Density Examples & Problems

Fifteen Examples

Example #1: A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?

Example #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.

Example #3: What is the mass of the ethyl alcohol that exactly fills a 200.0 mL container? The density of ethyl alcohol is 0.789 g/mL.

Example #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?

Example #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.

Example #7: Find the mass of 250.0 mL of benzene. The density of benzene is 0.8786 g/mL.

Example #8: A block of lead has dimensions of 4.50 cm by 5.20 cm by 6.00 cm. The block weighs 1591 g. From this information, calculate the density of lead.

Example #9: 28.5 g of iron shot is added to a graduated cylinder containing 45.5 mL of water. The water level rises to the 49.1 mL mark, From this information, calculate the density of iron.

Example #10: What volume of silver metal will weigh exactly 2500.0 g. The density of silver is 10.5 g/cm3.

Example #11: What is a Dord?

Example #12: A piece of copper foil has a mass of 4.924 g, a length of 3.62 cm, and a width of 3.02 cm. Calculate the thickness in mm, assuming the foil has uniform thickness.

Example #13: A golden-colored cube is handed to you. The person wants you to buy it for $100, saying that is a gold nugget. You pull out your chemistry text and look up gold's density and read that its density is 19.32 g/cm3. You measure the cube and find that it is 2.00 cm on each side, and weighs 40.0 g. What is its density? Is it gold? Should you buy it?

Example #14: Sapphire has a density of 3.98 g/cm3. The mass of gemstones is often measured in “carats,” where 1 carat equals 0.200 g. What is the volume (in cubic centimeters) of the 563.35 carat Star of India sapphire?

Example #15: Rather than end with another problem, I thought I'd post a link to some very nice density problems. The author starts with some standard density problems and then moves into several more complex density problems. Number 7 is a very good problem.


Probs #1-10

Problem #1: What mass of lead (density 11.4 g/cm3) would have an identical volume to 25.1 g of mercury (density 13.6 g/cm3)?

Problem #2: The density of pure aluminum is 2.70 g/cm3. 2.25 grams of pure aluminum is added to a graduated cylinder containing 11.20 mL of water. To what volume mark will the water level rise?

Problem #3: A 1.50 g piece of aluminum was rolled out into a thin sheet measuring 24.0 cm x 30.0 cm.

(a) Calculate the volume (density of Al = 2.70 g cm¯3
(b) Calculate the thickness of the piece of Al in mm

Problem #4: 'Copper' pennies actually contain very little copper. If a penny contains 92.276% of its total volume zinc and 7.724% of its total volume copper, what is its density? (d of Cu = 8.96 g/cm3; d of Zn = 7.14 g/cm3)

Problem #5: The element antimony has a density of 6.62 g cm¯3. Calculate the edge length in meters of a cube of antimony whose mass is 1.00 x 105 kg.

Problem #6: Iron has a density of 7.87 g/cm3. If 71.7 g of iron is added to 63.0 mL of water in a cylinder, to what volume reading will the water rise?

Problem #7: Suppose you are given two cylindrical rods, one aluminum and the other tin, with identical external dimensions. What fraction of the tin rod would have to be hollow in order to give the same average density for both rods? (The density of tin is 7.31 g/cm3 and for aluminum, it is 2.70 g/cm3.)

Problem #8: Osmium is one of the densest elements known. The standard density is 22.59 kg/L. What is the density in units of g/cm3?

Problem #9: A gold wire has a diameter of 1.000 mm. What length of this wire contains exactly 1.000 mol of gold? (The density of gold is 19.32 g cm¯3.)

Problem #10: The density of lead is 11.34 g/cm3. Which of the following contains the greatest mass of lead: 0.50 kg or 0.050 liter?


Probs #11-25

Problem #11: A cylindrical glass tube of length 27.75 cm and the radius 2.00 cm is filled with argon gas. The empty tube weighs 188.250 g. and the tube filled with argon weighs 188.870 g. Use the data to calculate the density of argon gas.

Problem #12: The density of silver is 10.50 g/cm3 and the density of benzene is 0.8786 g/cm3. What mass of silver will have the same volume as 15.55 grams of benzene?

Problem #13: Calculate the mass of copper in grams (density = 8.96 g/cm3) with the same volume as 100.0 grams of gold (density = 19.31 g/cm3)

Problem #14: Calculate the mass of zinc in grams (density = 7.14 g/cm3) with the same volume as 100.0 grams of aluminum (density = 2.70 g/cm3)

Problem #15: A spherical ball bearing has a radius of 8.50 mm and a mass of 2.315 g. Determine the density of the ball bearing in g/cm3.

