$\require{mhchem}$
Reference Sheet
===
## Periodic Table
## Elemental Groups
**Figure 2.27**
## Common Ions
**Figure 2.29**
## Common Polyatomic Ions
| Name | Formula | Related Acid | Formula |
| -------------------- | ------------- | ----------------- | ------------- |
| ammonium | NH~4~^+^ | | |
| hydronium | H~3~O^+^ | | |
| peroxide | O~2~^2−^ | | |
| hydroxide | OH^−^ | | |
| acetate | CH~3~COO^−^ | acetic acid | CH~3~COOH |
| cyanide | CN^−^ | hydrocyanic acid | HCN |
| azide | N~3~^−^ | hydrazoic acid | HN~3~ |
| carbonate | CO~3~^2−^ | carbonic acid | H~2~CO~3~ |
| bicarbonate | HCO~3~^−^ | | |
| nitrate | NO~3~^−^ | nitric acid | HNO~3~ |
| nitrite | NO~2~^−^ | nitrous acid | HNO~2~ |
| sulfate | SO~4~^2−^ | sulfuric acid | H~2~SO~4~ |
| hydrogen sulfate | HSO~4~^−^ | | |
| sulfite | SO~3~^2−^ | sulfurous acid | H~2~SO~3~ |
| hydrogen sulfite | HSO~3~^−^ | | |
| phosphate | PO~4~^3−^ | phosphoric acid | H~3~PO~4~ |
| hydrogen phosphate | HPO~4~^2−^ | | |
| dihydrogen phosphate | H~2~PO~4~^−^ | | |
| perchlorate | ClO~4~^−^ | perchloric acid | HClO~4~ |
| chlorate | ClO~3~^−^ | chloric acid | HClO~3~ |
| chlorite | ClO~2~^−^ | chlorous acid | HClO~2~ |
| hypochlorite | ClO^−^ | hypochlorous acid | HClO |
| chromate | CrO~4~^2−^ | chromic acid | H~2~CrO~4~ |
| dichromate | Cr~2~O~7~^2−^ | dichromic acid | H~2~Cr~2~O~7~ |
| permanganate | MnO~4~^−^ | permanganic acid | HMnO~4~ |
**Table 2.5**
<img src="https://openstax.org/apps/archive/20250522.165258/resources/808356928dd8effcf7d3638921e13388959bbf71" alt="This flowchart shows 10 rectangles connected by double headed arrows. To the upper left, a rectangle is shaded lavender and is labeled, “Volume of pure substance A.” This rectangle is followed by a horizontal double headed arrow labeled, “Density.” It connects to a second rectangle which is shaded yellow and is labeled, “Mass of A.” This rectangle is followed by a double headed arrow which is labeled, “Molar Mass,” that connects to a third rectangle which is shaded pink and is labeled, “Moles of A.” To the left of this rectangle is a horizontal double headed arrow labeled, “Molarity,” which connects to a lavender rectangle which is labeled, “Volume of solution A.” The pink, “Moles of A,” rectangle is also connected with a double headed arrow below and to the left. This arrow is labeled “Avogadro’s number.” It connects to a green shaded rectangle that is labeled, “Number of particles of A.” To the right of the pink “Moles of A,” rectangle is a horizontal double headed arrow which is labeled, “Stoichiometric factor.” It connects to a second pink rectangle which is labeled, “Moles of B.” A double headed arrow which is labeled, “Molar mass,” extends from the top of this rectangle above and to the right to a yellow shaded rectangle labeled, “Mass of B.” A horizontal double headed arrow which is labeled, “Density” links to a lavender rectangle labeled, “Volume of substance B,” to the right. A horizontal double headed arrow labeled, “Molarity,” extends right to the of the pink “Moles of B” rectangle. This arrow connects to a lavender rectangle that is labeled, “Volume of substance B.” Another double headed arrow extends below and to the right of the pink “Moles of B” rectangle. This arrow is labeled “Avogadro’s number,” and it extends to a green rectangle which is labeled, “Number of particles of B.”" style="zoom:80%" >
