Problem 6 - Chemistry: The Central Science in SI Units, Global Edition

Question

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 \(\left.1.5\right]\)

Step-by-Step Solution

Answer

(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 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: d) 100,000 km²

This quantity has the unit "km²" which stands for square kilometers. Square kilometers is a unit of area, so this measurement is classified as an area measurement.

Step 5: e) 1.06 µm

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

Step 6: f) 16 nm²

This quantity has the unit "nm²" which stands for square nanometers. Square nanometers is a unit of area, so this measurement is classified as an area measurement.

Step 7: g) -78°C

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

Step 8: h) 2.56 g/cm³

This quantity has the unit "g/cm³" 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.

Step 9: i) 28 cm³

This quantity has the unit "cm³" which stands for cubic centimeters. Cubic centimeters is a unit of volume, so this measurement is classified as a volume measurement.

Key Concepts

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.