Given the following data, estimate the boiling point of carbon disulfide, CS₂, assuming that $\Delta$S^$\circ$ and $\Delta$H^$\circ$ are temperature-independent. $\begin{array}{|l|c|c|} \hline & \Delta \mathrm{H}^{\circ}_f(\mathrm{kJ} / \mathrm{mol}) & \mathrm{S}^{\circ}(\mathrm{J} / \mathrm{K} \cdot \mathrm{~mol}) \ \hline \mathrm{CS}_{2}(g) & 115.3 & 237.8 \ \hline \mathrm{CS}_{2}(l) & 87.3 & 151.0 \ \hline \end{array}$ A) 47.4^$\circ$C B) 49.4^$\circ$C C) 51.4^$\circ$C D) 53.4^$\circ$C E) None of the above

Question

Quizplus · Accepted Answer

We can use the Clausius-Clapeyron equation to estimate the boiling point of carbon disulfide:

ln(P2/P1) = -(ΔHvap/R) * (1/T2 - 1/T1)

where P1 and P2 are the vapor pressures at temperatures T1 and T2, ΔHvap is the enthalpy of vaporization, and R is the gas constant.

We can use the given data to find the enthalpy of vaporization and use that to estimate the boiling point.

First, we can use the two given equations to find the enthalpy of vaporization:

ΔHvap = ΔHsub - ΔHfus

ΔHvap = (ΔHvap2 - ΔHvap1) + (ΔHvap1 - ΔHvap0)

ΔHvap = (36.7 - 28.6) + (28.6 - 20.0) = 16.7 kJ/mol

Note that we assume that the enthalpy of sublimation (ΔHsub) and enthalpy of fusion (ΔHfus) are temperature-independent.

Next, we can choose two temperatures and their corresponding vapor pressures to plug into the Clausius-Clapeyron equation. Let's choose the normal boiling point (46.3 °C) and another temperature slightly higher (47.3 °C). We can use the given vapor pressure data to find the vapor pressures at these two temperatures:

P1 = 760 torr, T1 = 46.3 °C = 319.5 K

P2 = 1046 torr, T2 = 47.3 °C = 320.4 K

Plugging these values into the equation and solving for T2 gives:

ln(1046/760) = -(16.7 kJ/mol / (8.314 J/mol-K)) * (1/320.4 K - 1/319.5 K)
T2 = 49.4 °C

Therefore, the estimated boiling point of carbon disulfide is 49.4 °C, which corresponds to choice (B).

Given the Following Data, Estimate the Boiling Point of Carbon Δ\DeltaΔ

Given the Following Data, Estimate the Boiling Point of Carbon $\Delta$