PS10Solutions

PS10Solutions - Chemistry 120B SP11 Problem Set 10...

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Unformatted text preview: Chemistry 120B SP11 Problem Set 10 Solutions Total: 50 points 1. (i) The Debye screening length is given by λ = r 4 πβ I where I is the ionic strength, I= ∑ j N j q 2 j /V and q = z/ √ 4 π . For 0.1 molar NaCl, I = e √ 4 π 2 × . 1 × N A +- e √ 4 π 2 × . 1 × N A = 0 . 2 × N A × e 2 4 π = 2 . 78 × 10- 5 So the screening length is about 9 . 7 ˚ A. (i) The typical distance between adjacent water molecules is ρ- 1 / 3 w = 1 g mL 1 mol 18 g N A molecules mol 10 6 mL m 3- 1 / 3 = 3 . 1 ˚ A (ii) The typical distance between adjacent ions in 0.1 molar NaCl is ρ- 1 / 3 I = . 2 mol L 10 3 L m 3 N A molecules mol- 1 / 3 = 20 ˚ A (iii) The Bjerrum length is the separation at which the interaction energy between two ions is com- parable to the thermal energy. For water, βe 2 4 π = 7 ˚ A (ii) The reversible work required to move a sodium ion to a distance r away from a chloride ion is w ( r ) = u ( ∞ )- u ( r ) The potential is u ( r ) = q 1 q 2 r 12 So w ( r ) = e 2 4...
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This note was uploaded on 09/12/2011 for the course CHEM 107B taught by Professor Jamesames during the Spring '09 term at UC Davis.

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PS10Solutions - Chemistry 120B SP11 Problem Set 10...

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