## Specific Heats of Common Substances at 25 °C and 1 bar
| Substance | Symbol (*state*) | Specific Heat (J/g °C) |
| -------------- | ---------------- | ---------------------- |
| helium | He(*g*) | 5.193 |
| water | H~2~O(*l*) | 4.184 |
| ethanol | C~2~H~6~O(*l*) | 2.376 |
| ice | H~2~O(*s*) | 2.093 (at −10 °C) |
| water vapor | H~2~O(*g*) | 1.864 |
| nitrogen | N~2~(*g*) | 1.040 |
| air | | 1.007 |
| oxygen | O~2~(*g*) | 0.918 |
| aluminum | Al(*s*) | 0.897 |
| carbon dioxide | CO~2~(*g*) | 0.853 |
| argon | Ar(*g*) | 0.522 |
| iron | Fe(*s*) | 0.449 |
| copper | Cu(*s*) | 0.385 |
| lead | Pb(*s*) | 0.130 |
| gold | Au(*s*) | 0.129 |
| silicon | Si(*s*) | 0.712 |
**Table 5.1**
## Standard Molar Enthalpies of Combustion
| Substance | Combustion Reaction | Enthalpy of Combustion, Δ*H^∘^~c~* (kJ/ mol at 25°C) |
| --------------- | -------------------------------------------------------- | ---------------------------------------------------- |
| carbon | $\ce{C(s) + O2(g) -> CO2(g)}$ | −393.5 |
| hydrogen | $\ce{H2(g) + 1/2O2(g) -> H2O(l)}$ | −285.8 |
| magnesium | $\ce{Mg(s) + 1/2O2(g) -> MgO(s)}$ | −601.6 |
| sulfur | $\ce{S(s) + O2(g) -> SO2(g)}$ | −296.8 |
| carbon monoxide | $\ce{CO(g) + 1/2O2(g) -> CO2(g)}$ | −283.0 |
| methane | $\ce{CH4(g) + 2O2(g) -> CO2(g) + 2H2O(l)}$ | −890.8 |
| acetylene | $\ce{C2H2(g) + 5/2O2(g) -> 2CO2(g) + H2O(l)}$ | −1301.1 |
| ethanol | $\ce{C2H5OH(l) + 3O2(g) -> 2CO2(g) + 3H2O(l)}$ | −1366.8 |
| methanol | $\ce{CH3OH(l) + 3/2O2(g) -> CO2(g) + 2H2O(l)}$ | −726.1 |
| isooctane | $\ce{C8H18(l) + 25/2O2(g) -> 8CO2(g) + 9H2O(l)}$ | −5461 |
**Table 5.2**
## Shape of Orbitals
**Figure 6.21**
## Quantum Rules
| Name | Symbol | Allowed values | Physical meaning |
|:----:|:------:|:---------------:|:-----------------:|
| principal quantum number | *n* | 1, 2, 3, 4, …. | shell, the general region for the value of energy for an electron on the orbital |
| angular momentum or azimuthal quantum number | *l* | 0 ≤ *l* ≤ *n* – 1 | subshell, the shape of the orbital |
| magnetic quantum number | *m~l~* | – *l* ≤ *ml* ≤ *l* | orientation of the orbital |
| spin quantum number | *m~s~* | ½ ,−½ | direction of the intrinsic quantum “spinning” of the electron |
**Table 6.1**
## Aufbau Principle
## Orbitals Blocks
**Figure 6.27**
## Electron Configuration
![This figure includes the element symbol N a, followed by the electron configuration for the element. The first part of the electron configuration, 1 s superscript 2 2 s superscript 2 2 p superscript 6, is shaded in purple and is labeled, “core electrons.” The last portion, 3 s superscript 1, is shaded orange and is labeled, “valence electron.” To the right of this configuration is the word “Abbreviation” followed by [ N e ] 3 s superscript 1.](https://openstax.org/apps/archive/20240625.161426/resources/b9202053d386a7428bd655f948e413fdde4731c1)
