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 4 of 4: Reaction enthalpy via van 't Hoff

← Previous Next →

\Delta H^\circ = \dfrac{R \ln(K_{p,2}/K_{p,1})}{\frac{1}{T_1} - \frac{1}{T_2}} = \dfrac{8.314 \times \ln(153.2/0.146)}{\frac{1}{800} - \frac{1}{1000}} = 231.4\ \text{kJ mol}^{-1}

Analysis

Substituting $\ln(153.2 / 0.146) = \ln(1049) \approx 6.956$ into van 't Hoff's relation gives $\Delta H^\circ = 8.314 \times 6.956 / 0.00025 = 231.4$ kJ mol $^{-1}$ (strongly endothermic, explaining why heating shifts equilibrium to products).