معادلات الكيمياء

Acid Ionization Constant

\[K_a = \frac{{\left[ {H^ + } \right]\left[ {A^ - } \right]}}{{\left[ {HA} \right]}}\]

Base Ionization Constant

\[K_b = \frac{{\left[ {OH^ - } \right]\left[ {HB^ + } \right]}}{{\left[ B \right]}}\]

Ion Product Constant for Water

\[\begin{array}{*{20}c} {K_w = \left[ {OH^ - } \right]\left[ {H^ + } \right] = K_a \times K_b } \\ {\begin{array}{*{20}c} { = 1.0 \times 10^{ - 14} } & {at} & {25^\circ C} \\ \end{array}} \\ \end{array}\]

pH Defined

\[pH = - \log \left[ {H^ + } \right]\]

pOH Defined

\[pOH = - \log \left[ {OH^ - } \right]\]

pH and pOH Relationship

\[14 = pH + pOH\]

Buffer Design Equation

\[pH \approx pK_a - \log \frac{{\left[ {HA} \right]_0 }}{{\left[ {A^ - } \right]_0 }}\]

pOH and Base Ionization Equilibrium Constant Relationship

\[pOH = pK_b + \log \frac{{\left[ {HB^ + } \right]}}{{\left[ B \right]}}\]

pKa Definition

\[pK_a = - \log K_a\]

pKb Definition

\[pK_b = - \log K_b\]

Gas Pressure and Concentration Relationship

\[K_p = K_c \left( {RT} \right)^{\Delta n}\]

Ideal gas equation

\[PV = nRT\]

Adibiatic change

\[PV = k\]

Charles' Law

\[\frac{V}{t} = k\]

Van der Waals equation

\[\left( {P + \frac{{an^2 }}{{V^2 }}} \right)\left( {V - bn} \right) = nRT\]

Molar Heat Capacity at Constant Pressure

\[C_p = \frac{{\Delta H}}{{\Delta T}}\]

Partial Pressure of a Gas

\[\begin{array}{*{20}c} {P_A = P_{total} X_A } \\ {\begin{array}{*{20}c} {where} & {X_A = \frac{{\begin{array}{*{20}c} {moles} & A \\ \end{array}}}{{\begin{array}{*{20}c} {total} & {moles} \\ \end{array}}}} \\ \end{array}} \\ \end{array}\]

Total Gas Pressure as Sum of Partial Pressures

\[P_{total} = P_A + P_B + P_C + \ldots\]

Number of Moles

\[n = \frac{m}{M}\]

Temperature in Kelvin from Degrees Celsius Conversion

\[K = ^\circ C + 273\]

Combined Gas Law

\[\frac{{P_1 V_1 }}{{n_1 T_1 }} = \frac{{P_2 V_2 }}{{n_2 T_2 }}\]

Density of a Material

\[D = \frac{m}{V}\]

Root Mean Square Velocity of Gas Molecules

\[u_{rms} = \sqrt {\frac{{3kT}}{m}} = \sqrt {\frac{{3RT}}{M}}\]

Kinetic Energy per molecule

\[\frac{{KE}}{{molecule}} = \frac{1}{2}m\upsilon ^2\]

Kinetic Energy per Mole

\[\frac{{KE}}{{mole}} = \frac{3}{2}RTn\]

Graham's Law of Effusion

\[\frac{{r_1 }}{{r_2 }} = \sqrt {\frac{{M_2 }}{{M_1 }}}\]

Molarity Defined

\[\begin{array}{*{20}c} {molarity,} & {M = \frac{{\begin{array}{*{20}c} {moles} & {solute} \\ \end{array}}}{{\begin{array}{*{20}c} {liter} & {solution} \\ \end{array}}}} \\ \end{array}\]

Molality Defined

\[\begin{array}{*{20}c} {molality,} & { = \frac{{\begin{array}{*{20}c} {moles} & {solute} \\ \end{array}}}{{\begin{array}{*{20}c} {kilogram} & {solvent} \\ \end{array}}}} \\ \end{array}\]

Freezing Point Depression

\[\Delta T_f = iK_f \times molality\]

Boiling Point Elevation

\[\Delta T_b = iK_b \times molality\]

Osmotic Pressure

\[\pi = \frac{{nRT}}{V}i\]

van't Hoff equation

\[\ln \left( {\frac{{K_2 }}{{K_1 }}} \right) = - \frac{{\Delta H^\circ }}{R}\left[ {\frac{1}{{T_2 }} - \frac{1}{{T_1 }}} \right]\]