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Raoult's law for a binary liquid mixture of volatile A and B: the partial pressures `pA` = x_A p°_A and `pB`, the `total`, the liquid fractions `xA`, `xB` and the vapour's `yA`, `yB` (Dalton). Pressures in the unit of p°.
pA0 (number) -- the vapour pressure of pure ApB0 (number) -- of pure BxA (number) -- the mole fraction of A in the liquidThe liquid in equilibrium with a vapour of mole fraction y_A (the same record as `raoult`).
pA0 (number) -- the vapour pressure of pure ApB0 (number) -- of pure ByA (number) -- the mole fraction of A in the vapourThe liquid whose total vapour pressure is p (between p°_B and p°_A; the same record as `raoult`).
pA0 (number) -- the vapour pressure of pure ApB0 (number) -- of pure Bp (number) -- the total vapour pressureHenry's law p = K_H x: the partial pressure of a gas over a solution in which its mole fraction is x.
KH (number) -- Henry's constant in the pressure's unitx (number) -- the mole fraction of the gas in the solutionHenry's law the other way: the mole fraction x = p/K_H dissolved under a partial pressure p.
KH (number) -- Henry's constantp (number) -- the partial pressure in the same unitHenry's constant K_H = p/x from one measurement.
p (number) -- the partial pressurex (number) -- the mole fraction dissolvedThe azeotrope of a non-ideal mixture in the one-parameter (Margules) model p_A = x_A p°_A exp(A x_B²), p_B = x_B p°_B exp(A x_A²): the composition where the vapour has the liquid's composition (the record of `raoult`), or the word none. A > 0 is a positive deviation (a minimum-boiling azeotrope), A < 0 negative.
pA0 (number) -- the vapour pressure of pure ApB0 (number) -- of pure BA (number) -- the deviation parameterThe relative lowering of vapour pressure (p° − p)/p°, equal to the solute's mole fraction.
p0 (number) -- the pure solvent's vapour pressurep (number) -- the solution'sThe vapour pressure of a solution of a non-volatile solute: p = p° n₁/(n₁ + i n₂).
p0 (number) -- the pure solvent's vapour pressuren2 (number) -- moles of soluten1 (number) -- moles of solventi (number) -- the van't Hoff factor (optional, 1)The molar mass of a solute from the relative lowering: exact from x₂ = n₂/(n₁ + n₂), or with the word dilute NCERT's x₂ ≈ n₂/n₁ (Ex 1.8).
p0 (number) -- the pure solvent's vapour pressurep (number) -- the solution'sw2 (number) -- the solute's mass in gw1 (number) -- the solvent's mass in gM1 (number) -- the solvent's molar mass in g/moldilute (word) -- optional: "dilute" for the approximationThe molality in mol/kg of w₂ g of a solute of molar mass M₂ in w₁ g of solvent.
w2 (number) -- the solute's mass in gM2 (number) -- its molar mass in g/molw1 (number) -- the solvent's mass in gThe elevation of the boiling point ΔT_b = i K_b m.
Kb (number) -- the ebullioscopic constant in K kg/molm (number) -- the molalityi (number) -- the van't Hoff factor (optional, 1)The depression of the freezing point ΔT_f = i K_f m.
Kf (number) -- the cryoscopic constant in K kg/molm (number) -- the molalityi (number) -- the van't Hoff factor (optional, 1)The molar mass of a solute from an elevation or a depression: M₂ = i K w₂ 1000/(ΔT w₁), in g/mol.
K (number) -- K_b or K_fdT (number) -- the ΔT measured in Kw2 (number) -- the solute's mass in gw1 (number) -- the solvent's mass in gi (number) -- the van't Hoff factor (optional, 1)The osmotic pressure π = i C R T in atm (R = 0.0821 L atm/K/mol), or in bar with the word bar (R = 0.083 as NCERT uses).
