Goal: To measure the density of an irregular solid.
This requires that you measure two properties directly (mass and volume), then compute the density as mass/volume. You will need to construct an equal-arm balance capable of measuring 1 gram differences, and a way to measure volume within 1 ml.
Making the scale
Materials: How you build your balance depends largely on the materials you have available. BE SURE THAT YOUR PARENTS AGREE TO YOUR USE OF ALL MATERIALS! The possibilities suggested should stimulate your imagination: improve on them and don't limit yourself to them.
NOTE: You will need to measure some of your containers, so be sure that the scale you build will handle the mass and shape of a small beaker as well as a test tube.
You will need
- the arm: a straight length of wood or metal, lightweight and rigid. Possibilities: a ruler or yardstick.
- a pivot mechanism: this will take the weight of the arm at the center; the arm must move around this point. Possibilities: suspend the arm on a needle/nail passed through a hole at the center and near the top edge of the arm.
- a support for the pivot: this keeps your pivot from moving and puts it high enough that your arm and pans swing freely above the table. Possibilities: a used milk carton of which you can fasten or embed your nail/needle pivot; a Styrofoam cup which you can put on top of a stack of books. Put something heavy in the bottom of the carton or cup to keep it from tipping over.
- a calibration weight: this should be something on one arm which you can slide along the arm to make the balance read zero when your pans are empty. It will compensate for irregularities in weight of the arm and pans. Possibilities: a bent paper clip from which you can suspend rubber bands or other small counterweights.
- weighing pans: these are lightweight containers fastened to the each end of the arm. In one you will place calibrated weights, in the other you will place the object(s) to be weighed. Possibilities: flat lids, suspended from the ends by thread, fishing line or wire; paper cones or cups tacked to the ends of the arms.
- pointer: this extends at right angles from the pivot point. When it is vertical, your pans are balanced. It needs to be lightweight and rigid. Possibilities: coffee stirring straw, small wooden skewer, taped to the arm at the pivot point.
- calibrated arc: this allows you to measure how far from true vertical your pointer is. You will need to place the arc (which should describe part of the circle made by the pointer when the scale is oscillating on its pivot) behind the pointer. How can you center the arc properly?
- weights: These are calibrated masses which you will use to counter the mass of the objects you measure. You will need to find or make masses to measure .1, 1 and 5 grams. Possibilities: a 1990 or later nickel weighs 5 grams when newly minted. How can you make a set of 1 gram standards? Some medicine tablets are pure substance: 500 mg of pure aspirin makes a good .5 g mass.
Making a Graduated Cylinder and a Graduated Pipette
- equal-arm balance
- tall, narrow jar for cylinder
- paper cup
- calibrated weights such as nickels
- eyedropper and rubber bulb
If you use a cylinder you make yourself, you will need to calibrate it. Clean and dry a tall, narrow, cylindrical jar (such as a fancy olive jar or spice jar). The sides of the jar must be straight (the inside diameter can not change).
Put a small paper cup on your scale and zero the scale by adding enough weights to offset the mass of the cup. Add 10 grams of water to the cup (use an eyedropper to add or remove water until you get it right!).
Transfer the water from the cup to your cylinder jar and mark the bottom of the meniscus. [Use a permanent marker that can write on glass, an etcher, or fasten a piece of tape to the side of the jar and write on it.] This is ten milliliters: remember that 1 gram of water at 20 degrees Centigrade at sea level is 1 milliliter. Make 9 marks evenly between the bottom of the jar and your 10 ml mark and label them: these are 1 ml each.
You can make a graduated pipette by drawing 1 ml into your eyedropper and marking it (be sure there are no bubbles in the water), then marking the eyedropper with 10 even divisions. This will allow you to measure .1 ml amounts.
NOTE: You may use plastic containers and eyedroppers only for neutral solutions. Be sure you have heat-resistant glassware for any experiments involving acids or bases, or any time you will be heating the containers.
Using the Calibrated Cylinder
To read your graduated cylinder, place a something with a solid color behind the top level of the liquid (if your commercial cylinder has a reading slide, move it into position), and move so that you are looking at the cylinder at a level with the surface of the liquid. This will help you see how the water level lines up with the calibration markings.
Notice that the water surface is curved, with the center lower than the sides. Surface tension in the water causes it to climb the sides of the cylinder. Most liquids form this curved surface, called a meniscus, with the graduated cylinder. Liquids such as water form a concave (curved downward) surface; on such liquids, use the lowest part of the meniscus to determine the amount of liquid in the cylinder. Some liquids (mercury, for example) form a convex (upward curved) surface in a cylinder. Use the highest point of the meniscus for convex-surface liquids.
Density Measurement Materials
You will need
- Graduated cylinder.
- An equal-arm balance.
- Irregular solids, including at least some metals (marbles, stones, nails, paper clips) which can fit into the graduated cylinder.
Density Measurement Procedure
This procedure rests on the fact that when you put a solid in water, it displaces a volume of water equal to its own volume. Using this procedure, we can measure volume directly, rather than measuring dimensions and calculating the volume. Pure substances have a characteristic density.
- Weigh your irregular solid on your scale, and determine the mass as accurately as possible. If you think your scale is accurate to .1 gm, then record the mass rounded to the nearest tenth of a gram.
- Place enough water in your graduated cylinder to cover your irregular solid. Record the volume of water.
- Add the irregular solid to the cylinder. Be sure that it is submerged! Record the new volume of water. The difference is the volume of the solid.
- Calculate the density of the solid from your measurements of mass and volume.
- Repeat this procedure for another irregular solid, preferably made out of a different material from the first.
Your lab should include
- A description of your scale. Estimate its accuracy.
- A description of your graduated cylinder, if you made it yourself. Estimate its accuracy.
- An account of the density measurements and calculations for at least two different objects or sets of objects, one of which should be metal. Be sure that your calculations follow the rules for significant figures based on the accuracy of your measurements!
- An account of how you could use the density measurements to determine the metallic composition of an unknown object.
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