**Figure 6.28**
**Figure 6.29**
## Atomic Radius
**Figure 6.30**
## First Ionization Energy
## Successive Ionization Energies for Selected Elements (kJ/mol)
| **Element** | **IE~1~** | **IE~2~** | **IE~3~** | **IE~4~** | **IE~5~** | **IE~6~** | **IE~7~** |
| ----------- | --------- | --------- | --------- | --------- | --------- | ------------- | ------------- |
| K | 418.8 | 3051.8 | 4419.6 | 5876.9 | 7975.5 | 9590.6 | 11343 |
| Ca | 589.8 | 1145.4 | 4912.4 | 6490.6 | 8153.0 | 10495.7 | 12272.9 |
| Sc | 633.1 | 1235.0 | 2388.7 | 7090.6 | 8842.9 | 10679.0 | 13315.0 |
| Ga | 578.8 | 1979.4 | 2964.6 | 6180 | 8298.7 | 10873.9 | 13594.8 |
| Ge | 762.2 | 1537.5 | 3302.1 | 4410.6 | 9021.4 | Not available | Not available |
| As | 944.5 | 1793.6 | 2735.5 | 4836.8 | 6042.9 | 12311.5 | Not available |
**Table 6.3**
## Electron Affinity
**Figure 6.35**
## Electronegativity
**Figure 7.6**
## Bonding Character
## Lewis Structures
![A table is shown that has three columns and nine rows. The header row reads “Atoms,” “Electronic Configuration,” and “Lewis Symbol.” The first column contains the words “sodium,” “magnesium,” “aluminum,” “silicon,” “phosphorus,” “sulfur,” “chlorine,” and “argon.” The second column contains the symbols and numbers “[ N e ] 3 s superscript 2,” “[ N e ] 3 s superscript 2, 3 p superscript 1,” “[ N e ] 3 s superscript 2, 3 p superscript 2,” “[ N e ] 3 s superscript 2, 3 p superscript 3,” “[ N e ] 3 s superscript 2, 3 p superscript 4,” “[ N e ] 3 s superscript 2, 3 p superscript 5,” and “[ N e ] 3 s superscript 2, 3 p superscript 6.” The third column contains Lewis structures for N a with one dot, M g with two dots, A l with three dots, Si with four dots, P with five dots, S with six dots, C l with seven dots, and A r with eight dots.](https://openstax.org/apps/archive/20240625.161426/resources/c7d8fb42087a4bc5245003783081923155a91ae1)
**Figure 7.9**
**Figure 7.10**
## VSEPR Geometry
## Bond Energy (kJ/mol)
| Bond | Bond Energy | Bond | Bond Energy | Bond | Bond Energy |
| ---- | ----------- | ---- | ----------- | ----- | ----------- |
| H–H | 436 | C–S | 260 | F–Cl | 255 |
| H–C | 415 | C–Cl | 330 | F–Br | 235 |
| H–N | 390 | C–Br | 275 | Si–Si | 230 |
| H–O | 464 | C–I | 240 | Si–P | 215 |
| H–F | 569 | N–N | 160 | Si–S | 225 |
| H–Si | 395 | N=N | 418 | Si–Cl | 359 |
| H–P | 320 | N≡N | 946 | Si–Br | 290 |
| H–S | 340 | N–O | 200 | Si–I | 215 |
| H–Cl | 432 | N–F | 270 | P–P | 215 |
| H–Br | 370 | N–P | 210 | P–S | 230 |
| H–I | 295 | N–Cl | 200 | P–Cl | 330 |
| C–C | 345 | N–Br | 245 | P–Br | 270 |
| C=C | 611 | O–O | 140 | P–I | 215 |
| C≡C | 837 | O=O | 498 | S–S | 215 |
| C–N | 290 | O–F | 160 | S–Cl | 250 |
| C=N | 615 | O–Si | 370 | S–Br | 215 |
| C≡N | 891 | O–P | 350 | Cl–Cl | 243 |
| C–O | 350 | O–Cl | 205 | Cl–Br | 220 |
| C=O | 741 | O–I | 200 | Cl–I | 210 |
| C≡O | 1080 | F–F | 160 | Br–Br | 190 |
| C–F | 439 | F–Si | 540 | Br–I | 180 |
| C–Si | 360 | F–P | 489 | I–I | 150 |
| C–P | 265 | F–S | 285 | | |
$$
\Large
