PS4Solutions

# PS4Solutions - Chemistry 120B SP11 Problem Set 4 Solutions...

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Unformatted text preview: Chemistry 120B SP11 Problem Set 4 Solutions Total: 50 points 1. (5 points) See MQS Solutions Manual. 2. (i) (4 points) The number of possible locations for a single particle is V/λ 3 , where λ is the thermal deBroglie wavelength, λ = h/ √ 2 πmk B T . q = V λ 3 Because the particles are statistically independent, the total partition function factorizes. Q = q N N ! = 1 N ! V λ 3 N ∝ V N Taking the log of the partition function, ln Q = N ln V + (stuff independent of V) Differentiating with respect to volume at constant temperature and number of molecules, ∂ ln Q ∂V β,N = βp = N V pV = Nk b T Or, pV = nRT where n is the number of moles. (ii) (3 points) Q ∝ ( V- Nb ) N lnQ = N ln( V- Nb ) + (stuff independent of V) ∂ ln Q ∂V β,N = βp = N V- Nb p ( V- Nb ) = Nk B T (iii) (3 points) Unlike particles in an ideal gas, the particles in this system take up space and interact with each other. For an interaction volume only slightly larger than a particle, a tagged particle sitting at the sphere’s center will restrict the number of other particles that can fit inside the sphere. Also, becausesphere’s center will restrict the number of other particles that can fit inside the sphere....
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PS4Solutions - Chemistry 120B SP11 Problem Set 4 Solutions...

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