Chemistry Labs

Problem 4

A vessel of volume 5.0 dm3^3 was filled with ethane at 300 K and 101.325 kPa, sealed, and then heated. The measured pressures were: at 300 K: 101.3 kPa (theoretical p′=101.3p'=101.3 kPa); at 500 K: 169.8 kPa (p′=168.7p'=168.7 kPa); at 800 K: 276.1 kPa (p′=269.9p'=269.9 kPa); at 1000 K: 500.7 kPa (p′=337.4p'=337.4 kPa). (a) Explain why the measured pressure exceeds p′p' at higher temperatures and write the reaction equation. (b) Calculate the degree of conversion α\alpha and equilibrium constant KpK_p at 800 K and 1000 K. (c) Using the integrated van 't Hoff equation ln⁡(Kp,2/Kp,1)=−ΔH∘R(1T2−1T1)\ln(K_{p,2}/K_{p,1}) = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right), calculate the mean reaction enthalpy ΔH∘\Delta H^\circ between 800 K and 1000 K. (R=8.314R = 8.314 J mol−1^{-1} K−1^{-1})
Step 1 of 4: Decomposition and conversion degree
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CX2HX6⇌CX2HX4+HX2;p=p′(1+α)⇒α=p−p′p′\ce{C2H6 <=> C2H4 + H2};\quad p = p'(1 + \alpha) \Rightarrow \alpha = \dfrac{p - p'}{p'}
Analysis

Ethane dehydrogenates to ethylene and hydrogen at high temperatures: 1 mole produces (1−α)+α+α=1+α(1 - \alpha) + \alpha + \alpha = 1 + \alpha moles of gas. Comparing measured pp to ideal unreacted pressure p′p' directly yields α=(p−p′)/p′\alpha = (p - p')/p'.