Density Answers to the End of module questions

Transcription

1 IDS 101 Density Answers to the End of module questions 1. You are experimenting with the mysterious substance X. You carefully measure the mass of a uniform 2 ml sample of pure substance X. You slice it into two identical pieces with a volume of 1 ml each. You then measure the density of one of the pieces. a) You would find that the density of this 1 ml piece is (choose one): i) Less than the density of the 2 ml piece i The same as the density of the 2 ml piece Greater than the density of the 2 ml piece The density of a substance is not dependent on the size of the piece, so answer ii is correct. b) You then discover that substance X has the wonderful property that you can change its volume without changing its mass. You squish one of the 1 ml pieces down so that it has a smaller volume but still has its original mass. In the process, the density of this piece (choose one): i) Decreased i Stayed the same Increased iii is correct If the mass of the object is the same, but the volume decreased, the density would increase. c) You then take the other 1 ml piece of substance X and roll it out into a large flat sheet. The sheet still has a volume of 1 ml, but now has a much larger surface area. In the course of rolling out this large flat piece, the density of this piece (choose one): i) Decreased i Stayed the same Increased ii is correct- if the mass and the volume stayed the same, the density is the same. Changing the surface area does not change the density.

2 2. You are on an oceanography cruise that has taken some water samples of fresh water from a river and some water from Puget Sound. Unfortunately, the samples were not labeled properly so we can t tell which samples are the salt water and which are the freshwater. We do not want to open the containers for fear of contamination, so let s use the density of the water as a way to tell them apart. If the containers are exactly one liter and we ignore the weight of the plastic in the bottles and the lids, what would be the mass of the freshwater samples if the density of freshwater is about 1000 kg/ m? If saltwater is about 1021 kg/ m, what will be the mass? 1 liter = 1000 ml= 1000 cm 1000Kg 1000cm cm = 1021Kg 1000cm 1m cm = 1Kg 1.021Kg. You have a block of unknown metal it is heavy, it looks like gold, could it be gold? If it is gold, the density should be 19. grams per cubic cm. When you put the metallic block into a graduated cylinder it raises the water level 12 ml. What should the mass of the block be, if it is gold? Density = mass/volume 12 ml of water displaced = 12 cm Mass = volume X density = 12 cm x 19. g/cm = 21.6 grams 4. In a previous class we collected the data for the mass and volume of various metals shown in the graph on the last page of this handout. You will be asked to refer to this graph in the questions that follow. a. Use the graph to find the mass of a piece of copper with a volume of 14 ml. Explain in words how you found the answer. There are many ways to do this. One way is to use the trend line for copper and find the mass value that corresponds to a volume of 14 ml. You could also use the equation of the trend line y = 8.55x and calculate the value of y for x= 14 ml. Either way, your answer should be close to 120 grams. b. Use the graph to find the volume, in cm, of a piece of aluminum with a mass of 50 g. Explain in words how you found the answer. Once again, use the trend line and read off the value of the volume for a mass of 50 g. Or, use the equation of the trend line, y = 2.78x. Now solve for x, with y = 50 g. Either way, your answer should be close to 18 cm.

3 c. Imagine that you have been handed two blocks of metal that have the exact same dimensions. The blocks have been painted black so that they look identical. If you were told that one block was copper and one was zinc, how would you determine which was which? Explain how your graph helps you answer this question. The graph tells you that copper (steeper trend line) has a greater density than zinc. Therefore the mass with the greater mass will be made of copper since M= D V. The graph shows that for a given volume (pick any number you wish), the mass value for zinc will be less than for copper. d. Imagine that you have been handed two blocks of metal that have the exact same mass. The blocks have been painted black so that they look identical. If you were told that one block was lead and one was aluminum, how would you determine which was which? Explain how your graph helps you answer this question. Once again, the graph tells you that lead (steeper trend line) has a greater density than aluminum. The graph shows that for a given mass (pick any value you wish), aluminum occupies a greater volume than lead. 5. In an experiment to investigate sinking and floating behavior, four solid objects (solids # 1, 2, and 4) are tested using three different liquids (liquids A, B and C). The results are shown below: i) Solid # 1 sinks in all three liquids Solids #2 floats in all three liquids i Solid # sinks in Liquid B but floats in liquids A and C. iv) Solid #4 sinks in liquids B and C, but floats in liquid A Based on this information, rank the three liquids and four solids in order of increasing density. Explain your reasoning. DENSE NOT SO DENSE solid #1 liquid A solid #4 liquid C solid # liquid B solid #2 Reasoning: Solid #1 sinks in all liquids and no other solid does, so #1 is the most dense. Most solids float on liquid A, so they are not as dense as liquid A. The only thing that sinks in liquid A is solid #1, so liquid A is slightly less dense than solid #1. Solid #4 sinks in the other liquids but floats on liquid A, so it is next in density. Solid #4 sinks in liquid C but # and #2 float on it, so liquid C is next in density.

4 Solid # only sinks in liquid B and floats in liquid C, so it is next in density. Only solid #2 floats on liquid B, so liquid B is second to lowest in density. Solid #2 floats on everything to it is the least dense. 6. In the table below we have listed five solid compounds and four liquids. We will put a sample of each solid in each liquid. Please help us predict which ones will float and which ones will sink. Place an X in the spaces for the solids that will float and predict the percentage of the solid that will be above the liquid. (For example coal will float in water and 17% of the coal will be above the surface of the water. This is an important process because this is how we separate coal from sandstone in mining!) water (1.0 g/cm ) coal (0.8 g/cm ) X (17%) alcohol salt water brine mercury (1.6 (0.79 g/cm ) (1.2 g/cm ) g/cm ) sink X (1%) X(94%) basalt (.0 g/cm ) beeswax (0.96 g/cm ) iron (7.8 g/cm ) magnesium (1.7 g/cm ) sink sink sink X(78%) X(4%) sink X(20%) X(9%) sink sink sink X(4%) sink sink sink X(88%) 7. Along the eastern part of North America, the Appalachian Mountains were formed more than 250 million years ago as North America and Africa converged to form a large supercontinent called Pangaea (more about this in IDS 102!). The rate of erosion for mountain ranges is such that the Appalachians should have been eroded many years ago. Using isostasy, suggest a reason why we still see the Appalachians today assuming the rates of erosion in the past were equivalent to today s rates. Isostasy is the application of buoyancy to the Earth s crust. The erosion of the Appalachians could be compared to removing the top part of an ice berg. The ice berg would rise to be in balance. The same has happened with the Earth s crust. As erosion has stripped away the mountains, the crust has uplifted to be in balance.

5 Mass (g) copper aluminum zinc lead Mass as a Function of Volume for Various Metals y = x y = 8.55x y = x Volume (ml)