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Common Equations Used in Chemistry
Equation for density: d=mv
Converting ˚F to ˚C: ˚C = (˚F - 32) x^59
Converting ˚C to ˚F: ˚F = ˚C x^95 + 32
Converting ˚C to K: K = (˚C + 273.15)
Percent composition of an element = n molar mass of compound^ x molar mass of element x 100%
- where n = the number of moles of the element in one mole of the compound
% yield = (^) theoretical yieldactual yield x 100%
molarity (M) = liters of solutionmoles of solute
Dilution of Solution: Mi V (^) i = MfV (^) f Boyle’s law - Constant T and n : PV = k Boyle’s law - For calculating changes in pressure or volume: P 1 V 1 = P 2 V (^2)
Charles’ law - Constant P and n : VT = k
Charles’ law - For calculating temperature or volume changes: V T^11 = V T^22
Avogadro’s law - Constant P and T: V = k n Ideal Gas equation: PV = n RT Calculation of changes in pressure, temperature, or volume of gas when n is constant: P 1 V (^1) T 1 =
P 2 V 2
T 2
Calculation of density or molar mass of gas: d = P RT M
Dalton’s law of partial pressures - for calculating partial pressures: Pi = Xi PT
Root-mean-square speed of gas molecules: u (^) rms = (3RT M )0.
Van der waals equation; for calculating the pressure of a nonideal gas: (P + a V n^ 22 ) (V - n b) = n RT
Definition of heat capacity, where s is specific heat: C = ms Calculation of heat change in terms of specific heat : q = ms∆t Calculation of heat change in terms of heat capacity: q = C∆t
Electrical force: Fel = kq^1 rq 22
Potential energy: V = kq^1 rq^2
Calculation of standard enthalpy of reaction: ∆H ˚ rxn = ∑n∆H ˚ f (products) - ∑m ∆H ˚ f (reactants) [where n and m are coefficients in equation] Mathematical statement of the first law of thermodynamics: ∆E = q + w Work done in gas expansion or compression: w = - P∆V Definition of enthalpy: H = E + PV Enthalpy (or energy) change for a constant-pressure process: ∆H = ∆E +P∆V Enthalpy (or energy) change for a constant-pressure process: ∆E = ∆H - RT∆ n , where n is the change in the number of moles of gas.
Relationship of wavelength and frequency: u = λν
Energy of a photon: E = hν
Entropy change of heat flow at constant temperature: ∆S = Tq
Calculating the molality of a solution: molality (m) = moles of solute1000 g solvent
Henry’s law for calculating solubility (c) of gases: c = kP Raoult’s law relating the vapor pressure of a liquid to its vapor pressure in a solution: P 1 = X 1 P ˚ (^1) Vapor pressure lowering in terms of the concentration of solution: ∆P = X 2 P ˚ (^1) Boiling point elevation: ∆Tb = Kbm Freezing point depression: ∆Tf = Kfm Osmotic pressure of a solution: π = MRT The van’t Hoff factor for an electrolyte solution: i = actual number of particles in soln after dissociationnumber of formula units initially dissoved in soln
Rate law expression. The sum (x+ y) gives the overall order of the reaction: rate = k[A]x[B]y Relationship between concentration and time for a first-order reaction: ln [A]o [A] = kt Equation for the graphical determination of k for a first-order reaction: ln [A] = -kt + ln [A]o
Half-life for a first-order reaction: t1/2 = ln 2k = 0.693k
Relationship between concentration and time for a second-order reaction: (^) [A]^1 = (^) [A]o^1 + kt
The Arrhenius equation expressing the dependence of the rate constant on activation energy and temperature: k = Ae-Ea/RT
Equation for the graphical determination of activation energy: ln k = (- E Ra ) (T^1 ) + ln A
Relationships of rate constants at two different temperatures: ln k k^12 = Ea R (
T 1 - T 2
T 1 T 2 )
Law of Mass Action - General expression of equilibrium constant: K = [A][C]ca[D][B]db
Relationship between Kp and Kc: Kp = Kc(0.0821*T)∆n The equilibrium constant for the overall reaction is given by the product of the equilibrium constants for the individual reactions: Kc = K’cK”c Ion-product constant of water: Kw = [H+][OH-]
Definition of pH of a solution: pH = -log [H+]
Definition of pOH of a solution: pOH = -log [OH-] Another form of ion-product constant of water: pH + pOH = 14.
Percent ionization = ionized acid concentration at equilibriuminitial concentration of acid x 100%
Relationship between the acid and base ionization constants of a conjugate acid-base pair: KaKb = Kw
Henderson-Hasselbach equation: pH = pKa + log [conjugate base][acid]
The second law of thermodynamics (spontaneous process): ∆Suniv = ∆Ssys +∆Ssurr > 0 The second law of thermodynamics (equilibrium process): ∆Suniv = ∆Ssys + ∆Ssurr = 0
