what is the E0valye for zinc chloride given that it has a MW of 136 and a dissociation factor of 2.6? Remember the MW of NaCl is 58.5 and the dissociation factor of NaCl is 1.8
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Calculate ΔG (in kJ) at 298 K for some solid ZnF2, 0.024 M Zn2+ and 0.017 M F-(aq). Hint given in feedback.
Shaiju T.
$42.48^{\circ}$ CALC The one-dimensional calculation of Example 42.4 (Section 42.3 ) can be extended to three dimensions. For the threedimensional fce $\mathrm{NaCl}$ lattice, the result for the potential energy of a pair of $\mathrm{Na}^{+}$ and $\mathrm{Cl}^{-}$ ions due to the electrostatic interaction with all of the ions in the crystal is $U=-\alpha e^{2} / 4 \pi \epsilon_{0} r,$ where $\alpha=1.75$ is the Madelung constant. Another contribution to the potential energy is a repulsive interaction at small ionic separation $r$ due to overlap of the electron clouds. This contribution can be represented by $A / r^{8},$ where $A$ is a positive constant, so the expression for the total potential energy is $$ U_{\mathrm{tot}}=-\frac{\alpha e^{2}}{4 \pi \epsilon_{0} r}+\frac{A}{r^{8}} $$ (a) Let $r_{0}$ be the value of the ionic separation $r$ for which $U_{\text {tot }}$ is a minimum. Use this definition to find an equation that relates $r_{0}$ and $A,$ and use this to write $U_{\text {tot }}$ in terms of $r_{0}$. For $\mathrm{NaCl}$, $r_{0}=0.281 \mathrm{nm} .$ Obtain a numerical value (in electron volts) of $U_{\text {tot }}$ for $\mathrm{NaCl}$. (b) The quantity $-U_{\text {tot }}$ is the energy required to remove a $\mathrm{Na}^{+}$ ion and a $\mathrm{Cl}^{-}$ ion from the crystal. Forming a pair of neutral atoms from this pair of ions involves the release of $5.14 \mathrm{eV}$ (the ionization energy of Na) and the expenditure of $3.61 \mathrm{eV}$ (the electron affinity of $\mathrm{Cl}$ ). Use the result of part (a) to calculate the energy required to remove a pair of neutral Na and Cl atoms from the crystal. The experimental value for this quantity is $6.39 \mathrm{eV}$ how well does your calculation agree?
First Second Third Fourth Fifth 419 3052 4410 5900 8000 (j) The ionic compound ZF2 is not known to exist. Explain why, using the data in the table above to support your explanation. For a compound, the energy required to separate the ions in a crystal lattice into individual gaseous ions is known as the lattice energy of the compound. The following table shows the dissociation reactions and the lattice energies for ZCl and for Z2O. Dissociation Reaction Lattice Energy (kJ/mol) ZCl(s) → Z+(g) + Cl-(g) 829 Z2O(s) → 2Z+(g) + O2-(g) ? (k) A student predicts that the lattice energy of ZCl is greater than the lattice energy of Z2O. If the ionic radii of Cl- and O2- are approximately the same, is the student's prediction correct? Explain your answer in terms of periodic properties and Coulomb's law.
David C.
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