\Delta H = \Sigma D_{\text{Bonds Broken}} - \Sigma D_{\text{Bonds Formed}}
$$
## Average Bond Lengths and Bond Energies for Some Common Bonds
| Bond | Bond Length (Å) | Bond Energy (kJ/mol) |
| ---- | --------------- | -------------------- |
| C–C | 1.54 | 345 |
| C=C | 1.34 | 611 |
| C≡C | 1.20 | 837 |
| C–N | 1.43 | 290 |
| C=N | 1.38 | 615 |
| C≡N | 1.16 | 891 |
| C–O | 1.43 | 350 |
| C=O | 1.23 | 741 |
| C≡O | 1.13 | 1080 |
**Table 7.3**
## Pressure Units
| Unit Name and Abbreviation | Definition or Relation to Other Unit |
| ------------------------------ | ------------------------------------------------------------ |
| pascal (Pa) | 1 Pa = 1 N/m^2^ recommended IUPAC unit |
| kilopascal (kPa) | 1 kPa = 1000 Pa |
| pounds per square inch (psi) | air pressure at sea level is ~14.7 psi |
| atmosphere (atm) | 1 atm = 101,325 Pa = 760 torr air pressure at sea level is ~1 atm |
| bar (bar, or b) | 1 bar = 100,000 Pa (exactly) commonly used in meteorology |
| millibar (mbar, or mb) | 1000 mbar = 1 bar |
| inches of mercury (in. Hg) | 1 in. Hg = 3386 Pa used by aviation industry, also some weather reports |
| torr | 1 torr = 1760 atm named after Evangelista Torricelli, inventor of the barometer |
| millimeters of mercury (mm Hg) | 1 mm Hg ~ 1 torr |
**Table 9.1**
## Manometer
**Figure 9.5**
## Values of van der Waals Constants for Some Common Gases
| Gas | *a* (L^2^ atm/mol^2^) | *b* (L/mol) |
| ------ | --------------------- | ----------- |
| N~2~ | 1.39 | 0.0391 |
| O~2~ | 1.36 | 0.0318 |
| CO~2~ | 3.59 | 0.0427 |
| H~2~O | 5.46 | 0.0305 |
| He | 0.0342 | 0.0237 |
| CCl~4~ | 20.4 | 0.1383 |
**Table 9.3**
## Value of the Gas Constant, $R$
### SI units
| Value | Unit |
| ---------------- | :------------------------: |
| 8.31446261815324 | $\displaystyle\frac{\textsf{J}}{\textsf{K⋅mol}}$ |
| 8.31446261815324 | $\displaystyle\frac{\textsf{m}^3⋅\textsf{Pa}}{\textsf{K⋅mol}}$ |
| 8.31446261815324 | $\displaystyle\frac{\textsf{kg⋅m}^2}{\textsf{s}^2\textsf{⋅K⋅mol}}$ |
### Other common units
| Value | Unit |
| ------------------------- | :---------------------------: |
| 8314.46261815324 | $\displaystyle\frac{\textsf{L⋅Pa}}{\textsf{K⋅mol}}$ |
| 8.31446261815324 | $\displaystyle\frac{\textsf{L⋅kPa}}{\textsf{K⋅mol}}$ |
| 0.0831446261815324 | $\displaystyle\frac{\textsf{L⋅bar}}{\textsf{K⋅mol}}$ |
| 8.31446261815324 × 10^7^ | $\displaystyle\frac{\textsf{erg}}{\textsf{K⋅mol}}$ |
| 0.730240507295273 | $\displaystyle\frac{\textsf{atm⋅ft}^3}{\textsf{lbmol⋅°R}}$ |
| 10.731577089016 | $\displaystyle\frac{\textsf{psi⋅ft}^3}{\textsf{lbmol⋅°R}}$ |
| 1.985875279009 | $\displaystyle\frac{\textsf{BTU}}{\textsf{lbmol⋅°R}}$ |
| 297.031214 | $\displaystyle\frac{\textsf{inH2O⋅ft}^3}{\textsf{lbmol⋅°R}}$ |
| 554.98431918 | $\displaystyle\frac{\textsf{torr⋅ft}^3}{\textsf{lbmol⋅°R}}$ |
| 0.08205736608096 | $\displaystyle\frac{\textsf{L⋅atm}}{\textsf{K⋅mol}}$ |
| 62.363598221529 | $\displaystyle\frac{\textsf{L⋅torr}}{\textsf{K⋅mol}}$ |
| 1.98720425864083 | $\displaystyle\frac{\textsf{cal}}{\textsf{K⋅mol}}$ |
| 8.20573660809596 × 10^−5^ | $\displaystyle\frac{\textsf{m}^3⋅\textsf{atm}}{\textsf{K⋅mol}}$ |