Question

What type of quantity (for example, length, volume, density) do the following units indicate: (a) \(\mathrm{mL},(\mathbf{b}) \mathrm{cm}^{2},(\mathrm{c}) \mathrm{mm}^{3}\) (d) \(\mathrm{mg} / \mathrm{L},(\mathrm{e}) \mathrm{ps},(\mathrm{f}) \mathrm{nm},(\mathrm{g}) \mathrm{K} ?\)

Short answer

(a) mL represents a volume. (b) \(\mathrm{cm}^{2}\) represents an area. (c) \(\mathrm{mm}^{3}\) represents a volume. (d) \(\mathrm{mg}/\mathrm{L}\) represents a concentration. (e) ps represents a time. (f) nm represents a length. (g) K represents a temperature.

Step-by-step solution

(a) mL

Milliliter (mL) is a unit of volume. It represents 1/1000 of a liter (L).

(b) cm^2

Square centimeter (\(\mathrm{cm}^{2}\)) is a unit of area. It represents the area of a square with sides of length 1 centimeter.

(c) mm^3

Cubic millimeter (\(\mathrm{mm}^{3}\)) is a unit of volume. It represents the volume of a cube with sides of length 1 millimeter.

(d) mg/L

Milligram per liter (\(\mathrm{mg}/\mathrm{L}\)) is a unit of concentration. It is often used to measure the concentration of a solute in a given volume of solvent.

(e) ps

Picosecond (ps) is a unit of time. It represents 1/1,000,000,000,000 of a second.

(f) nm

Nanometer (nm) is a unit of length. It represents 1/1,000,000,000 of a meter.

(g) K

Kelvin (K) is a unit of temperature. It is the SI unit for temperature, and is based on the thermodynamic temperature scale.

Key concepts

Volume and Capacity (mL)

When studying chemistry, understanding the measurement of liquids is indispensable. Milliliters (mL) are a common unit used to gauge volume and capacity, especially in laboratory settings. A milliliter is a thousandth of a liter, denoting the space occupied by a liquid. It equates to the volume of a cube with each side measuring one centimeter.

For instance, if a student needs to measure 20 mL of water for an experiment, they are measuring out 20 thousandths of a liter of water. Such measurements are vital because the outcomes of chemical reactions often depend on precise volumes of reactants.

Area Units (cm^2)

The surface of a two-dimensional space is quantified in units like square centimeters (cm²). Imagine a square where each side is precisely one centimeter in length; the area encased by this square is one square centimeter. This unit is not just limited to squares; it’s used to measure the area of any shape, with all measurements ultimately being converted back to square centimeters.

It is frequent in chemistry to use this unit when examining cross-sectional areas in materials science or when needing to grasp the distribution of a substance across a specific surface area.

Concentration Units (mg/L)

In chemical solutions, concentration is a key concept, and it's often represented by units such as milligrams per liter (mg/L). This unit illustrates how much of a substance, say a solute like salt, is present in a certain volume of solvent, like water. It's equivalent to expressing how much mass of the solute exists in one liter of the solution.

Understanding concentration is pivotal because it affects the solution's properties—including color, viscosity, and reactivity—which are crucial for accurate experimentation and production in fields like pharmacology and environmental science.

Time Measurement (ps)

In the realm of chemistry and physics, very rapid processes such as molecular vibrations are measured in picoseconds (ps). A picosecond is one-trillionth of a second. Although this time frame might seem inconceivably brief, for atoms and molecules involved in chemical reactions, these tiny fractions of a second can be the difference between different states of a reaction.

High-speed phenomena like the transition states in chemical reactions or the lifetime of excited states in spectroscopy are areas where time measurement in picoseconds is particularly important.

Length Units (nm)

The world of the incredibly small, such as atoms and molecules, calls for a unit of length like the nanometer (nm). A nanometer is a billionth of a meter. This unit of measurement is critical when working in fields like nanotechnology or when studying the wavelengths of light in spectrophotometry.

For example, DNA strands and small particles like viruses are often measured in nanometers, emphasizing the practical use of this unit in biochemistry and molecular biology.

Temperature Scale (K)

Temperature measurement in chemistry is typically performed using the Kelvin (K) scale, a fundamental unit in the International System of Units (SI). Kelvin is unique because it starts at absolute zero, the theoretical point where molecular motion ceases. At this scale, 0 K is absolute zero, and each increment represents the same temperature change as one degree Celsius.

This scale is preferred in scientific environments because it facilitates straightforward calculations in thermodynamics and kinetic studies, allowing scientists to use direct proportionalities in their calculations without having to factor in the shifts associated with Celsius or Fahrenheit scales.