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1) Why Does Ar Have the Lowest CP of Any Gas? Monatomic Gas, Only 3 Degrees of Freedom (Dof) Per “Gas Species” (Atom

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1) Why Does Ar Have the Lowest CP of Any Gas? Monatomic Gas, Only 3 Degrees of Freedom (Dof) Per “Gas Species” (Atom (1) Why does Ar have the lowest CP of any gas? monatomic gas, only 3 degrees of freedom (dof) per “gas species” (atom). (2) Why does Cl2(g) have a larger CP than F2(g)? it has a longer softer bond; in a rough way of speaking, it’s closer to being dis- sociated (2 atoms, 6 dof) whereas F2 is closer to a hypothetical rigidly bonded diatomic (5 dof). (3) Estimate the CP of C16H34(ℓ) Everything else being equal, molecules with more atoms have more dof and there- fore a bigger CP . 255×2 = 510; or 255+((16−5)/(8−5))×(255−167.2) = 518; or any other reasonable way to extrapolate from the CP ’s of the smaller alkanes pentane and octane. (4) Compare the liquid and gas forms of H2O and of pentane. Why does a liquid have a larger CP than a gas? In a liquid, part of the heat goes into changing the relative positions (or ar- rangement) of the molecules, ie it increases potential energy, not kinetic energy. So the temperature increase, for a given heat, is (normally) less in a liquid than in a gas. Why is the ratio (75.3/33.6) so much bigger than (167.2/120.1)? Probably because the intermolecular interactions in water are a lot stronger (H bonds) so there are more ways to “soak up heat” into potential energy changes. (BTW: in a phase transition, all of the heat is taken up for rearranging molecules, it all goes into potential energy, which is why temperature does not change dur- ing a phase transition, it’s as if the heat capacity is infinite.) (5) Why is CP so small in diamond? (even smaller than Ar(g)) First, the CP is per mole of C atoms, so only 3 dof at most (like a monoatomic gas). But in addition, all C atoms are bonded rigidly to 4 neighbours in dia- mond: they do not move freely along 3 directions. If the bonds in diamond were absolutely rigid (hypothetical case), there would zero dof! In fact, the bonds are quite rigid, but C atom motions are still possible: the effective number of dof is somewhere between 0 and 3, surely less than 3, hence smaller CP than in Ar(g). (6) C2H6(g) has 4 times as many atoms as N2: why does it have a Cp only twice as large? The effective number of dof in N2 is roughly 5 assuming a completely rigid N-N bond. In C2H6(g), it is at most 8 × 3 = 24; but the covalent chemical bonds prevent free motion of the 8 atoms; there are 7 bonds that constrain the motions, so in a very rough estimate, an effective number of dof equal to 14. Note: there are also further constraints on motion of atoms in ethane from the favored bond angles of 109 degrees around C atoms. Even ignoring the effect of favored angles, we’d get a ratio of number of dof of 14/5=2.8: that’s not a factor of 2.0, but it’s smaller than 4.0, and it illustrates how bonds (and bond angles) constrain atomic motions and give smaller heat capacities on a per atom basis (not on a per molecule basis)..
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