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11 Verified Equations

CSCA Chemistry Formula Catalog

CSCA 化学核心定律与计算公式库

Essential repository of all 17 CSCA Chemistry formulas: stoichiometry, gas laws, chemical equilibrium constants, Arrhenius equation, and electrochemistry.

Basic Chemical Concepts and Calculations

5 Formulas

Amount of Substance, Mass & Particle Count Relations

物质的量、微粒数与质量换算公式

The fundamental quantitative relation in chemistry linking moles (n), mass in grams (m), molar mass (M in g/mol), particle count (N), and Avogadro's constant (N_A ≈ 6.02 × 10²³ mol⁻¹).

$\[ n = \frac{m}{M} = \frac{N}{N_A} \]$
Proof

Gas Volume and Moles at STP

气体摩尔体积与标况状态公式

Calculates moles (n) of any ideal gas at Standard Temperature and Pressure (STP: 0°C, 101.3 kPa) where molar volume V_m is exactly 22.4 L/mol.

$\[ n = \frac{V}{V_m} \quad (V_m = 22.4\text{ L/mol at } 0^\circ\text{C, } 101.3\text{ kPa}) \]$
Proof

Molar Concentration of Solution & Dilution Law

物质的量浓度公式与稀释定律

Defines molar concentration c in mol/L. During solution dilution by adding solvent, the amount of solute in moles remains strictly constant (n = c₁V₁ = c₂V₂).

$\[ c = \frac{n}{V}, \quad c_1 V_1 = c_2 V_2 \]$
Proof

Conversion between Mass Fraction and Molar Concentration

质量分数与物质的量浓度的换算公式

Converts mass percentage fraction (w) of a concentrated liquid reagent to molarity (c), where ρ is density in g/cm³ and M is solute molar mass in g/mol.

$\[ c = \frac{1000 \rho w}{M} \]$
Proof

Ideal Gas Law Equation of State

理想气体状态方程（克拉珀龙方程）

Relates pressure (P), volume (V), moles (n), temperature (T in Kelvin), and gas constant (R). Derived form PM = ρRT allows direct molar mass calculation from gas density.

$\[ PV = nRT = \frac{m}{M}RT \implies PM = \rho RT \]$
Proof

Chemical Theories and Laws

6 Formulas

Chemical Reaction Rate & Rate Ratio Law

化学反应速率与化学计量数比值规律

Reaction rate is the rate of change of molar concentration over time. The ratio of reaction rates for different substances strictly equals the ratio of their stoichiometric coefficients.

$\[ v = \frac{\Delta c}{\Delta t}, \quad \frac{v(\text{A})}{a} = \frac{v(\text{B})}{b} = \frac{v(\text{C})}{c} \]$
Proof

Chemical Equilibrium Constant Expression

化学平衡常数表达式与转化率公式

Calculates the dynamic equilibrium constant K for aA + bB ⇌ cC + dD using equilibrium concentrations. K depends ONLY on temperature.

$\[ K = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b}, \quad \alpha = \frac{\Delta n}{n_0} \times 100\% \]$
Proof

pH, pOH & Water Ion Product Equilibrium

pH定义式与水的离子积常数

Defines acidity on the logarithmic pH scale. In any aqueous solution at 25°C, pH + pOH = 14. Water ionization is endothermic, so K_w increases with rising temperature.

$\[ \text{pH} = -\log_{10}[\text{H}^+], \quad K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14} \text{ at } 25^\circ\text{C} \]$
Proof

Arrhenius Activation Energy Equation

阿伦尼乌斯公式与活化能

Relates reaction rate constant k to activation energy E_a and Kelvin temperature T. Catalysts lower E_a, exponentially increasing rate constant k.

$\[ k = A e^{-\frac{E_a}{RT}} \implies \ln k = -\frac{E_a}{R}\frac{1}{T} + \ln A \]$
Proof

Gibbs Free Energy Spontaneity Criterion

吉布斯自由能判据与反应自发性

Determines the thermodynamic spontaneity of a chemical reaction at constant T and P. Spontaneous when ΔG < 0, at equilibrium when ΔG = 0.

$\[ \Delta G = \Delta H - T\Delta S \quad (\Delta G < 0 \implies \text{Spontaneous}) \]$
Proof

Galvanic & Electrolytic Cell Electrode Reactions

原电池与电解池电极反应规律

Electrochemical fundamental rule: Oxidation always occurs at the Anode (负极 in galvanic, 阳极 in electrolytic), and Reduction always occurs at the Cathode (正极 in galvanic, 阴极 in electrolytic).

$\[ \text{Anode: Oxidation (loss of } e^-), \quad \text{Cathode: Reduction (gain of } e^-) \]$
Proof