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Chapter 1: Problem 10

Which of these properties are intensive and which are extensive? (a) area, (b) color, (c) density.

Short Answer

Expert verified
Area is an extensive property. Color and density are intensive properties.

Step by step solution

01

Understanding Intensive and Extensive Properties

Intensive properties are properties that do not depend on the amount of material. These properties remain the same whether there is a lot or a little of the material. Some examples of intensive properties include color, taste, temperature, and density. On the other hand, extensive properties are those that do depend on the amount of material. These properties change when the quantity of the material changes. Some examples of extensive properties include volume, mass, and area.
02

Categorizing the Given Properties

(a) Area: The area of a material depends on how much of the material there is. Thus, area is an extensive property. (b) Color: The color of a material doesn't change no matter how much or how little of it you have. Therefore, color is an intensive property. (c) Density: Density is a measure of mass per unit volume and does not change with the amount of substance. Therefore, density is an intensive property.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Intensive Properties
Intensive properties are fundamental characteristics of substances that remain constant regardless of the amount present. These properties are intrinsic to the material and proof of their independence is that they don't change with scale. For example, the boiling point of water is always 100°C at standard atmospheric pressure, whether you have a cup or an ocean of it.

Other common intensive properties include hardness, melting point, and refractive index. For students, remembering the distinctive feature of intensive properties—an indifference to size or mass—can be a handy rule for categorizing such properties in future exercises.
Extensive Properties
In contrast to intensive properties, extensive properties scale with the amount of substance involved. They are additive for subsystems, meaning the total value for the system is the sum of its parts. Extensive properties include volume, mass, and the aforementioned area. These properties are dependent on the sample's size; if you double the quantity of a substance, you double these properties.

In educational contexts, an understanding of extensive properties is crucial when discussing conservation laws and stoichiometry, as these laws are governed by changes in extensive properties.
Chemical Property Categorization
Chemical properties describe a substance's potential to undergo a specific chemical change. These can be intensive, such as reactivity with acid, or extensive, like the amount of heat released during a reaction. Students often confront the challenge of identifying which chemical properties fall into each category.

Teaching the methodology to categorize these properties enhances students' comprehension of chemical behavior and prediction of reaction outcomes. The emphasis here should be on transformative properties that refer to a substance's ability to form new substances, such as combustibility or oxidation states, which are inherently intensive.
Density as an Intensive Property
Density, the ratio of mass to volume, is an excellent example of an intensive property. It is independent of how much matter is present. Students can explore this by calculating the density of different samples of a substance—regardless of size, the density remains constant.

Understanding density's role as an intensive property helps in identifying pure substances and mixtures, and is vital in various scientific disciplines like material science and engineering. It underscores the distinction between how a property measures up in conjunction to the quantity of material (extensive) versus its quality (intensive).

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Most popular questions from this chapter

(a) Normally the human body can endure a temperature of \(105^{\circ} \mathrm{F}\) for only short periods of time without permanent damage to the brain and other vital organs. What is this temperature in degrees Celsius? (b) Ethylene glycol is a liquid organic compound that is used as an antifreeze in car radiators. It freezes at \(-11.5^{\circ} \mathrm{C}\). Calculate its freezing temperature in degrees Fahrenheit. (c) The temperature on the surface of the sun is about \(6300^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit? (d) The ignition temperature of paper is \(451^{\circ} \mathrm{F}\). What is the temperature in degrees Celsius?

The medicinal thermometer commonly used in homes can be read to \(\pm 0.1^{\circ} \mathrm{F}\), whereas those in the doctor's office may be accurate to \(\pm 0.1^{\circ} \mathrm{C}\). In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of \(38.9^{\circ} \mathrm{C}\).

Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value: Percent error \(=\) \(\frac{\mid \text { true value }-\text { experimental value } \mid}{\mid \text { true value } \mid} \times 100 \%\) where the vertical lines indicate absolute value. Calculate the percent error for these measurements: (a) The density of alcohol (ethanol) is found to be \(0.802 \mathrm{~g} / \mathrm{mL}\). (True value: \(0.798 \mathrm{~g} / \mathrm{mL} .\) ) (b) The mass of gold in an earring is analyzed to be \(0.837 \mathrm{~g}\). (True value: 0.864 g.)

Magnesium (Mg) is a valuable metal used in alloys, in batteries, and in chemical synthesis. It is obtained mostly from seawater, which contains about \(1.3 \mathrm{~g}\) of Mg for every kilogram of seawater. Calculate the volume of seawater (in liters) needed to extract \(8.0 \times 10^{4}\) tons of \(\mathrm{Mg}\), which is roughly the annual production in the United States. (Density of seawater = \(1.03 \mathrm{~g} / \mathrm{mL} .)\)

Tums is a popular remedy for acid indigestion. A typical Tums tablet contains calcium carbonate plus some inert substances. When ingested, it reacts with the gastric juice (hydrochloric acid) in the stomach to give off carbon dioxide gas. When a 1.328 -g tablet reacted with \(40.00 \mathrm{~mL}\) of hydrochloric acid (density: \(1.140 \mathrm{~g} / \mathrm{mL}\) ), carbon dioxide gas was given off and the resulting solution weighed 46.699 g. Calculate the number of liters of carbon dioxide gas released if its density is \(1.81 \mathrm{~g} / \mathrm{L}\).
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