Question

Elementary Principles of Chemical Processes, 4th edition, Chapter 4, question 89

an unknown paraffinic hydrocarbon is defineed by the chemical formula CxH2x+2. the paraffin is burned with air and there is no CO in the combustion products.

A) use a degree of freedom analysis to determine how many variable must be specified to determine the flowrates of all components enetering and leaving the combustion unit. express the fraction excess air as Y and write element balances in terms of X, Y, and the molar flowrate of CxH2x+2.

B) calculate the molar composition of the combustion product gas in terms of X for each of the following 3 cases: (i) theoretical air supplied Y=0, 100% conversion of the paraffin, (ii) 20% excess air Y=0.2, 100% paraffin conversion, and (iii) Y=0.2 20% excess air, 90% paraffin conversion

C) suppose x=3 (a.k.a the paraffin is propane). assuming complete combustion of the hydrocarbon, what is the ratio of CO2 to H2O in the product gas? use this result to suggest a method for determining the molecular formula of the paraffin.

Answer 1

Hello! This is a hard problem without numbers so I'll do my best to help you! Sorry if there's any step missing, but you can easily complete them with logic.

An unknown paraffinic hydrocarbon is defined by the chemical formula CxH2x+2. The paraffin is burned with air and there is no CO in the combustion products.

A) Use a degree of freedom analysis to determine how many variable must be specified to determine the flowrates of all components entering and leaving the combustion unit. Express the fraction excess air as Y and write element balances in terms of X, Y, and the molar flowrate of CxH2x+2.

B) Calculate the molar composition of the combustion product gas in terms of X for each of the following 3 cases: (i) theoretical air supplied Y=0, 100% conversion of the paraffin, (ii) 20% excess air Y=0.2, 100% paraffin conversion, and (iii) Y=0.2 20% excess air, 90% paraffin conversion

C) Suppose x=3 (a.k.a the paraffin is propane). Assuming complete combustion of the hydrocarbon, what is the ratio of CO2 to H2O in the product gas? Use this result to suggest a method for determining the molecular formula of the paraffin.

Solution:

a)      Step 1: Write the reaction equation

CxH2x+2 + ath [O2 + 3.76 N2] -----> X CO2 + N (x+1) H2O + ath 3.76 N2

Where ath : theoric moles of air or:

CxH2x+2 + (3X +1)/2 [O2 + 3.76 N2] ---> X CO2 + (x+1) H2O + (3X+1)/2 3.76 N2

Step 2: The combustion unit has 3 flow currents (paraffin, air and products), so 3 is the total amount of lines. The total amount of compounds is 5 (paraffin, oxygen, nitrogen, CO2 and water). T and P are not given but they are necessary for energy balances.

The degree freedom analysis is given by:

Nd = Nv – Nr (Number of variables – number of independent equations)

Nv:

Currents: 3

Nr:

Mass Balances (5-1) = 4

Excess air = 1

Nd = 3 – 5 = 2 ---> number of variables that must be specified.

b)

(i) theoretical air supplied Y=0, 100% conversion of the paraffin,

XCO2 = X / (X + X+1 + [3x+1)/2]*(3.76 + Y)) = X / (X + X+1 + [3x+1)/2]*(3.76))

(ii) 20% excess air Y=0.2, 100% paraffin conversion

XCO2 = X / (X + X+1 + [3x+1)/2]*(3.76 + 0.2))

(iii) Y=0.2 20% excess air, 90% paraffin conversion

XCO2 = 0.9 X / (0.9X + 0.9X+0.9 + 0.1*NCxH2x+2 + (Y+0.1)* [3x+1)/2] + [3x+1)/2]*(3.76))

c) Assuming complete combustion of the paraffin, lead us to assume theoretical air, so Y = 0.

C3H8 + 5 [O2 + 3.76 N2] ---> 3 CO2 + 4 H2O + (5* 3.76) N2

Ratio = 3/4 or (x / x +1)

Using the above deduction you can easily develope a method, using the formula x/(x+1).

Hope this helps!