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Chemistry 232 Electrolyte Solutions

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Thermodynamics of Ions in Solutions Electrolyte solutions – deviations from ideal behaviour occur at molalities as low as 0.01 mole/kg. How do we obtain thermodynamic properties of ionic species in solution?

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Thermodynamics (II) For the H + (aq) ion, we define f H = 0 kJ/mole at all temperatures S = 0 J/(K mole) at all temperatures f G = 0 kJ/mole at all temperatures

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Activities in Electrolyte Solutions For the following discussion Solvent “s” Cation “+” Anion “-“ Consider 1 mole of an electrolyte dissociating into + cations and - anions G = n s s + n = n s s + n + + + n - - Note – since = = + -

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The Mean Ionic Chemical Potential We define = / We now proceed to define the activities = + RT ln a + = + + RT ln a + - = - + RT ln a - = + RT ln a

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The Relationship Between a and a Since = / = + RT ln a = ( + RT ln a ) Since = / This gives us the relationship between the electrolyte activity and the mean activity (a ) = a

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The Relationship Between a , a - and a + We note that = + - and = / This gives us the following relationship ( + RT ln a ) = + ( + + RT ln a + ) + - ( - + RT ln a - ) Since = + + + - - (a ) = (a + )+ (a - )-

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Activities in Electrolyte Solutions The activities of various components in an electrolyte solution are defined as follows a + = + m + a - = - m - a + = + m + As with the activities ( ) = ( + )+ ( - )- (m ) = (m + )+ (m - )-

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The Chemical Potential Expression This can be factored into two parts The ideal part Deviations from ideal behaviour

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KCl CaCl 2 H 2 SO 4 HCl LaCl 3 Activity Coefficients As a Function of Molality Data obtained from Glasstone et al., Introduction to Electrochemistry, Van Nostrand (1942). CRC Handbook of Chemistry and Physics, 63 rd ed.; R.C. Weast Ed.; CRC Press, Boca Raton, Fl (1982).

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Determination of Activity Coefficients in Solution Two ways Use the Gibbs-Duhem equation and for the solvent to estimate for the solute. Determination of osmotic coefficients from colligative properties vapour pressure measurements

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Estimates of Activity Coefficients in Electrolyte Solutions A few have been proposed to allow the theoretical estimation of the mean activity coefficients of an electrolyte. Each has a limited range of applicability.

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u This is valid in the up to a concentration of molal! The Debye Hűckel Limiting Law Z + = charge of cation; z - = charge of anion

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Debye Hűckel Extended Law This equation can reliably estimate the activity coefficients up to a concentration of 0.10 mole/kg. B = 1.00 (kg/mole) 1/2

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The Davies Equation This equation can reliably estimate the activity coefficients up to a concentration of 1.00 mole/kg. k = 0.30 (kg/mole)

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The Equilibrium Constant For a nonideal system, the nonstandard Gibbs energy of reaction is written

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The Equilibrium Condition If we apply the equilibrium conditions to the above equation

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The Autoionization of Water Water autoionizes (self-dissociates) to a small extent 2H 2 O(l) ⇌ H 3 O + (aq) + OH - (aq) H 2 O(l) ⇌ H + (aq) + OH - (aq) These are both equivalent definitions of the autoionization reaction. Water is amphoteric.

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The Autoionization Equilibrium From the equilibrium chapter u But we know a(H 2 O) is 1.00!

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The Defination of K w K w = a(H + ) a(OH - ) Ion product constant for water, K w, is the product of the activities of the H + and OH - ions in pure water at a temperature of K K w = a(H + ) a(OH - ) = 1.0x at K

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The pH scale Attributed to Sørenson in 1909 We should define the pH of the solution in terms of the hydrogen ion activity in solution pH -log a(H + ) Single ion activities and activity coefficients can’t be measured

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Determination of pH What are we really measuring when we measure the pH? pH -log a(H + ) a (H + ) is the best approximation to the hydrogen ion activity in solution. How do we measure a(H + )?

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For the dissociation of HCl in water HCl (aq) Cl - (aq) + H + (aq) We measure the mean activity of the acid a(HCl) = a(H + ) a(Cl - ) a(H + ) a(Cl - ) = (a (HCl)) 2

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Under the assumption a(H + ) = a(Cl - ) We obtain a´(H + ) = (a(HCl)) 1/2 = a (HCl)

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Equilibria in Aqueous Solutions of Weak Acids/ Weak Bases By definition, a weak acid or a weak base does not ionize completely in water ( <<100%). How would we calculate the pH of a solution of a weak acid or a weak base in water?

