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Chapter 1: Problem 6

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(25 \mathrm{ps}\), (b) \(374.2 \mathrm{mg}\) (c) \(77 \mathrm{~K}\) (d) \(100,000 \mathrm{~km}^{2}\) (e) \(1.06 \mu \mathrm{m}\) (f) \(16 \mathrm{nm}^{2},(\mathrm{~g})-78^{\circ} \mathrm{C}\) (h) \(2.56 \mathrm{~g} / \mathrm{cm}^{3}\) (i) \(28 \mathrm{~cm}^{3}\). [Section \(\left.1.5\right]\)

Short Answer

Expert verified
(a) Time measurement: \(25 \mathrm{ps}\) (b) Mass measurement: \(374.2 \mathrm{mg}\) (c) Temperature measurement: \(77 \mathrm{~K}\) (d) Area measurement: \(100,000 \mathrm{~km}^{2}\) (e) Length measurement: \(1.06 \mu \mathrm{m}\) (f) Area measurement: \(16 \mathrm{nm}^{2}\) (g) Temperature measurement: \(-78^{\circ} \mathrm{C}\) (h) Density measurement: \(2.56 \mathrm{~g} / \mathrm{cm}^{3}\) (i) Volume measurement: \(28 \mathrm{~cm}^{3}\)

Step by step solution

01

a) 25 ps

This quantity has the unit "ps" which stands for picoseconds. A second is a unit of time, so this measurement is classified as a time measurement.
02

b) 374.2 mg

This quantity has the unit "mg" which stands for milligrams. A gram is a unit of mass, so this measurement is classified as a mass measurement.
03

c) 77 K

This quantity has the unit "K" which stands for kelvins. Kelvin is a unit of temperature, so this measurement is classified as a temperature measurement.
04

d) 100,000 km虏

This quantity has the unit "km虏" which stands for square kilometers. Square kilometers is a unit of area, so this measurement is classified as an area measurement.
05

e) 1.06 碌m

This quantity has the unit "碌m" which stands for micrometers. A meter is a unit of length, so this measurement is classified as a length measurement.
06

f) 16 nm虏

This quantity has the unit "nm虏" which stands for square nanometers. Square nanometers is a unit of area, so this measurement is classified as an area measurement.
07

g) -78掳C

This quantity has the unit "掳C" which stands for degrees Celsius. Celsius is a unit of temperature, so this measurement is classified as a temperature measurement.
08

h) 2.56 g/cm鲁

This quantity has the unit "g/cm鲁" which stands for grams per cubic centimeter. Grams per cubic centimeter is a unit of density, so this measurement is classified as a density measurement.
09

i) 28 cm鲁

This quantity has the unit "cm鲁" which stands for cubic centimeters. Cubic centimeters is a unit of volume, so this measurement is classified as a volume measurement.

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Key Concepts

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

Length Measurement
Length measurement refers to determining how long something is from one end to the other. It involves using units like meters, centimeters, and millimeters. In scientific contexts, the meter (m) is often the standard unit.
For smaller lengths, we use micrometers (\(\mu \text{m}\)) and nanometers (nm). These units are helpful when dealing with very tiny objects or distances, like cells or molecules. Engaging with different scales and knowing how to convert between them ensures accuracy in many fields, from architecture to microbiology.
  • Micrometer (\(\mu \text{m}\)): One millionth of a meter
  • Nanometer (nm): One billionth of a meter
Mass Measurement
Mass measurement is a way to determine how much matter is in an object. The most common unit for mass is the kilogram (kg), but grams (g) and milligrams (mg) are also frequently used.
  • Kilogram (kg): The standard SI unit of mass
  • Gram (g): One thousandth of a kilogram
  • Milligram (mg): One thousandth of a gram
These measurements are important in daily life and professional fields like chemistry and cooking. Understanding mass helps in tasks requiring precision, such as measuring ingredients in recipes or creating chemical solutions.
Temperature Measurement
Temperature measurement is crucial to understanding how hot or cold something is. Common units include Celsius (\(\degree\text{C}\)) and Kelvin (K). While Celsius is widely used in everyday life, Kelvin is often used in scientific contexts because it is based on an absolute scale.
Kelvin begins at absolute zero, a concept that represents the lowest possible temperature where particles have minimal kinetic energy.
  • Celsius (\(\degree\text{C}\)): Used for most temperature measuring around the world
  • Kelvin (K): Used primarily in scientific measurements, with 0 K being absolute zero
Converting between Celsius and Kelvin is straightforward: \(K = \degree\text{C} + 273.15\). Understanding temperature is vital in fields like meteorology, cooking, and physics.
Volume Measurement
Volume measurement refers to the amount of space an object or substance occupies. The most common unit for volume is the cubic meter (\(\text{m}^3\)), but liters (L) and milliliters (mL) are more frequent in everyday contexts.
In scientific studies, smaller units like cubic centimeters (\(\text{cm}^3\)) are used, especially in laboratory settings.
  • Cubic meter (\(\text{m}^3\)): The SI unit for volume
  • Liter (L): Equals 1000 cubic centimeters
  • Milliliter (mL): One thousandth of a liter
  • Cubic centimeter (\(\text{cm}^3\)): Equivalent to a milliliter
Volume measurement is essential in activities like cooking, chemistry, and calculating the capacity of containers.

