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Estimate the spin-only molar susceptibility of CuSO4⋅5H2O at 25 °C.
Spin only molar susceptibility of CuSO4 .5H2O
At 25 degre celcius
Molar susceptibility= ____? (In
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- 3. Consider a 2 × 2 square lattice of spins interacting via the Ising Hamiltonian in the absence of a magnetic field: H = - ΣSi Sj, (ij) we have set J = 1. (a) Write down all the possible configurations and calculate the energy for each one of them. (b) Calculate the partition function Z, as a function of temperature, by summing over all configurations. (c) Repeat question (3a) and (3b), using periodic boundary condi- tions.What is the highest possible degeneracy of a vibration of a Cr(CO)6 molecule? Explain your answer.The rotational constant of 12C16O2 (from Raman spectroscopy) is 11.70 GHz. What is the CO bond length in the molecule?
- Calculate the relative numbers of Cl2 molecules ( ᷉v = 559.7 cm−1) in the ground and first excited vibrational states at (i) 298 K, (ii) 500 K.Now consider the London interaction between the phenyl groups of two Phe residues (see Problem P14B.5). (a) Estimate the potential energy of interaction between two such rings (treated as benzene molecules) separated by 0.4 nm. For the ionization energy, use I = 5.0 eV. (b) Given that force is the negative slope of the potential, calculate the distance-dependence of the force acting between two non-bonded groups of atoms, such as the phenyl groups of Phe, in a polypeptide chain that can have a London dispersion interaction with each other. What is the separation at which the force between the phenyl groups (treated as benzene molecules) of two Phe residues is zero? Hint: Calculate the slope by considering the potential energy at r and r + δr, with δr << r, and evaluating {V(r + δr) − V(r)}/δr. At the end of the calculation, let δr become vanishingly small.Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of carbon dioxide gas, (ii) a sample of graphite, (iii) a sample of diamond, (iv) ice.
- Calculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.Starting from the formula for the rotational energy levels: ħ² EJ J(J+1) = J = 0, 1, 2... 21 Show that: ħ² AE = 1/² (J+1) Δε J = 0,1,2...Calculate the CO and CS bond lengths in OCS from the rotational constants B(16O12C32S) = 6081.5MHz, B(16O12C34S) = 5932.8MHz.
- Consider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance equal to the bond length of the molecule). The rotational constant of the diatomic AB is 25.5263 cm-1. (a) What is the difference in energy, expressed in wavenumbers, between the energy levels of AB with J = 10 and J = 6? (b) Consider now a diatomic A'B', for which the atomic masses are ma 0.85 mA and mB' 0.85 mB and for its bond length ra'B' = 0.913 rAB. What is the difference in energy, expressed in wavenumbers, between the energy levels of the A'B' molecule with J = 9 and J = 7?The 1H35Cl molecule is quite well described by the Morse potential energy with hc ᷉ De = 5.33 eV, ᷉v = 2989.7 cm−1, and xe ᷉v = 52.05 cm−1. Assuming that the potential is unchanged on deuteration, predict the dissociation energies (hc ᷉ D0, in electronvolts) of (a) 1H35Cl, (b) 2H35Cl.Use eqn 14D.4 to deduce expressions for (a) the root-mean-square separation of the ends of the chain, (b) the mean separation of the ends, and (c) their most probable separation. Evaluate these three quantities for a fully flexible chain with N = 4000 and l = 154 pm.