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Chapter 4: Debye Huckel limiting law

Chapter 4: Debye Huckel limiting law. Distribution of an uncharged solute in an ideal solution, compared with positive (red) and negative (blue) ions in an electrolyte. The ions are much closer, on average to ions of the opposite charge than ions of the same charge. CHEM 471: Physical Chemistry.

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Chapter 4: Debye Huckel limiting law

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  1. Chapter 4: Debye Huckel limiting law Distribution of an uncharged solute in an ideal solution, compared with positive (red) and negative (blue) ions in an electrolyte. The ions are much closer, on average to ions of the opposite charge than ions of the same charge. CHEM 471: Physical Chemistry For water at 298 K Aγ = 1.17 mol–1/2 kg1/2

  2. Chapter 4: Debye Huckel activity coefficients FIGURE 4.9  Mean activity coefficient of various electrolytes at The activity coefficients are much less than 1 even for 0.1-M solutions; at concentrations above 1 M, the activity coefficients for some electrolytes increase and become even greater than 1. CHEM 471: Physical Chemistry

  3. Chapter 4: Debye Huckel limiting law: example Compute the activity of sodium ions and sulfate ions in a 10 mm solution of sodium sulfate. Sodium sulfate dissociates as follows Na2SO4 → 2 Na+ + SO42– I =(Z2Na+mNa+ + Z2SO42–mSO42–)/2 = (12 × 0.02 + 22 × 0.01)/2 = 0.03 m ln γNa = –1.17 × 12 × √0.03 = –0.202 ⇒ γNa = 0.817 ⇒ aNa = 16.34 mm ln γSO4 = –1.17 × 22 × √0.03 = –0.811 ⇒ γSO4 = 0.445 ⇒ aSO4 = 4.45 mm CHEM 471: Physical Chemistry

  4. Chapter 4: Dissociation of water H2O → H+ + OH– H+ + OH– → H2O H2O ⇌ H+ + OH– At 1 bar and 25 C, the concentrations of H+ and OH– ions are both 1.006 × 10-7m. Is this an ideal solution? Calculate the activity of H+ ions in pure water Since the ions are both univalent, the ionic strength in molality units is obviously 1.006 × 10–7m. Applying the formula for the Debye Huckel activity coefficient (given in eqn. 5.48) we get ln γH+ = ln γOH– = –l.17 × (±1)2 × √(1.006 × 10–7) = 0.00037 γH+ = γOH– = 0.9996. aH+ = aOH– = γH+mH+ = γOH–mOH– = 0.9996 × 1.006 × 10–7m = 1.006 × 10–7m, identical within experimental accuracy CHEM 471: Physical Chemistry

  5. Chapter 4: Biochemists’ standard state The normal standard state has aH+ = 1 M or 1 m. This is not healthy. We therefore define the biochemist’s standard state as being identical to the normal ‘standard state, but at pH 7. A biochemists’ standard free energy of reaction is written as ΔG°′. Concentrations are also equal to total concentrations, and ionic strength is specified (usually 0.25 M) G3P + phosphate + NAD+ → 1,3-dPG + NADH + H+ a1,3-dPG aNADH aH+ a1,3-dPG aNADH aH+ K = K’ = aG3P aNAD+ aPi aG3P aNAD+ aPi 10–7m CHEM 471: Physical Chemistry ΔG°’ = –RT ln K’ ΔG° = –RT ln K ΔG°’ = +6.3 kJ mol–1 ΔG° = +6.3 kJ mol–1 + 2.303 RT × 7 = 46.3 kJ mol–1

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