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Most popular questions from this chapter

Ethyl chloride is sold as a liquid (see photo) under pressure for use as a local skin anesthetic. Ethyl chloride boils at \(12^{\circ} \mathrm{C}\) at atmospheric pressure. When the liquid is sprayed onto the skin, it boils off, cooling and numbing the skin as it vaporizes. (a) What changes of state are involved in this use of ethyl chloride? (b) What is the boiling point of ethyl chloride in degrees Fahrenheit? (c) The bottle shown contains \(103.5 \mathrm{~mL}\) of ethyl chloride. The density of ethyl chloride at \(25^{\circ} \mathrm{C}\) is \(0.765 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the mass of ethyl chloride in the bottle?

(a) A child has a fever of \(101^{\circ} \mathrm{F}\). What is the temperature in \({ }^{\circ} \mathrm{C} ?\) (b) In a desert, the temperature can be as high as \(45^{\circ} \mathrm{C},\) what is the temperature in \({ }^{\circ} \mathrm{F} ?\) (c) During winter, the temperature of the Arctic region can drop below \(-50^{\circ} \mathrm{C}\), what is the temperature in degree Fahrenheit and in Kelvin? (d) The sublimation temperature of dry ice is \(-78.5^{\circ} \mathrm{C}\). Convert this temperature to degree Fahrenheit and Kelvin. (e) Ethanol boils at \(351 \mathrm{~K}\). Convert this temperature to degree Fahrenheit and degree Celsius.

A solid white substance \(A\) is heated strongly in the absence of air. It decomposes to form a new white substance \(\mathrm{B}\) and a gas C. The gas has exactly the same properties as the product obtained when carbon is burned in an excess of oxygen. Based on these observations, can we determine whether solids A and \(\mathrm{B}\) and gas \(\mathrm{C}\) are elements or compounds?

(a) To identify a liquid substance, a student determined its density, Using a graduated cylinder, she measured out a \(45-\mathrm{mL}\). sample of the substance. She then measured the mass of the sample, finding that it weighed \(38.5 \mathrm{~g}\). She knew that the substance had to be either isopropyl alcohol (density \(0.785 \mathrm{~g} / \mathrm{mL}\) ) or toluene (density \(0.866 \mathrm{~g} / \mathrm{mL}\) ). What are the calculated density and the probable identity of the substance? (b) An experiment requires \(45.0 \mathrm{~g}\) of ethylene glycol, a liquid whose density is \(1.114 \mathrm{~g} / \mathrm{mL}\). Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use? (c) Is a graduated cylinder such as that shown in Figure 1.21 likely to afford the (d) A cubic piece of metal accuracy of measurement needed? measures \(5.00 \mathrm{~cm}\) on each edge. If the metal is nickel, whose density is \(8.90 \mathrm{~g} / \mathrm{cm}^{3}\), what is the mass of the cube?

Is the use of significant figures in each of the following statements appropriate? (a) The 2005 circulation of National Geographic was \(7,812,564 .\) (b) On July 1, 2005, the population of Cook County, Illinois, was \(5,303,683 .(\mathbf{c})\) In the United States, \(0.621 \%\) of the population has the surname Brown. (d) You calculate your grade point average to be \(3.87562 .\)
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