Reading Chapter Three: 3.4

Connecting to Your World Have you ever wondered why some objects float in water, while others sink? If you think that these lily pads float because they are lightweight, you are only partially correct. The ratio of the mass of an object to its volume can be used to determine whether an object floats or sinks in water. For pure water at 4°C, this ratio is 1.000 g/cm3. If an object has a mass-to-volume ratio less than 1.000 g/cm3, it will float in water. If an object has a mass-to-volume ratio greater than this value, it will sink in water.



Key Concepts

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What determines the density of a substance?
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How does a change in temperature affect density?

Vocabulary

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density

Reading Strategy

Identifying Main Idea As you read, write the main idea of the text that follows each heading.

Determining Density

Perhaps someone has tricked you with this question: “Which is heavier, a pound of lead or a pound of feathers?” Most people would not give the question much thought and would incorrectly answer “lead.” Of course, a pound of lead has the same mass as a pound of feathers. What concept, instead of mass, are people really thinking of when they answer this question?

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Simulation 1 Rank materials according to their densities.

Most people are incorrectly applying a perfectly correct idea: namely, that if a piece of lead and a feather of the same volume are weighed, the lead would have a greater mass than the feather. It would take a much larger volume of feathers to equal the mass of a given volume of lead.

The important relationship in this case is between the object’s mass and its volume. This relationship is called density. Density is the ratio of the mass of an object to its volume.

A 10.0-cm3 piece of lead, for example, has a mass of 114 g. What, then, is the density of lead? You can calculate it by substituting the mass and volume into the equation above.

Note that when mass is measured in grams, and volume in cubic centimeters, density has units of grams per cubic centimeter (g/cm3).

Figure 3.13 compares the density of three substances. Why does each10-g sample have a different volume? The volumes vary because the substances have different densities. Density is an intensive property that depends only on the composition of a substance, not on the size of the sample. With a mixture, density can vary because the composition of a mixture can vary.

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Figure 3.13

What do you think will happen if corn oil is poured into a glass containing corn syrup? Using Table 3.6, you can see that the density of corn oil is less than the density of corn syrup. For that reason, the oil floats on top of the syrup, as shown in Figure 3.14.

Figure 3.14 Because of differences in density, corn oil floats on top of corn syrup.

You have probably seen a helium-filled balloon rapidly rise to the ceiling when it is released. Whether a gas-filled balloon will sink or rise when released depends on how the density of the gas compares with the density of air. Helium is less dense than air, so a helium-filled balloon rises. The densities of various gases are listed in Table 3.6.

Determining Density

Perhaps someone has tricked you with this question: “Which is heavier, a pound of lead or a pound of feathers?” Most people would not give the question much thought and would incorrectly answer “lead.” Of course, a pound of lead has the same mass as a pound of feathers. What concept, instead of mass, are people really thinking of when they answer this question?

View HTML
Simulation 1 Rank materials according to their densities.

Most people are incorrectly applying a perfectly correct idea: namely, that if a piece of lead and a feather of the same volume are weighed, the lead would have a greater mass than the feather. It would take a much larger volume of feathers to equal the mass of a given volume of lead.

The important relationship in this case is between the object’s mass and its volume. This relationship is called density. Density is the ratio of the mass of an object to its volume.

A 10.0-cm3 piece of lead, for example, has a mass of 114 g. What, then, is the density of lead? You can calculate it by substituting the mass and volume into the equation above.

Note that when mass is measured in grams, and volume in cubic centimeters, density has units of grams per cubic centimeter (g/cm3).

Figure 3.13 compares the density of three substances. Why does each10-g sample have a different volume? The volumes vary because the substances have different densities. Density is an intensive property that depends only on the composition of a substance, not on the size of the sample. With a mixture, density can vary because the composition of a mixture can vary.

PDF
Figure 3.13

What do you think will happen if corn oil is poured into a glass containing corn syrup? Using Table 3.6, you can see that the density of corn oil is less than the density of corn syrup. For that reason, the oil floats on top of the syrup, as shown in Figure 3.14.

Figure 3.14 Because of differences in density, corn oil floats on top of corn syrup.

You have probably seen a helium-filled balloon rapidly rise to the ceiling when it is released. Whether a gas-filled balloon will sink or rise when released depends on how the density of the gas compares with the density of air. Helium is less dense than air, so a helium-filled balloon rises. The densities of various gases are listed in Table 3.6.

Key Concepts

3.1 Measurements and Their Uncertainty

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Measurements are fundamental to the experimental sciences.Hint
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To evaluate accuracy, the measured value must be compared to the correct value. To evaluate precision, you must compare the values of repeated measurements.Hint
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Calculated answers often depend on the number of significant figures in the values used in the calculation.Hint
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In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.Hint

3.2 The International System of Units

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Five commonly used SI base units are the meter, kilogram, kelvin, second, and mole.Hint
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Common metric units of length: cm, m, km. Common metric units of volume: μL, mL, L, cm3. Common metric units of mass: mg, g, kg. Common units of temperature: °C and K. Common units of energy: J and cal.Hint

3.3 Conversion Problems

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Multiplying by a conversion factor does not change the actual size of a measurement.Hint
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Dimensional analysis provides an alternative approach to problem solving.Hint
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Conversion problems are easily solved using dimensional analysis.Hint

3.4 Density

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Density is an intensive property that depends only on the composition of a substance.Hint
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The density of a substance generally decreases as its temperature increases.Hint

Vocabulary

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Vocabulary Review

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absolute zero
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accepted value
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accuracy
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calorie (cal)
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Celsius scale
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conversion factor
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density
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dimensional analysis
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energy
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error
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experimental value
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gram (g)
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International System of Units (SI)
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joule (J)
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Kelvin scale
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kilogram (kg)
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liter (L)
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measurement
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meter (m)
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percent error
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precision
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scientific notation
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significant figures
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temperature
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weight

Key Equations

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Error = experimental value − accepted value Hint
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Hint

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K = °C + 273and °C = K − 273Hint
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1 J = 0.2390 cal and 1 cal = 4.184 JHint
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Hint