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Problem 3. The vapor phase decomposition of phosphine, which is irreversible and first order, follows the reaction: 4PH3(g) ? P4(g) + 6H2(g) Pure phosphine is fed to a tubular-flow reactor, operating at 1 atm and adiabatically with a feed temperature of 953 K. The reaction is endothermic, ?HR = 23,900 J/mol of phosphine at 25°C. The molar heat capacities (J/mol K) are P4(g) Cp = 25.1 + 0.0040 T PH3(g) Cp = 28.0 + 0.027 T H2(g) Cp = 30.1 The rate constant k, (s)-1, is the following function of temperature: ln k = 27.94 + 2 ln T - 43672/T , T (K) What volume to initial molar feed rate ratio (V/FAo) would be required to obtain a conversion of 10% in one pass through the reactor? What would be the conversion for the same V/FAo if the reactor operated isothermally at 953 K? Hint: From the energy balance get a quadratic expression on T, and use the positive solution to get an expression of T as a function of XA. Add this expression as an explicit equation to the ODE software.

          Problem 3. The vapor phase decomposition of phosphine, which is irreversible and first order, follows the reaction:

4PH3(g) ? P4(g) + 6H2(g)

Pure phosphine is fed to a tubular-flow reactor, operating at 1 atm and adiabatically with a feed temperature of 953 K. The reaction is endothermic, ?HR = 23,900 J/mol of phosphine at 25°C. The molar heat capacities (J/mol K) are

P4(g) Cp = 25.1 + 0.0040 T

PH3(g) Cp = 28.0 + 0.027 T

H2(g) Cp = 30.1

The rate constant k, (s)-1, is the following function of temperature:

ln k = 27.94 + 2 ln T - 43672/T , T (K)

What volume to initial molar feed rate ratio (V/FAo) would be required to obtain a conversion of 10% in one pass through the reactor? What would be the conversion for the same V/FAo if the reactor operated isothermally at 953 K?

Hint: From the energy balance get a quadratic expression on T, and use the positive solution to get an expression of T as a function of XA. Add this expression as an explicit equation to the ODE software.

Problem 3. The vapor phase decomposition of phosphine, which is irreversible and first order, follows the reaction:

4PH3(g) ? P4(g) + 6H2(g)

Pure phosphine is fed to a tubular-flow reactor, operating at 1 atm and adiabatically with a feed temperature of 953 K. The reaction is endothermic, ?HR = 23,900 J/mol of phosphine at 25°C. The molar heat capacities (J/mol K) are

P4(g) Cp = 25.1 + 0.0040 T

PH3(g) Cp = 28.0 + 0.027 T

H2(g) Cp = 30.1

The rate constant k, (s)-1, is the following function of temperature:

ln k = 27.94 + 2 ln T - 43672/T , T (K)

What volume to initial molar feed rate ratio (V/FAo) would be required to obtain a conversion of 10% in one pass through the reactor? What would be the conversion for the same V/FAo if the reactor operated isothermally at 953 K?

Hint: From the energy balance get a quadratic expression on T, and use the positive solution to get an expression of T as a function of XA. Add this expression as an explicit equation to the ODE software.

Added by John P.

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