Given the data, calculate ΔSvap for each of the first four liquids. (ΔSvap =ΔHvap / T., where T

Given the data, calculate ΔSvap for each of the first four...

Given the data, calculate $\Delta S_{\mathrm{vap}}$ for each of the first four liquids. $\left(\Delta S_{\text {vap }}=\Delta H_{\text {vap }} / T\right.$, where $T$ is in $\left.\mathrm{K}\right)$ $$ \begin{array}{llcc} \hline \text { Compound } & \text { Name } & \text { BP }\left({ }^{\circ} \mathbf{C}\right) & \Delta H_{\text {vap }}(\mathbf{k J} / \text { mol }) \text { at BP } \\ \hline \mathrm{C}_{4} \mathrm{H}_{10} 0 & \text { Diethyl ether } & 34.6 & 26.5 \\ \hline \mathrm{C}_{3} \mathrm{H}_{6} 0 & \text { Acetone } & 56.1 & 29.1 \\ \hline \mathrm{C}_{6} \mathrm{H}_{6} 0 & \text { Benzene } & 79.8 & 30.8 \\ \hline \mathrm{CHCl}_{3} & \text { Chloroform } & 60.8 & 29.4 \\ \hline \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & \text { Ethanol } & 77.8 & 38.6 \\ \hline \mathrm{H}_{2} \mathrm{O} & \text { Water } & 100 & 40.7 \\ \hline \end{array} $$ All four values should be close to each other. Predict whether the last two liquids in the table have $\Delta S_{\mathrm{vap}}$ in this same range. If not, predict whether it is larger or smaller and explain. Verify your prediction.

Given the data, calculate $\Delta S_{\mathrm{vap}}$ for each of the first four liquids. $\left(\Delta S_{\text {vap }}=\Delta H_{\text {vap }} / T\right.$, where $T$ is in $\left.\mathrm{K}\right)$
$$
\begin{array}{llcc}
\hline \text { Compound } & \text { Name } & \text { BP }\left({ }^{\circ} \mathbf{C}\right) & \Delta H_{\text {vap }}(\mathbf{k J} / \text { mol }) \text { at BP } \\
\hline \mathrm{C}_{4} \mathrm{H}_{10} 0 & \text { Diethyl ether } & 34.6 & 26.5 \\
\hline \mathrm{C}_{3} \mathrm{H}_{6} 0 & \text { Acetone } & 56.1 & 29.1 \\
\hline \mathrm{C}_{6} \mathrm{H}_{6} 0 & \text { Benzene } & 79.8 & 30.8 \\
\hline \mathrm{CHCl}_{3} & \text { Chloroform } & 60.8 & 29.4 \\
\hline \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & \text { Ethanol } & 77.8 & 38.6 \\
\hline \mathrm{H}_{2} \mathrm{O} & \text { Water } & 100 & 40.7 \\
\hline
\end{array}
$$
All four values should be close to each other. Predict whether the last two liquids in the table have $\Delta S_{\mathrm{vap}}$ in this same range. If not, predict whether it is larger or smaller and explain. Verify your prediction.

Key Concepts

Enthalpy of Vaporization

This is the energy required to convert one mole of a liquid into vapor at its boiling point. It reflects the strength of the intermolecular forces holding the liquid together; stronger interactions require a higher enthalpy input to overcome these forces during the phase change.

Entropy of Vaporization

Represented by ?S?vap?, this is calculated as the ratio ?H?vap?/T, where T is the boiling temperature in Kelvin. It measures the change in disorder when a liquid goes to a gas, quantifying the increased randomness in the gas phase relative to the liquid phase.

Trouton's Rule

Trouton's Rule is an empirical observation stating that for many non-associated liquids, the entropy of vaporization at the boiling point is approximately constant, typically around 85-88 J/(mol·K). This rule provides a useful benchmark for estimating ?S?vap? and detecting deviations caused by specific molecular interactions.

Molecular Interactions and Deviations

Certain liquids, such as those that engage in hydrogen bonding or have specific association phenomena, can deviate from Trouton's Rule. In these cases, the ordering in the liquid phase is affected by these interactions, often leading to larger values of ?S?vap? when the liquid structure is significantly disrupted upon vaporization.

Transcript

00:01 In this question we've been given some liquids and we've been asked to determine the entropy change associated with vaporizing them.

00:08 And this is equal to the enthalpy change of vaporization divided by the temperature.

00:14 So for the first liquid, we are looking at dye, ethyther and the delta s vaporization is going to be equal to the enthalpy change of vaporization, which is 26 .5, terms 10 to the power 3 divided by the 3.

00:33 Temperature which is 34 .6 degrees celsius plus 273 .15 when you want to convert this into kelvin.

00:42 So delta s -web this is going to be equal to 86 .1 in joules per kelvin.

00:49 Now moving on to the next liquid we are looking at acetone, acetone and delta s vep this is equal to 29 .1 multiplied by 10 to 4 3 divided by 516 .1 plus 273 .15 in kelvin.

01:18 So delta s valve, this is going to be 88 .4 in joules per kelvin.

01:26 Then moving on to the next liquid, benzene.

01:33 If we look at benzene, delta s vaporization, this is going to.

01:38 To be equal to 30 .8 times 10 to the power 3 divided by the temperature in kelvin which is 79 .8 plus 273 .15.

01:50 So delta s, this is going to be equal to 8 .7 .3 in joles per kelvin.

02:02 Now moving to the fourth liquid where we have chloroform, delta s vep, this is going to be equal to to 29 .4 times 10 to the power 3 divided by the temperature which is 60 .8 plus 273 .15.

02:26 So delta s, this is going to be equal to 88 .04 and this is in joules per kelvin.

02:38 So when we compare these, all these four values are close to each other...

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