Developed by Dr E. Ramanathan
Target Audience: High School, Higher Secondary Students, NEET-JEE Aspirants, Chemists, Engineers, Operators from Surface Coating Technology Field.
Terms, Definitions, Symbols – TDS
Concentration Terms and Definitions — SaitechAI
| Term | Definition / Formula | Units |
|---|---|---|
| Weight/Weight % (w/w%) | \(\%w/w = \dfrac{w_2}{W}\times 100\) | % (g solute per 100 g solution) |
| Weight/Volume % (w/v%) | \(\%w/v = \dfrac{w_2}{V}\times 100\) | % (g solute per 100 mL solution) |
| Volume/Volume % (v/v%) | \(\%v/v = \dfrac{V_2}{V}\times 100\) | % (mL solute per 100 mL solution) |
| Molarity (M) | \(M = \dfrac{n_2}{V} = \dfrac{w_2}{M_2 \cdot V}\) | mol·L⁻¹ |
| Molality (m) | \(m = \dfrac{n_2}{w_1(\mathrm{kg})} = \dfrac{w_2}{M_2 \cdot w_1(\mathrm{kg})}\) | mol·kg⁻¹ |
| Normality (N) | \(N = \dfrac{eq_2}{V} = \dfrac{w_2}{\text{GEW}_2 \cdot V}, \ \text{GEW}_2 = \dfrac{M_2}{e}\) | eq·L⁻¹ |
| Mole Fraction (\(x_2\)) | \(x_2 = \dfrac{n_2}{n_1+n_2}\) | Dimensionless |
| Parts per million (ppm) | \(\text{ppm} = \dfrac{w_2}{W}\times 10^6\) For aqueous solutions: \(1 \ \text{mg·L}^{-1} \approx 1 \ \text{ppm}\) |
ppm (mg·L⁻¹) |
Symbols: \(w_2\) = solute mass (g), \(w_1\) = solvent mass (g or kg), \(W = w_1+w_2\) = solution mass, \(V\) = solution volume (L), \(V_2\) = solute volume, \(M_2\) = molar mass of solute (g·mol⁻¹), \(e\) = equivalence factor.
Data, Equations, Formulations
Expressions of Concentration — SaitechAI
Symbols & Definitions
- \(w_2\): mass (weight) of solute; \(w_1\): mass of solvent; \(W=w_1+w_2\): mass of solution.
- \(M_2\): molar mass of solute; \(M_1\): molar mass of solvent.
- \(n_2=\dfrac{w_2}{M_2}\): moles of solute; \(\;n_1=\dfrac{w_1}{M_1}\): moles of solvent.
- \(V_2\): volume of liquid solute; \(V_1\): volume of solvent; \(V\): volume of solution.
Unless stated otherwise: masses in grams, volumes in litres (L) for molarity, and kilograms (kg) for molality denominator.
Percent Concentrations
- w/w %: \(\displaystyle \%\,\frac{w}{w}=\frac{w_2}{W}\times 100\)
- w/v %: \(\displaystyle \%\,\frac{w}{v}=\frac{w_2}{V}\times 100\)
- v/v %: \(\displaystyle \%\,\frac{v}{v}=\frac{V_2}{V}\times 100\)
Molarity (\(M\))
\[ M \;=\; \frac{n_2}{V}\;=\;\frac{w_2/M_2}{V}\quad\text{(mol L}^{-1}\text{)} \]
Normality (\(N\))
\[ N \;=\; \frac{\text{equivalents of solute}}{V} \;=\; \frac{eq_2}{V},\qquad eq_2 \;=\; \frac{w_2}{\text{GEW}_2} \]
\[ \text{GEW}_2 \;=\; \frac{M_2}{e} \] where \(e\) is the valence (equivalence) factor determined by the reaction context (acid–base, redox, precipitation, etc.).
| Solute (typical context) | \(e\) | Notes |
|---|---|---|
| \(\mathrm{HCl}\), \(\mathrm{NaOH}\) (acid–base) | 1 | Monoprotic acid / monobasic base |
| \(\mathrm{H_2SO_4}\) (acid–base) | 2 | Diprotic acid (can donate 2 H\(^+\)) |
| \(\mathrm{CaSO_4}\) (precipitation/ionic) | 2 | In ionic reactions, \(e\) equals total charge change per mole participating |
Molality (\(m\))
Defined per kilogram of solvent (not solution).
\[ m \;=\; \frac{n_2}{\;w_1\;(\mathrm{kg})}\;=\;\frac{w_2/M_2}{w_1(\mathrm{kg})}\quad\text{(mol kg}^{-1}\text{)} \]
Mole Fraction
Sum of all mole fractions equals 1.
\[ x_2 \;=\; \frac{n_2}{n_1+n_2},\qquad x_1 \;=\; \frac{n_1}{n_1+n_2},\qquad x_1+x_2=1 \]
Parts Per Million (ppm)
- Mass fraction (general): \[ \mathrm{ppm} \;=\; \frac{w_2}{W}\times 10^{6} \]
- Aqueous, dilute (practical): \[ \mathrm{ppm} \;\approx\; \frac{\text{mg solute}}{\text{L solution}} \] (since \(1~\mathrm{mg\,L^{-1}}\approx 1~\mathrm{ppm}\) for water-like density)
- Volume basis (less common): if using \(w/v\) fraction, \[ \mathrm{ppm} \;=\; \bigl(\tfrac{w}{v}\bigr)\times 10^{6} \] with consistent units.
Quick Reference
| Quantity | Primary Formula | Common Rearrangement |
|---|---|---|
| Molarity, \(M\) | \(M=\dfrac{n_2}{V}\) | \(M=\dfrac{w_2}{M_2\,V}\) |
| Normality, \(N\) | \(N=\dfrac{eq_2}{V}\) | \(N=\dfrac{w_2}{\text{GEW}_2\,V}\) |
| Molality, \(m\) | \(m=\dfrac{n_2}{w_1(\mathrm{kg})}\) | \(m=\dfrac{w_2}{M_2\,w_1(\mathrm{kg})}\) |
| Mole fraction, \(x_2\) | \(x_2=\dfrac{n_2}{n_1+n_2}\) | \(x_1=\dfrac{n_1}{n_1+n_2}\) |
| w/w% | \(\dfrac{w_2}{W}\times 100\) | — |
| w/v% | \(\dfrac{w_2}{V}\times 100\) | — |
| v/v% | \(\dfrac{V_2}{V}\times 100\) | — |
| ppm (mass) | \(\dfrac{w_2}{W}\times 10^{6}\) | \(\approx\dfrac{\text{mg}}{\text{L}}\) (aqueous) |
Always specify temperature and density assumptions when converting between mass- and volume-based measures.
