Example 14-6 examined the thermal decomposition of butane forming propylene:

C₄ H₁₀ ↔ C₃ H₆ + CH₄

But a competing thermal decomposition reaction forming ethylene and ethane is also possible: 

C₄ H₁₀ ↔ C₂ H₄ + C₂ H₆ 

and ethane can react further as 

C₂ H₆ ↔ C₂ H₄ + H₂ 

Assume these are the only three reactions that occur. Use the shortcut van ’t Hoff method to calculate rate constants.

A. 10 mol/s of butane enter a reactor at T = 298   K and P = 1 bar. The exiting stream is at   T = 1000 K and P = 1 bar and is at equilibrium. At what rate is heat added to the reactor, and what is the composition of the exiting stream?  

B. 10 moles/s of butane and 10 mol/s of nitrogen enter a reactor at T = 298 K and P = 1 bar. The exiting stream is at T = 1000 K and P = 1 bar and is at equilibrium. At what rate is heat added to the reactor, and what is the composition of the exiting stream? 

C. 10 mol/s of butane enter a reactor at T = 1000 K and P = 1 bar. The reactor is isobaric, adiabatic, and large enough for the contents to reach equilibrium. Find the temperature and composition of the outlet stream.

D. 10 moles/s of butane and 10 mol/s of nitrogen enter a reactor at T = 1000 K and P = 1 bar. The reactor is isobaric, adiabatic, and large enough for the contents to reach equilibrium. Find the temperature and composition of the outlet stream.

Example 14-6.

Propylene (CH₃-CH₅CH₂) can be formed by the gas phase thermal cracking of n-butane:

C₄H₁₀↔C₃H₆ + CH₄

A steady-state reactor (Figure 14-5) is maintained at a constant T = 500 K and a constant P. The feed to the reactor is 10 mol/s of n-butane. Assuming the stream leaving the reactor is at equilibrium, find the flow rate of propylene in the stream for each of the following cases.

A. The vessel has P = 1 bar.

B. The vessel has P = 25 bar, and the contents are modeled as an ideal gas mixture.

C. The vessel has P = 25 bar, and the mixture fugacity of each compound is determined from the Peng-Robinson equation.

The reaction at 500 K has an equilibrium constant K₅₀₀ = 0.931.

Transcribed Image Text:

Butane- ? mol/s Propylene- ? mol/s Methane- ? mol/s Butane 10 mol/s Steady-state reactor T = 500 K, P = Constant C4H10→→→ C3H6+ CH4 FIGURE 14-5 Thermal cracking of n-butane modeled in Example 14-6.