Chemistry Formulas and Physical Constants Review

Comprehensive vocabulary flashcards covering fundamental physical chemistry formulas, physical constants, thermodynamic relationships, electrochemistry equations, and periodic trend proportionalities.

Molar mass ($M$)

$$M = \frac{\text{mass}}{\text{number of moles}}$$

Number of moles ($n$)

$$n = \frac{\text{mass}}{\text{molar mass}}$$

Molarity

Moles of solute / volume of solution (in $\text{L}$)

Molality

Moles of solute / mass of solvent (in $\text{kg}$)

Mole fraction of $A$ ($x_A$)

$$x_A = \frac{n_A}{n_A + n_B}$$

Percentage by mass

$$\left(\frac{\text{mass of solute}}{\text{mass of solution}}\right) \times 100$$

Empirical formula

Simplest whole-number ratio of atoms

Molecular formula

$$n \times (\text{empirical formula})$$

Ideal gas equation

$$PV = nRT$$

Bohr's quantization equation

$$mvr = \frac{nh}{2\pi}$$

Radius of $n\text{th}$ Bohr orbit

$r_n = \frac{n^2 h^2 \varepsilon_0}{\pi m e^2} = n^2 a_0$, where $a_0 = 0.529\,\text{Å}$

Energy of $n\text{th}$ orbit ($\text{H}$ atom)

$$E_n = -\frac{13.6}{n^2}\,\text{eV} = -\frac{2.18 \times 10^{-18}}{n^2}\,\text{J}$$

Frequency of revolution (Bohr)

$$\nu = \frac{v}{2\pi r_n}$$

Ionisation energy of $\text{H}$ atom

$$E_i = \frac{13.6}{n^2}\,\text{eV}$$

De Broglie equation

$$\lambda = \frac{h}{mv}$$

Planck's constant ($h$)

$$6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$$

Mass of electron ($m_e$)

$$9.11 \times 10^{-31}\,\text{kg}$$

Effective nuclear charge ($Z_{\text{eff}}$)

$Z_{\text{eff}} = Z - \sigma$ (where $\sigma = \text{shielding constant}$)

Atomic radius proportionality

Proportional to $\frac{1}{Z_{\text{eff}}}$

Ionization enthalpy proportionality

Proportional to $\frac{Z_{\text{eff}}}{n}$

Electron gain enthalpy proportionality

Proportional to $-\frac{Z_{\text{eff}}}{n}$

Electronegativity proportionality

Proportional to $\frac{Z_{\text{eff}}}{n^2}$

Trends across a period (left to right)

Atomic radius decreases, ionization enthalpy increases, electron affinity becomes more negative, electronegativity increases

Trends down a group (top to bottom)

Atomic radius increases, ionization enthalpy decreases, electron affinity becomes less negative, electronegativity decreases

Percent ionic character

$$\left(\frac{\mu_{\text{observed}}}{\mu_{\text{ionic}}}\right) \times 100$$

Dipole moment ($\mu$)

$$\mu = q \times r$$

Percent s-character

$$\left(\frac{1}{1 + e^{\Delta E / RT}}\right) \times 100$$

Bond order

$\frac{N_b - N_a}{2}$ (bonding minus antibonding electrons, over 2)

$sp$ hybridisation bond angle

$180^\circ$ (linear)

$sp^2$ hybridisation bond angle

$120^\circ$ (trigonal planar)

$sp^3$ hybridisation bond angle

$109.5^\circ$ (tetrahedral)

$sp^3d$ hybridisation bond angles

$90^\circ$ and $120^\circ$ (trigonal bipyramidal)

$sp^3d^2$ hybridisation bond angle

$90^\circ$ (octahedral)

Dipole moment in Debye

$$\mu\,(\text{D}) = 4.803 \times q\,(\text{esu}) \times r\,(\text{cm})$$

Gas constant $R$ (two values)

$$0.0821\,\text{L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1} = 8.314\,\text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$$

Boyle's law

$PV = \text{constant}$ (at constant $T$ and $n$)

Charles' law

$V \propto T$ at constant $P$; $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Avogadro's law

$V \propto n$ at constant $P$ and $T$; $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

van der Waals equation

$$\left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT$$

van der Waals constants $a$ and $b$

$a = \text{attraction constant}$, $b = \text{volume constant}$

Heat at constant pressure ($q$)

$$q = n C_p \Delta T$$

Heat at constant volume ($q$)

$$q = n C_v \Delta T$$

First law of thermodynamics

$$\Delta U = q + w$$

Pressure-volume work

$$w = -P_{\text{ext}} \Delta V$$

Relation between $\Delta H$ and $\Delta U$

$$\Delta H = \Delta U + \Delta(n_g) RT$$

Gibbs free energy

$$\Delta G = \Delta H - T\Delta S$$

$\Delta G$ for a cell reaction

$$\Delta G = -nFE$$

Relation between $\Delta G^\circ$ and $K_{\text{eq}}$

$\Delta G^\circ = -RT \ln K_{\text{eq}}$, or $K_{\text{eq}} = e^{-\Delta G^\circ / RT}$

