g of iron shot is added to a graduated cylinder**containing 45.50 mL of water. The water level rises to the 49.10 mL mark, From this information, calculate the density of iron. Given: Mass = 28.5 g Volume = 49.10 mL - 45.50 mL = 3.60 mL Density = Density = 28.5 g = 7.91666666667 g/mL 3.60 mL= 7.92 g/mL**10) What volume of silver metal will weigh exactly 2500.0 g?**The density of silver is 10.5 g/cm3. Given: Mass = 2500.0 g Density = 10.5g/cm3 Density = D V = M and then V = M/D Volume = 2500.0 g = 238.095238095 cm3 10.5g/cm3= 238 cm3**Density Problem Set (#2)**Practice Problems**1) Iron has a density of 7.87 g/ cm3. What is the mass of**26.3 g of Fe?The answer is the mass = 26.3 grams but if you assumed there was a typo…. Given: Mass = 26.3 g Density = 7.87 g/cm3 Density = V = M/D Volume = 26.3 g = 3.34180432020 cm3 7.87g/cm3= 3.34 cm3**2) If 1.00 km3 of air has a mass of 1.2 billion kg, what is**the density of air? Given: Volume = 1.00 km3 Mass = 1.2 x 109 kg Density = Density = 1.2 x 109 kg = 1.2 x 109 kg/km3 1.00km3**3) Aluminum, because of its light density and strength, has**been used for making aircraft. It has a density of 2.70 g/ cm3. Magnesium has similar properties and it has a density of 1.74 g/ cm3. What would the difference in mass if 1000 cm3 of magnesium are used instead of 1000 cm3 of aluminum? AluminumMagnesium Given: Given: Density = 2.70 g/ cm3 Density = 1.74 g/ cm3 Volume = 1000 cm3 Volume = 1000 cm3 Density = M Density = M V V M = D V M = D V M = (2.70 g/ cm3)(1000 cm3) M = (1.74 g/ cm3)(1000 cm3) M = 2700 g M = 1740 g Difference in mass = 2700 g - 1740 g = 960 g**4) Find the density of gasoline if 9.00 dm3 have a mass of**6120 g. Given: Volume = 9.00 dm3 Mass = 6120 g Density = Density = 6120 g = 680 g/dm3 9.00 dm3**5) The density of nitrogen gas is 1.25 g/dm3. What is the**mass of 1 m3 of nitrogen? Given: Density = 1.25 g/dm3 Density = DV = M 1.25 g 1,000 dm3 1m3 1250 g dm3 1m3**6) Illegal ivory is sometimes detected on the basis of**density. What is the density of a sample of ivory whose volume is 14.5 cm3 and whose mass is 26.8 g? Given: Volume = 14.5 cm3 Mass = 26.8 g Density = Density = 26.8 g = 1.848275862 g/ cm3 14.5 cm3 = 1.85 g/ cm3**7) What is the density of a rectangular piece of concrete**5.00 cm x 10.0 cm x 23.0 cm having a mass of 3.22 kg? Given: Volume = (5.00cm)(10.0cm)(23.0cm) = 1150cm3 Mass = 3.22 kg Density = Density = 3.22 g = 0.00280 g/ cm3 1150 cm3**8) Vanadium hardens steel. Vanadium steel is used in armor**plate on tanks, for example. If its density is 5.96 g/cm3, a cubic meter would have a mass of how many kg? Given: Density = 5.96 g/cm3 Volume = 1m3 D = D V = M 5.96 g 1,000,000 cm3 1m3 5,960,000 g cm3 1m3**9) Hydrogen has a density of 0.089 g/dm3 whereas helium has**a density of 0.178 g/dm3, about twice that of hydrogen. What is the mass of helium in a 10,000 m3 blimp? Given: Density = 0.178 g/dm3 Volume = 10,000m3 D = D V = M 0.178 g 1,000 dm3 10,000m3 1,780,000 g dm3 1m3 M =**10) The diameter of the sun is estimated to be about 865,000**miles. Astronomers also estimate its average density to be 1.4 g/cm3. What is its mass in kilograms? Remember the volume formula for a sphere. Given: Density = 1.4 g/cm3 Diameter = 865,000 mi so Radius = 432,500 mi V = 4 π r3 = 4 π(69,604,128,000cm)3 3 3 V = 1.41251673 x 1033 cm3 D = M so M = DV = (1.4 g/cm3)(1.41251673 x 1033 cm3) V M = 1.977523422 x 1033 g 432500mi5280 ft 12 in 2.54cm 69,604,128,000cm 1 mi 1ft 1 in R =**METRIC CONVERSION WORKSHEET**Answers**How many seconds are there in three (3) days?**3 days 24 hrs 60 min 60 sec = 2,592,000 sec 1 day 1hr 1 min**A hydrogen electron moves at 2000 km/sec. Convert that to**ft/sec. 2000 km 1,000m 100 cm 1in 1ft 1km 1m 2.54 cm 12 in 2000km = 6561679.79 ft Answer = 6561679.79 ft/sec**3. 82 F is what in C?**Given: Temp. = 82 F C = ( F - 32 ) 5/9 C = ( 82 - 32 ) 5/9 C = (50) 5/9 = 250/9 = 27.77777777 C = 28 C**4. Your new living room has the dimensions of 14 ft. by 16**ft. The tile that you want to put down is on sale, but the store has only 15m2 of tile. Will this be enough to cover your living room floor? Given: Dimensions = 14 ft x 16 ft 14 ft 12 in 2.54 cm 1m = 4.2672 m = 4.3 m 1ft 1in 100cm 16 ft 12 in 2.54 cm 1m = 4.8768 m = 4.9 m 1ft 1in 100cm Tile needed = (4.3 m) (4.9 m) = 21.07 m2 NO**5. The density of magnesium is 1.74 g/cc. What is the**volume of a 42g piece of magnesium? Given: Density = 1.74 g/cc Mass = 42 g D = M So V = M V D V = 42g 24.13793103 cc = 24 cc 1.74 g/cc**Convert 876,000,000,000 and .00000000000457 into scientific**notation. 876,000,000,000 = 8.76 x 1011 .00000000000457 = 4.57 x 10-12**7. How many kilometers are in 27.2 miles?**27.2 mi 5280 ft 12 in 2.54 cm 1m 1 km = 43.7741568 km 1mi 1ft 1in 100 cm 1,000m = 43.8 km Note: The number of significant figures is from the 27.2 miles (which has 3 significant figures). We usually do not worry about the number of significant figures in the conversion units.**8. The doctor says that I need to give my child 3.5cc of**cough medicine. How many tablespoons will that be? 3.5 cc 1 Tbsp = 0.236646382 Tbsp = 0.24 Tbsp 14.79cc Note: 1 Tbsp = 14.79 mL but since cc, cm3, mL are all the same amount, the conversion can be written as… 1 Tbsp = 14.79 cc Also the significant figures were based on the unit to be converted, 3.5 cc which has 2 significant figures.**9. You have to be 1.4 meters tall to ride the roller**coaster. How many meters tall are you, and will you be able to ride the roller coaster? (your height in inches) 2.54 cm 1m = (your height in m) 1in 100cm compare with 1.4 m to answer the question**All I have are metric sockets (mm). The bolt takes a 1/2**inch socket. What is the closest metric socket? 0.5 in 2.54 cm 10 mm = 12.7 mm 1 in 1cm so the choice would be the 13mm socket

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