C (number) -- the concentration in mol/LT (number) -- the temperature in Ki (number) -- the van't Hoff factor (optional, 1)bar (word) -- optional: "bar"The molar mass from the osmotic pressure of w g of solute in V litres at T: M = i w R T/(π V), π in atm or (with the word bar) in bar.
pi (number) -- the osmotic pressurew (number) -- the solute's mass in gV (number) -- the solution's volume in LT (number) -- the temperature in Ki (number) -- the van't Hoff factor (optional, 1)bar (word) -- optional: "bar"The concentration in mol/L that is isotonic with (has the same osmotic pressure as) a solution of osmotic pressure π at T.
pi (number) -- the osmotic pressure in atm, or bar with the wordT (number) -- the temperature in Ki (number) -- the van't Hoff factor (optional, 1)bar (word) -- optional: "bar"The van't Hoff factor i = observed colligative property / calculated, or calculated molar mass / observed molar mass.
observed (number) -- the measured ΔT, π or lowering (or the normal molar mass)calculated (number) -- the value for no dissociation or association (or the observed molar mass)The degree of dissociation α = (i − 1)/(n − 1) of a solute that gives n particles.
i (number) -- the van't Hoff factorn (number) -- the particles one formula unit givesThe degree of association α = (1 − i) n/(n − 1) of a solute that forms n-mers.
i (number) -- the van't Hoff factorn (number) -- the molecules in one associated particle (2 for a dimer)i = 1 + (n − 1) α for a degree of dissociation α into n particles.
alpha (number) -- the degree of dissociationn (number) -- the particles giveni = 1 − α (1 − 1/n) for a degree of association α into n-mers.
alpha (number) -- the degree of associationn (number) -- the molecules per associated particleK_b = R T_b² M/(1000 ΔH_vap) in K kg/mol.
Tb (number) -- the solvent's boiling point in KM (number) -- its molar mass in g/moldHvap (number) -- its enthalpy of vaporisation in J/molK_f = R T_f² M/(1000 ΔH_fus) in K kg/mol.
Tf (number) -- the solvent's freezing point in KM (number) -- its molar mass in g/moldHfus (number) -- its enthalpy of fusion in J/molA solvent of NCERT XII Table 1.3: `bp` and `fp` in K, `Kb` and `Kf` in K kg/mol, `M` in g/mol. Water, ethanol, cyclohexane, benzene, chloroform, carbon tetrachloride (CCl4), carbon disulphide (CS2), diethyl ether, acetic acid.
name (word) -- the solventDraws Raoult's law on a diagram: p_A, p_B and p = p_A + p_B against x_A (pure B at the left, pure A at the right). With "positive", "negative" or a Margules parameter A the observed curves are drawn over the dashed ideal lines and the azeotrope is marked; a final x_A marks that composition with its pressures in the caption.
d (word) -- the diagrampA0 (number) -- the vapour pressure of pure ApB0 (number) -- of pure Bkind (word) -- optional: "ideal", "positive", "negative" or a number AxA (number) -- optional: a composition to markDraws Henry's law on a diagram: the partial pressure of a gas against its mole fraction in the solution, a line of slope K_H.
d (word) -- the diagramKH (number) -- Henry's constantxMax (number) -- optional: the largest mole fraction shownDraws the vapour-pressure curves of a solvent and its solution against temperature: "boiling" shows the solution reaching 1 atm later (ΔT_b), "freezing" the solid's curve met earlier (ΔT_f), "both" the two ends. Not to scale: the gaps are drawn large; the caption gives the real ΔT_b and ΔT_f of the solvent (water unless named) at the molality (1 mol/kg unless given).
d (word) -- the diagramkind (word) -- "boiling", "freezing" or "both"solvent (word) -- optional: a Table 1.3 solventm (number) -- optional: the molalityDraws osmosis: a vessel parted by a semipermeable membrane, solvent at the left and solution at the right. "flow" the solvent passing in, "equilibrium" the solution's level higher by h, "pressure" the piston whose pressure π just stops the flow, "reverse" a pressure above π driving solvent out.
d (word) -- the diagramkind (word) -- "flow", "equilibrium", "pressure" or "reverse"pi (number) -- optional: the osmotic pressure to write in the caption