Equilibrium constant $K_c$

$$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$

Relation between $K_p$ and $K_c$

$$K_p = K_c (RT)^{\Delta n}$$

$\Delta n$ in $K_p = K_c(RT)^{\Delta n}$

Moles of gaseous products $$-$ moles of gaseous reactants

$\Delta G^\circ$ in terms of $\log K_c$

$$\Delta G^\circ = -2.303 RT \log K_c$$

Value of $2.303 R$

$$19.14\,\text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$$

Nernst equation (at $298\,\text{K}$)

$$E_{\text{cell}} = E^\circ_{\text{cell}} - \left(\frac{0.0591}{n}\right) \log Q$$

EMF of a concentration cell

$$E_{\text{cell}} = \left(\frac{0.0591}{n}\right) \log\left(\frac{C_2}{C_1}\right)$$

Relation between $\Delta G^\circ$ and $E^\circ$

$$\Delta G^\circ = -nFE^\circ$$

Faraday's law of electrolysis

$m = Z I t$, where $Z = \frac{E}{96500}$ ($E = \text{equivalent weight}$, $I = \text{current in A}$, $t = \text{time in s}$)

1 Faraday

$$96500\,\text{C}$$

pH

$$\text{pH} = -\log[\text{H}^+]$$

pOH

$$\text{pOH} = -\log[\text{OH}^-]$$

$\text{pH} + \text{pOH}$ at $298\,\text{K}$

$$14$$

Ionic product of water $K_w$

$[\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$ at $298\,\text{K}$

$K_a$ for a weak acid $\text{HA}$

$$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$$

$K_b$ for a weak base $\text{B}$

$$K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]}$$

Relation between $K_a$ and $K_b$

$$K_a \times K_b = K_w$$

Relation between $\text{pK}_a$ and $\text{pK}_b$

$$\text{pK}_a + \text{pK}_b = 14$$

Hydration enthalpy proportionality

Proportional to $\frac{1}{\text{ionic radius}}$

Lattice enthalpy proportionality

Proportional to $\frac{z^+ z^-}{r_0}$

Solubility product for $\text{A}_m\text{B}_n$

$$K_{\text{sp}} = [\text{A}^{n+}]^m [\text{B}^{m-}]^n$$

Common ion effect

Solubility decreases on adding a common ion

Acidic strength of oxyacids of the same element

Increases with number of $\text{O}$ atoms

Oxidising strength of oxyacids

Increases with oxidation number of the central atom

Disproportionation of $\text{H}_2\text{O}_2$

$2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2$ ($\text{H}_2\text{O}_2$ acts as both oxidising and reducing agent)

General formula of alkanes

$$\text{C}_n\text{H}_{2n+2}$$

General formula of alkenes

$$\text{C}_n\text{H}_{2n}$$

General formula of alkynes

$$\text{C}_n\text{H}_{2n-2}$$

General formula of mono-aromatics

$$\text{C}_n\text{H}_{2n-6}$$

Degree of unsaturation

$\text{DU} = \frac{2C + 2 + N - H - X}{2}$, where $X = \text{halogen}$

Wurtz reaction

$$2\text{R–X} + 2\text{Na} \rightarrow \text{R–R} + 2\text{NaX}$$

Wurtz–Fittig reaction

$$\text{R–X} + \text{R'–X} + 2\text{Na} \rightarrow \text{R–R'} + 2\text{NaX}$$

Kolbe's electrolysis

$$2\text{RCOO}^-\text{Na}^+ + 2\text{H}_2\text{O} \rightarrow \text{R–R} + 2\text{CO}_2 + \text{H}_2 + 2\text{NaOH}$$

Avogadro's number

$$N_A = 6.022 \times 10^{23}\,\text{mol}^{-1}$$

Speed of light

$$c = 3.00 \times 10^8\,\text{m}\cdot\text{s}^{-1}$$

Charge on an electron

$$e = 1.602 \times 10^{-19}\,\text{C}$$

Faraday constant

$$F = 96500\,\text{C}\cdot\text{mol}^{-1}$$

Boltzmann constant

$$k_B = 1.381 \times 10^{-23}\,\text{J}\cdot\text{K}^{-1}$$

Standard pressure

$$1\,\text{atm} = 1.013 \times 10^5\,\text{Pa}$$

Standard temperature

$$298\,\text{K} = 25\,^\circ\text{C}$$

$\Delta G$ in terms of $\Delta G^\circ$ and $Q$

$$\Delta G = \Delta G^\circ + RT \ln Q$$