Problem #16: 57.0 kg of copper is drawn into a wire with a diameter of 9.50 mm. What is the length of wire in meters? Cu density = 8.96 g/cm3.

Problem #17: In the United States, 'copper' pennies made since 1983 actually contain very little copper. If a penny contains 93.975% of its total volume zinc and 6.025% of its total volume copper, what is its apparent density? (density of Cu = 8.96 g/cm3; density of Zn = 7.14 g/cm3.)

Problem #18: Antarctica has an ice sheet covering 1.42 x 1018 cm2 and averaging 1.61 x 105 cm deep. Calculate the total mass if ice has a density of 0.92 g/cm3.

Problem #19: Object A is less dense than object B. If both objects are the same mass, what can be said about the volume of A as compared to the volume of B?

Problem #20: An ice cube with a volume of 45.0 mL and a density of 0.900 g/cm3 floats in a liquid with a density of 1.36 g/mL. What volume of the cube is submerged in the liquid?

Problem #21: Copper can be drawn into thin wires. How many meters of 34-gauge wire (diameter = 6.304 x 10¯3 inches) can be produced from the copper that is in 5.88 pounds of covellite, an ore of copper that is 66% copper by mass? (Hint: treat the wire as a cylinder. The density of copper is 8.96 g cm¯3; one kg weighs 2.2046 lb; 1 inch is 2.54 cm and the volume of a cylinder is πr2h)

Problem #22: A copper ingot has a mass of 2.15 kg. If the copper is drawn into wire whose diameter is 2.27 mm, how many inches of copper wire can be obtained from the ingot?

Problem #23: If the copper is drawn into wire whose diameter is 8.06 mm, how many feet of copper can be obtained from a 200.0 pound ingot?

Problem #24: A cube of copper was found to have a mass of 0.630 kg. What are the dimensions of the cube? (The density of copper is 8.96 g/cm3.)

Problem #25: Calculate the volume (in m3) of a 5,020 tonne iceberg. (1 tonne = 1,000 kg, the density of ice = 0.92 g/cm3)


Probs #26-45

Problem #26: A graduated cylinder is filled to the 40.00 mL mark with mineral oil. The masses of the cylinder before and after the addition of mineral oil are 124.966 g and 159.446 g. In a separate experiment, a metal ball bearing of mass 18.713 g is placed in the cylinder and the cylinder is again filled to the 40.00 mL mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g. Calculate the density of the ball bearing.

Problem #27: A calibrated flask was filled to the 25.00 mark with ethyl alcohol. By weighing the flask before and after adding the alcohol, it was determined that the flask contained 19.7325 g of alcohol. In a second experiment, 25.9880 g of metal beads were added to the flask, and the flask was again filled to the 25.00 ml mark with ethyl alcohol. The total mass of the metal plus alcohol in the flask was determined to be 38.5644 g. What is the density of the metal in g/mL?

Problem #28: A bar of magnesium metal attached to a balance by a fine thread weighed 31.13 g in air and 19.35 g when completely immersed in hexane (density = 0.659 g/cm3). Calculate the density of this sample of magnesium.

Problem #29: Brass is a zinc and copper alloy. What is the mass of brass in a brass cylinder that is 1.2 in long and a diameter of 1.5 in if the brass is made of 67% copper by mass and 33% zinc by mass? The density of copper is 8.94 g/cm3 and 7.14 g/cm3 of zinc? Assume brass varies linearly with composition.

Problem #30: The density of osmium is 22.57 g/cm3. If a 1.00 kg rectangular block of osmium has two dimensions of 4.00 cm x 4.00 cm, calculate the third dimension of the block.

Problem #31: A 15.8 g object was placed into an open container that was full of ethanol. The object caused some ethanol to spill, then it was found that the container and its contents weighed 10.5 grams more than the container full of ethanol only. What is the density of the object?

Problem #32: A sheet of aluminum foil measures 30.5 cm by 75.0 cm and has a mass of 9.94 g. What is the thickness of the foil?

Problem #33: The mass of a gold nugget is 84.0 oz. What is its volume in cubic inches? (Density of gold: 19.31 g/cm3; 435.6 g = 1.00 pound; 16.0 oz = 1.00 pound; 16.387 cm3 = 1.00 in3)

Problem #34: Gold can be hammered into extremely thin sheets called gold leaf. If a 204 mg piece of gold (density = 19.32 g/cm3) is hammered into a sheet measuring 2.4 feet by 1.0 feet, what is the average thickness of the sheet in meters?

