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ME 300 Special Problem Homework Set #13 SP36-SP38
Due Wednesday, April 26, 2017
SP 36. Water vapor (H2O) enters Section 1 of a high pressure flow reactor at T1 = 700 K and
p1 = 10 atm at a molar flow rate of 1.0 kmol/s. At the exhaust of the reactor (Section 2), the
species H2O, O2, and H2 leave the reactor in the product stream. The exhaust stream pressure is
p2 = 9.6 atm and the mole fraction of O2 in the exhaust stream, y2,O2 , is measured to be 0.0030.
Assume that the following reaction is in equilibrium in the product gas mixture:
H 2O  H 2 + 12 O2
(a) Determine the temperature T2 ( K ) and the mole fractions for H2O and H2 in the product gas
mixture.
(b) Calculate the required heat transfer rate Q CV (kJ/s). (A table of properties for H2 is attached.)
SP 37. One kg of n-butane (C4H10) is burned in a constant volume reactor with 80 percent
theoretical air. The initial temperature and pressure in the reactor are T1 = 298.15 K
and p1 = 1 bar .
The final products of combustion, consist of an equilibrium mixture
containing only O2, CO, CO2, H2, H2O, and N2. The temperature of the products is measured
to be T2 = 2400 K . Determine the equilibrium composition at this state. Determine the heat
transfer to or from the constant volume reactor. The enthalpy of formation of n-butane is 124,733 kJ/kmol at 298.15 K. (Hint: the concentration of O2 will be much lower than the
other concentrations, it can be ignored in the heat transfer calculations and the O2
concentration can then be calculated after the other species concentrations are determined).
SP 38. Verify the van’t Hoff equation for the reaction
CO2  CO + 12 O2
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at temperatures of 1400 K and 3200 K. Do this by calculating the enthalpy of reaction ∆H R at
each temperature in two different ways: (1) directly using values given in Table A-23 and (2) by
calculating the derivative of the ln K (given in Table A-27, note that log10 values are listed in
Table A-27) using the van’t Hoff equation (14.43). What conclusions can you draw from this
comparison?
You can use either a second-order or a fourth order approximation of the derivative of a variable
y with respect to x :
− y−1 + y+1
 dy 
2nd order :  
≅
=
D 2 ( x0 )
2∆x
 dx  x = x0
y − 8 y−1 + 8 y+1 − y+2
 dy 
4th order :  
≅ −2
=
D 4 ( x0 )
12∆x
 dx  x = x0
In the above expressions, it is assumed that the variable y is tabulated as a function of x , and
the spacing between tabulated values of y is equal to ∆x .
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