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Equilibria of Weak Acids in Water: The K a Value Define the acid dissociation constant K a For a general weak acid reaction HA (aq) ⇌ H + (aq) + A - (aq)

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Equilibria of Weak Acids in Water For the dissolution of HF(aq) in water. HF (aq) H + (aq) + F - (aq)

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The Nonelectrolyte Activity HF (aq) ⇌ H + (aq) + F - (aq) The undissociated HF is a nonelectrolyte a(HF) = (HF) m[HF] m[HF] (HF) 1

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Equilibria of Weak Bases in Water Calculate the percentage dissociation of a weak base in water (and the pH of the solutions) CH 3 NH 2 (aq) + H 2 O ⇌ CH 3 NH 3 + (aq) + OH - (aq)

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The K b Value Define the base dissociation constant K b For a general weak base reaction with water B (aq) + H 2 O (aq) ⇌ B + (aq) + OH - (aq)

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Calculating the pH of Solutions of Strong Acids For the dissolution of HCl, HI, or any of the other seven strong acids in water HCl (aq) H + (aq) + Cl - (aq) The pH of these solutions can be estimated from the molality and the mean activity coefficient of the dissolved acid pH = -log ( (acid) m[H + ])

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Calculating the pH of Solution of Strong Bases For the dissolution of NaOH, Ba(OH) 2, or any of the other strong bases in water NaOH (aq) Na + (aq) + OH - (aq) pOH = -log ( (base) m[OH - ])

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Calculating the pH of a Weak Acid Solution The pH of a weak acid solution is obtained via an iterative procedure. We begin by making the assumption that the mean activity coefficient of the dissociated acid is We ‘correct’ the value of (H + ) by calculating the mean activity coefficient of the dissociated acid. Repeat the procedure until (H + ) converges.

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The Definition of a Buffer Buffer a reasonably concentrated solution of a weak acid and its conjugate base Buffers resist pH changes when an additional amount of strong acid or strong base is added to the solutions.

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How would we calculate the pH of a buffer solution?

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note pH = -log a(H + ) Define pK a = -log (K a )

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The Buffer Equation Substituting and rearranging

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The Generalized Buffer Equation The pH of the solution determined by the ratio of the weak acid to the conjugate base. Henderson-Hasselbalch equation often used for buffer calculations!

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Buffer CH 3 COONa (aq) and CH 3 COOH (aq)) CH 3 COOH (aq) ⇄ CH 3 COO - (aq) + H + (aq) The Equilibrium Data Table n(CH 3 COOH)n(H + )n(CH 3 COO - ) StartA0B Change - eq + eq m m(A- eq )( eq )(B+ eq )

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The pH of the solution will be almost entirely due to the original molalities of acid and base!!

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Solubility Equilibria Examine the following systems AgCl (s) ⇌ Ag + (aq) + Cl - (aq) BaF 2 (s) ⇌ Ba 2+ (aq) + 2 F - (aq) Using the principles of chemical equilibrium, we write the equilibrium constant expressions as follows

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The Common Ion Effect What about the solubility of AgCl in solution containing NaCl (aq)? AgCl (s) ⇌ Ag + (aq) + Cl - (aq) NaCl (aq) Na + (aq) + Cl - (aq) AgCl (s) ⇌ Ag + (aq) + Cl - (aq) Equilibrium is displaced to the left by LeChatelier’s principle (an example of the common ion effect).

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Solubility in the Presence of an Inert Electrolyte What happens when we try to dissolve a solid like AgCl in solutions of an inert electrolyte (e.g., KNO 3 (aq))? We must now take into account of the effect of the ionic strength on the mean activity coefficient!

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The Salting-In Effect AgCl (s) ⇌ Ag + (aq) + Cl - (aq). Designate the solubility of the salt in the absence of the inert electrolyte as s o = m(Ag + ) = m(Cl - ) at equilibrium.

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For a dilute solution u Designate s as the solubility of the salt in the presence of varying concentrations of inert electrolyte.

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Reaction Equilibria in Nonideal Gaseous Systems For a nonideal system gaseous, the nonstandard Gibbs energy of reaction is written

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The Equilibrium Condition Calculate the equilibrium composition from the fugacity coefficients from compression factor data

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Temperature and Pressure Dependence of K o As a function of temperature As a function of pressure

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