Problem #35: How long is a 22.0 gram piece of copper wire with a diameter of 0.250 millimeters? Density = 8.96 g/cm3

Problem #36: How long is a copper wire with a diameter of 0.250 millimeters? The density of copper is 8.96 g/cm3 and the mass of the wire is 22.0 g.

Problem #37: A 12.0 cm long cylindrical glass tube, sealed at one end is filled with ethanol. The mass of ethanol needed to fill the tube is found to be 9.60 g. The density of ethanol is 0.789 g/mL. What is the inner diameter of the tube in centimeters?

Problem #38: A 23.200 g sample of copper is hammered to make a uniform sheet of copper with a thickness of 0.100 mm. What is the area of this sheet in cm2 given the density of copper to be 8.96 g/cm3?

Problem #39: A piece of copper foil has a mass of 4.924 g, a length of 3.62 cm, and a width of 3.02 cm Calculate the thickness in mm, assuming the foil has uniform thickness.

Problem #40: A 50.00 g block of wood shows an apparent mass of 5.60 g when suspended in water at 20.0 °C water (the density of water at 20.0 °C is 0.99821 g/mL). What is the density of the block?

Problem #41: What is the mass of a flask filled with acetone (d = 0.792 g/cm3) if the same flask filled with water (d = 1.000 g/cm3) weighs 75.20 gram? The empty flask weighs 49.74 g.

Problem #42: A container is filled with water at 20.0 °C, just to an overflow spout. A cube of wood with edges of 1.00 in. is submerged so its upper face is just at the level of water in the container. When this is done, 10.8 mL of water is collected through the overflow spout. Calculate the density of the wood.

Problem #43: A pycnometer is a device used to determine density. It weighs 20.578 g empty and 31.609 g when filled with water (density = 1.000 g/cm3). Some pieces of a metal are placed in the empty, dry pycnometer and the total mass is 44.184 g. Water is then added to exactly fill the pycnometer and the total mass is determined to be 54.115 g. What is the density of the metal?

Problem #44: Vinaigrette salad dressing consists mainly of oil and vinegar. The density of olive oil is 0.918 g/mL, the density of vinegar is 1.006 g/mL, and the two do not mix. If a certain mixture of olive oil and vinegar has a total mass of 402.3 g and a total volume of 421.0 mL, what is the volume of oil and what is the volume of vinegar in the mixture?

Problem #45: What is the radius of 0.663 g of copper wire (density = 8.96 g/cm3) that is 22.6 cm in length?

Problem #46: A thin coating of gold was placed onto a tray that measured 277.5 mm by 142.5 mm. The mass of the tray increased by 0.0624 g during the process. The density of gold is 19.32 g/cm3. (a) Calculate the thickness of the plating. (b) Determine the approximate number of gold atoms in the thin coating. (c) How many atoms of gold are in the thickness of the layer?

Problem #47: Mercury is often used as an expansion medium in a thermometer. The mercury sits in a bulb on the bottom of the thermometer and rises up a thin capillary as the temperature rises. Suppose a mercury thermometer contains 3.400 g of mercury and has a capillary that is 0.1900 mm in diameter

How far does the mercury rise in the capillary when the temperature changes from 0.0 °C to 25.0 °C? The density of mercury at these temperatures is 13.596 g/cm3 and 13.534 g/cm3, respectively.

Problem #48: A container (open to the atmosphere) is filled to a volume of 1.40 L with water at 25 °C and then frozen to −10 °C. What new volume does the ice occupy? Water has a density of 0.997 g/cm3 at 25 °C; ice has a density of 0.917 g/cm3 at −10 °C

Problem #49: Rolls of aluminum foil are 306 mm wide and 0.0140 mm thick. What maximum length of aluminum foil can be made from 0.834 kg of aluminum? (The density of Al is 2.70 g/cm3)

Problem #50: What would be the volume in cubic inches of a sample of aluminum with a mass of 250.5 grams?

Bonus Problem: The density of a liquid is determined by successively weighing a graduated cylinder containing 10, 20, 30, 40 and 50 mL. If the volume is plotted along the vertical axis and the total weight of the cylinder and the liquid is plotted on the horizontal axis:

(a) the slope of the line is the inverse of the density of the liquid
(b) none of the above statements are correct
(c) the slope of the line is 1.0
(d) the line will pass through the (0,0) origin
(e) the intercept on the x axis is the value of the weight of the cylinder