stoichiometry
Constants & unit traps, the mole, solutions & gases, limiting reagents, yields, titration.
constants & unit traps · mole & formulas · solutions & gases · reaction stoichiometry · titration & analysis
Constants & unit traps
| Constant | Value |
|---|---|
| \(N_A\) | \(6.02\times10^{23}\ \mathrm{mol^{-1}}\) |
| \(R\) | \(8.31\ \mathrm{J\,mol^{-1}\,K^{-1}}\) |
| \(h\) | \(6.63\times10^{-34}\ \mathrm{J\,s}\) |
| \(c\) | \(3.00\times10^{8}\ \mathrm{m\,s^{-1}}\) |
| \(F\) | \(9.65\times10^{4}\ \mathrm{C\,mol^{-1}}\) |
| \(K_w\) | \(1.00\times10^{-14}\) at 298 K |
| \(V_m\) (STP) | \(22.7\ \mathrm{dm^3\,mol^{-1}}\) |
| \(c_w\) | \(4.18\ \mathrm{J\,g^{-1}\,K^{-1}}\) |
| STP | 273.15 K, 100 kPa |
| SATP | 298.15 K, 100 kPa |
Unit traps. \(T/\mathrm{K}={}^{\circ}\mathrm{C}+273.15\); \(1\ \mathrm{dm^3}=1\ \mathrm{L}=10^{3}\ \mathrm{cm^3}=10^{-3}\ \mathrm{m^3}\); \(1\ \mathrm{kPa}=10^{3}\ \mathrm{Pa}\); \(\Delta S\) in \(\mathrm{J\,K^{-1}\,mol^{-1}}\) but \(\Delta H\) in \(\mathrm{kJ\,mol^{-1}}\) — convert before \(\Delta G\).
The mole & formulas
Molar mass. \(n=\frac{m}{M}\); \(M=M_r\) in \(\mathrm{g\,mol^{-1}}\).
Formulas. Empirical formula = simplest ratio; molecular formula \(=(\text{empirical})\times n\) with \(n=M_r/\mathrm{EFM}\).
Solutions & gases
Solutions. \(c=n/V\), so \(n=CV\); dilution \(C_1V_1=C_2V_2\).
Avogadro's law. Equal gas volumes at the same \(T,P\) contain the same particle number. Gas density \(\rho=PM/RT\); molar mass \(M=\rho RT/P\).
Ideal vs real. Ideal gas: negligible particle volume + no IMFs + elastic collisions. Real gases deviate at high \(P\), low \(T\), large/polar particles.
Gas laws. \(PV=nRT\); combined \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\). Boyle \(P\propto1/V\); Charles \(V\propto T\); Gay-Lussac \(P\propto T\); Avogadro \(V\propto n\).
Reaction stoichiometry
Workflow. Balanced coefficients = mole ratios. Balance → convert known to mol → use the ratio → convert to the requested unit.
Limiting reagent. Smallest \(n/\nu\); the excess remains. Theoretical yield from the limiting reagent.
Yield & purity. \(\%Y=\frac{\text{actual}}{\text{theoretical}}\times100\); purity \(=\frac{\text{mass pure}}{\text{mass impure}}\times100\); atom economy \(\%AE=\frac{M_r\ \text{desired}}{\sum M_r\ \text{reactants}}\times100\). Atom economy and yield are separate green metrics.
Titration & analysis
Titration. At equivalence \(\frac{n_A}{a}=\frac{n_B}{b}\) for \(a\,\ce{A} + b\,\ce{B}\).
Combustion analysis. \(n_\mathrm{C}=n_{\ce{CO2}}\), \(n_\mathrm{H}=2n_{\ce{H2O}}\); oxygen by mass difference.
Hydrates. Heat to constant mass; \(x\) in \(\text{salt}\cdot x\ce{H2O}\) from the mole ratio.