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Chapter 1: Problem 60

For a material to float on the surface of water, the material must have a density less than that of water \((1.0 \mathrm{~g} / \mathrm{mL})\) and must not react with the water or dissolve in it. A spherical ball has a radius of \(0.50 \mathrm{~cm}\) and weighs \(2.0 \mathrm{~g}\). Will this ball float or sink when placed in water? (Note: Volume of a sphere \(=\frac{4}{3} \pi r^{3}\).)

Short Answer

Expert verified
The volume of the sphere is calculated using the formula \(V = \frac{4}{3} \pi (0.50\mathrm{~cm})^{3}\), which yields approximately \(0.52 \mathrm{~mL}\). Then, we calculate the density of the sphere using the formula \(Density = \frac{2.0\mathrm{~g}}{0.52 \mathrm{~mL}} \approx 3.85 \mathrm{~g} / \mathrm{mL}\). Since the density of the sphere (3.85 \(\mathrm{g/mL}\)) is greater than the density of water (1.0 \(\mathrm{g/mL}\)), the ball will sink when placed in water.

Step by step solution

01

Calculate the volume of the sphere

The formula to calculate the volume of a sphere is given: \[ V = \frac{4}{3} \pi r^{3} \] With the given radius (\(r = 0.50\mathrm{~cm}\)), we can calculate the volume: \[ V = \frac{4}{3} \pi (0.50\mathrm{~cm})^{3} \]
02

Calculate the density of the sphere

The density formula is: \[ Density = \frac{Weight}{Volume} \] Using the sphere's given weight of \(2.0\mathrm{~g}\) and the volume calculated in Step 1 (assuming you already calculated it), we can calculate the density: \[ Density = \frac{2.0\mathrm{~g}}{V} \]
03

Compare the density of the sphere to the density of water

If the calculated density of the sphere is less than \(1.0\mathrm{~g} / \mathrm{mL}\) (the density of water), the sphere will float. If it is greater than \(1.0\mathrm{~g} / \mathrm{mL}\), the sphere will sink.

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Most popular questions from this chapter

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation? a. The surface area of the marble is not large enough to be held up by the surface tension of the water. b. The mass of the marble is greater than that of the water. c. The marble weighs more than an equivalent volume of the water. d. The force from dropping the marble breaks the surface tension of the water. e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.

Perform the following mathematical operations, and express each result to the correct number of significant figures. a. \(\frac{0.102 \times 0.0821 \times 273}{1.01}\) b. \(0.14 \times 6.022 \times 10^{23}\) c. \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\) d. \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)

If you place a glass rod over a burning candle, the glass appears to turn black. What is happening to each of the following (physical change, chemical change, both, or neither) as the candle burns? Explain each answer. a. the wax b. the wick c. the glass rod

Indicate the number of significant figures in each of the following: a. This book contains more than 1000 pages. b. A mile is about \(5300 \mathrm{ft}\). c. A liter is equivalent to \(1.059\) qt. d. The population of the United States is approaching \(3.0 \times 10^{2}\) million. e. A kilogram is \(1000 \mathrm{~g}\). f. The Boeing 747 cruises at around \(600 \mathrm{mi} / \mathrm{h}\).

Give four examples illustrating each of the following terms. a. homogeneous mixture d. element b. heterogeneous mixture e. physical change c. compound f. chemical change
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