Problem 4

A vessel of volume 5.0 dm

^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'=101.3

kPa); at 500 K: 169.8 kPa (

p'=168.7

kPa); at 800 K: 276.1 kPa (

p'=269.9

kPa); at 1000 K: 500.7 kPa (

p'=337.4

kPa). (a) Explain why the measured pressure exceeds

p'

at higher temperatures and write the reaction equation. (b) Calculate the degree of conversion

\alpha

and equilibrium constant

K_p

at 800 K and 1000 K. (c) Using the integrated van 't Hoff equation

\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

\Delta H^\circ

between 800 K and 1000 K. (

R = 8.314

J mol

^{-1}

^{-1}

)

Step 2 of 4: Calculate conversion at 800 K and 1000 K

\alpha_{800} = \dfrac{276.11 - 269.93}{269.93} = 0.023; \quad \alpha_{1000} = \dfrac{500.75 - 337.41}{337.41} = 0.484

Analysis

At 800 K only 2.3 % of ethane is dehydrogenated, but at 1000 K the conversion rises dramatically to 48.4 %.