Important Equations and Relationships from Chapters 3 and 4

CHM101

Kelvin Temperature Conversion ($K = ^\circ\text{C} + 273.15$)

Used to convert a temperature reading from degrees Celsius to Kelvin by adding $273.15$.

Fahrenheit Temperature Conversion ($^\circ\text{F} = \frac{9}{5}^\circ\text{C} + 32$)

Used to convert a temperature reading from degrees Celsius to degrees Fahrenheit.

Average Atomic Weight Equation ($AW_{\text{ave}} = \sum_{i=1}^{i=n} (m_i a_i)$)

Used to calculate the weighted average atomic weight of an element by summing the products of each isotope's mass ($m_i$) and its fractional abundance ($a_i$).

Coulomb's Law ($F_e = k_e \frac{|q_1 q_2|}{r^2}$)

Used to calculate the magnitude of the electrostatic force ($F_e$) between two charges ($q_1$ and $q_2$) separated by a distance ($r$).

Atomic Mass Unit to Grams Conversion ($1\,\text{amu} = 1.66054 \times 10^{-24}\,\text{g}$)

Used as a conversion factor to convert mass between atomic mass units ($\text{amu}$) and grams ($\text{g}$).

Inch to Centimeter Conversion ($1\,\text{in} = 2.54\,\text{cm}$)

Used as a conversion factor to convert length measurements between inches and centimeters.

Pound to Gram Conversion ($1\,\text{lb} = 453.6\,\text{g}$)

Used as a conversion factor to convert mass or weight between pounds and grams.

Milliliter to Cubic Centimeter Equivalence ($1\,\text{mL} = 1\,\text{cm}^3$)

Used to convert between liquid volume in milliliters and solid volume in cubic centimeters.

Volume of a Rectangular Solid ($V_{\text{rectangle}} = lwh$)

Used to calculate the volume of a rectangular prism or block by multiplying length ($l$), width ($w$), and height ($h$).

Volume of a Cylinder ($V_{\text{cylinder}} = \pi r^2 h$)

Used to calculate the volume of a cylinder using its radius ($r$) and height ($h$).

Volume of a Sphere ($V_{\text{sphere}} = \frac{4}{3}\pi r^3$)

Used to calculate the volume of a spherical object from its radius ($r$).

Avogadro's Number ($N_A = 6.022 \times 10^{23}$)

Represents the number of constituent entities (such as atoms or molecules) per mole, used to convert between moles and number of particles.

Speed of Light Constant ($c = 3.00 \times 10^8\,\text{m/s}$)

Represents the constant speed at which light and other electromagnetic radiation travel in a vacuum.

Planck's Constant ($h = 6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$)

A fundamental proportionality constant used to calculate the energy of a photon from its frequency.

Wave Relationship for Light ($c = \lambda \nu$)

Used to relate the speed of light ($c$) to wavelength ($\lambda$) and frequency ($\nu$), allowing conversion between frequency and wavelength.

Photon Energy from Frequency ($E = h\nu$)

Used to calculate the energy ($E$) of a quantum or photon of light given its frequency ($\nu$).

Photon Energy from Wavelength ($E = \frac{hc}{\lambda}$)

Used to calculate the energy ($E$) of a photon directly from its wavelength ($\lambda$).