Clausius–Clapeyron for vapor pressure vs temperature: which assumptions are typically invoked to obtain the integrated form used in engineering calculations?

Introduction / Context:The Clausius–Clapeyron equation relates saturation pressure to temperature and is widely used to estimate vapor pressures and heats of vaporization. To obtain a simple, integrable expression, standard simplifying assumptions are made. Recognizing these assumptions guides correct application and awareness of limitations.

Given Data / Assumptions:

• Phase equilibrium between a liquid and its vapor.
• Narrow temperature range for data fitting.
• Engineering-level accuracy, not high-precision thermodynamic modeling.

Concept / Approach:The integrated Clausius–Clapeyron form ln P = −(ΔHvap/R)(1/T) + C comes from: (1) treating the vapor as an ideal gas; (2) assuming the molar latent heat ΔHvap is approximately constant over the temperature interval; and (3) neglecting the liquid molar volume compared with the vapor molar volume so that Δv ≈ v_vapor. These together simplify the differential form to an easily integrated linear relation in 1/T.

Step-by-Step Solution:

Verification / Alternative check:Comparisons to Antoine correlations show improved accuracy when temperature dependence of ΔHvap is allowed; the CC form is nonetheless valuable for quick estimates under the stated assumptions.

Why Other Options Are Wrong:

• Picking only a subset misses at least one essential simplification.

Common Pitfalls:Applying the simple CC equation near the critical point or over wide temperature spans where ΔHvap varies significantly and liquid volumes are not negligible.

Final Answer:All (a), (b), and (c).