Analytical Chemistry

the text will be hard
11.18 21:55 stop down here. too sleepy.

1. Analytical Fundamentals & Statistics

1.1. Moles and Concentration

• Moles:

  \[1 u = 1.66053906660×10^{−27} kg \]
  \[u×N_A​ = Da×N_A​ = MW = \frac{g}{mol} = 0.001\frac{kg}{mol} \]
  \[\text{Moles} = \frac{\text{grams}}{\text{formula weight (Molecular Weight, MW, g/mol)}} \quad (5.1) \]

• Molarity (M):

  \[M = \frac{mol}{L} = \frac{mol}{{dm}^3} = 0.001\frac{mol}{m^3} \]
  \[\text{Moles} = M \times \text{Liters} \quad (5.4) \]
  \[\text{Millimoles} = M \times \text{mL} \quad (5.5) \]

• Normality (N) & Equivalents:

  potenzH: hydrogen ion concentration, pH. Soren Peter Lauritz Sorensen, a Denmark biochemist.

  Acid-base reactions: H⁺ transfer = removal of electron from hydrogen

  Redox(reduction oxidation) reactions: e⁻ transfer = movement of elementary charge

  Precipitation: Ion formation = electron gain/loss

  The fundamental unit of chemical change is the electron charge: e = 1.602 × 10⁻¹⁹ C

  \[\text{Number of equivalents (eq)} = N_A × (\text{number of reactive units per molecule}) = \text{ 6.02214076×10²³ × Z }mol^{-1} \]

  there, Z is the number of reactive units per molecule, which is dimensionless. ()

  \[\text{Number of equivalents (eq)} = \text{Normality (eq/L)} \times \text{Volume (L)} \quad (5.6) \]
  \[\text{Equivalent weight} = \frac{\text{Formula Weight}}{\text{number of reacting units (e.g., H⁺, e⁻)}} \]

1.2. Expression of Results

• %

• ppm parts per million

• ppb parts per billion

• ppt parts per trillion/thousand

  \[\text{ppm(wt/vol)} = \frac{\text{wt solute(g)}}{\text{vol sample(mL)}} \times 10^6 \]

Avoid "ppm" entirely in reporting. Use explicit units.

1.3. Statistical Treatment of Data

• Standard Deviation (Sample):
  \[s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{N-1}} \]

• Standard Deviation of the Mean:
  \[s_{\bar{x}} = \frac{s}{\sqrt{N}} \]

• Least-Squares Linear Calibration:
  \[y = mx + b \]
  \[m = \frac{\sum x_i y_i - [(\sum x_i \sum y_i)/n]}{\sum x_i^2 - [(\sum x_i)^2/n]} \quad ; \quad b = \bar{y} - m\bar{x} \]

2. Chemical Equilibrium & Thermodynamics

2.1. General Equilibrium
For a reaction: $ aA + bB \rightleftharpoons cC + dD $

\[K = \frac{[C]^c[D]^d}{[A]^a[B]^b} = \frac{k_{fwd}}{k_{rev}} \quad (6.5) \]

2.2. Gibbs Free Energy & Equilibrium

\[\Delta G^\circ = -RT \ln K = -2.303RT \log K \quad (6.10) \]

\[K = e^{-\Delta G^\circ / RT} \quad (6.9) \]

2.3. Temperature Dependence (Clausius-Clapeyron form)

\[\ln \frac{K_1}{K_2} = \frac{\Delta H}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \quad (\text{Page 56}) \]

2.4. Activity and Ionic Strength

• Activity:
  \[a_i = C_i f_i \quad (6.17) \]
  where $ f_i $ is the activity coefficient.
• Ionic Strength (μ):
  \[\mu = \frac{1}{2} \sum C_i Z_i^2 \quad (6.18) \]

• Debye-Hückel Equation (Extended):
  \[-\log f_i = \frac{A Z_i^2 \sqrt{\mu}}{1 + B a_i \sqrt{\mu}} \quad (6.19b) \]

• Davies Modification:
  \[-\log f_i = 0.51 Z_i^2 \left( \frac{\sqrt{\mu}}{1 + \sqrt{\mu}} - 0.3\mu \right) \quad (6.21) \]