The relative permittivities of methanol (with a melting point of \(-95^{\circ} \mathrm{C}\) ) corrected for density variation are given below. What molecular information can be deduced from these values? Take \(\rho=0.791 \mathrm{~g} \mathrm{~cm}^{-3}\).

\(\begin{array}{lcccccccccc}\theta /{ }^{\circ} \mathrm{C} & -185 & -170 & -150 & -140 & -110 & -80 & -50 & -20 & 0 & 20 \\ \varepsilon_{\mathrm{r}} & 3.2 & 3.6 & 4.0 & 5.1 & 67 & 57 & 49 & 43 & 38 & 34\end{array}\)

Text Transcription:

-95^circ C

rho=0.791 g cm^-3

theta/^circ C

\varepsilon_r

12.3 Each substance has a standard molar entropy which tells how dispersed the energy is in one mole of the substance at 1 bar of pressure and 25ºCconditions at which it remains in its standard state. This is influenced by the molecules’ molar masses (the greater mass, the more entropy), the amount of organization of the structure if a solid (which impacts how rigid the substance is; think about a bunch of things held together tightly, they cannot move as much as if they were loosely connected, therefore the more rigid the less microstates, less entropy), and the ways all the molecules interact with each other within the substance. These interactions depend on rotational motion, or how they bump into each other, which changes with the ways that their mass is distributed through the molecule. Longer molecules have more ways that they can rotate and tumble than molecules with more centralized mass (think of a tumbling pen vs a rolling sphere (a sphere really only has a couple ways to move)) The biggest factor into standard entropies is whether the substance in its standard state is a solid (low entropy), liquid (more entropy), or gas (very high entropy). Considering entropy change, entropy increases directly with temperature, volume, and the number of particles. In general, the more microstates it has as possibilities, the higher the entropy. 12.4 A spontaneous reaction will always result in greater distribution of energ