Problem 6 - Chemistry The Central Science

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) \(16 \mathrm{nm}^{2},(\mathrm{g})-78^{\circ} \mathrm{C},(\mathbf{h}) 2.56 \mathrm{g} / \mathrm{cm}^{3},(\mathrm{i}) 28 \mathrm{cm}^{3} \cdot[\) Section 1.5\(]\)

Step-by-Step Solution

Answer

(a) 25 ps is a measurement of \(\textbf{time}\). (b) 374.2 mg is a measurement of \(\textbf{mass}\). (c) 77 K is a measurement of \(\textbf{temperature}\). (d) 100,000 km² is a measurement of \(\textbf{area}\). (e) 1.06 μm is a measurement of \(\textbf{length}\). (f) 16 nm² is a measurement of \(\textbf{area}\). (g) −78°C is a measurement of \(\textbf{temperature}\). (h) 2.56 g/cm³ is a measurement of \(\textbf{density}\). (i) 28 cm³ is a measurement of \(\textbf{volume}\).

Step 1: (a) 25 ps

In this measurement, "ps" stands for picosecond, which is a unit of time (1 picosecond = 1 × 10^(-12) seconds). So, 25 ps refers to a time measurement.

Step 2: (b) 374.2 mg

Here, "mg" stands for milligrams, which is a unit of mass (1 milligram = 1 × 10^(-3) grams). Therefore, 374.2 mg refers to a mass measurement.

Step 3: (c) 77 K

The "K" in this case stands for Kelvin, which is a unit of temperature. Thus, 77 K represents a temperature measurement.

Step 4: (d) 100,000 km²

In this measurement, "km²" stands for square kilometers, which is a unit of area. Therefore, 100,000 km² denotes an area measurement.

Step 5: (e) 1.06 μm

Here, "μm" stands for micrometers, which is a unit of length (1 micrometer = 1 × 10^(-6) meters). Thus, 1.06 μm is a measurement of length.

Step 6: (f) 16 nm²

In this case, "nm²" stands for square nanometers, which is a unit of area (1 square nanometer = 1 × 10^(-18) square meters). Therefore, 16 nm² represents an area measurement.

Step 7: (g) −78°C

The "°C" here stands for degrees Celsius, which is a unit of temperature. Consequently, -78°C is a temperature measurement.

Step 8: (h) 2.56 g/cm³

In this measurement, "g/cm³" denotes grams per cubic centimeter, which is a unit of density. Thus, 2.56 g/cm³ refers to a density measurement.

Step 9: (i) 28 cm³

Here, "cm³" stands for cubic centimeters, which is a unit of volume (1 cubic centimeter = 1 × 10^(-6) cubic meters). As such, 28 cm³ represents a volume measurement.

Key Concepts

Units of Length

Understanding units of length is foundational in chemistry, as it allows you to gauge the dimensions of atoms, molecules, and distances between them. Commonly, length is measured in meters (m), which is the standard unit in the International System of Units (SI). However, for much smaller lengths, such as the width of a DNA helix or the size of a virus, we use subunits like micrometers (\(1 \text{μm} = 1 \times 10^{-6} \text{m}\)) and nanometers (\(1 \text{nm} = 1 \times 10^{-9} \text{m}\)).

For instance, the length of a typical molecule might be given in nanometers, such as the 1.06 μm mentioned in our exercise, which emphasizes the molecule's extremely small scale.

Equipping yourself with this knowledge allows you to mentally visualize and understand the microscopic world with greater clarity.

Units of Mass

Mass is a fundamental concept in chemistry, related to the amount of substance present. The standard SI unit of mass is the kilogram (kg), but in a chemistry lab, you're more likely to encounter grams (g) and milligrams (mg), which are smaller divisions of the kilogram (\(1 \text{g} = 1 \times 10^{-3} \text{kg}\) and 1 mg = 1 × 10^(-3) g).

When measuring out chemicals for a reaction, precision is key. For example, 374.2 mg, as mentioned in the exercise, indicates a specific small quantity of a substance. Mastering these units' conversions is vital for accuracy in chemical formulations and understanding the stoichiometry of reactions.

Units of Volume

Volume measures the space that a substance or an object occupies. It's essential in chemistry when dealing with liquids and gases, or any material to understand its concentration. The cubic meter (m³) is the SI unit, but for practical laboratory uses, liters (L) and milliliters (mL), or even cubic centimeters (cm³), are often used (\(1 \text{L} = 1 \times 10^{-3} \text{m}^3\) and 1 mL = 1 cm³).

In the exercise, 28 cm³ is a volume measurement that might refer to the volume of a liquid in a small container. Recognizing the relationship between these units makes it easier to switch between scales when different measurements are needed.

Units of Density

Density is a central concept in chemistry, describing how compact a substance is. It's defined as mass per unit volume and commonly expressed in g/cm³ or kg/m³. High density means a material is tightly packed, whereas low density indicates that the particles are more spread out.

For example, when we express a density of 2.56 g/cm³, as in the exercise (h), it tells us that each cubic centimeter of that substance has a mass of 2.56 grams. This is particularly useful in determining the purity of a substance or predicting whether it will float or sink in a particular liquid.

Units of Temperature

Temperature measurements provide critical information in chemistry, from reaction rates to substance properties at various temperatures. The Kelvin (K) is the base unit in the SI, which sets absolute zero as 0 K, but we often use the Celsius scale (°C) in practical scenarios.

The exercise provided us with -78°C and 77 K as examples. The Celsius scale is used for everyday temperatures, while the Kelvin scale is preferred in scientific contexts to avoid negative numbers and to use in thermodynamic calculations. Appreciating the difference and conversion between these scales is essential for communicating and understanding temperature in different contexts.

Units of Time

Time, while not unique to chemistry, is important for tracking the progress of reactions and processes. The second (s) is the SI base unit of time. However, for observing the incredibly fast pace of molecular events, we often resort to shorter units like milliseconds (ms), microseconds (μs), and even picoseconds (ps), reflective of the immense speed at which molecular interactions can occur (\(1 \text{ms} = 1 \times 10^{-3} \text{s}\) and 1 ps = 1 × 10^(-12) s).

In the exercise, a duration of 25 ps might relate to the time it takes for a specific quantum event or a reaction step at the atomic level. Thus, being familiar with these tiny fractions of a second is essential in advanced chemical kinetics.

Units of Area

Area measurements in chemistry can apply to surfaces of reactions or cross-sections of molecular layers. The square meter (m²) is the standard SI unit for area, but in different contexts, one might see square kilometers (km²) for larger areas or square nanometers (nm²) for molecular surfaces (\(1 \text{nm}^{2} = 1 \times 10^{-18} \text{m}^{2}\)).

In our exercise, we encountered both large scales, such as 100,000 km² (d), which could refer to geospatial data, and at the very small scale, 16 nm² (f), which could relate to the area of a cross-section of a nanoscale object. Understanding these various scales helps in visualizing the extent of surfaces in different scientific applications.