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Density and Significant Figures in Calculations

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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  1. Density and Significant Figures in Calculations Practice Problems

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. Density Problem Set (#2) Practice Problems

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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 =

  22. 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 =

  23. METRIC CONVERSION WORKSHEET Answers

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. Convert 876,000,000,000 and .00000000000457 into scientific notation. 876,000,000,000 = 8.76 x 1011 .00000000000457 = 4.57 x 10-12

  30. 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.

  31. 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.

  32. 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

  33. 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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