Question 16.CSGP.102: A space heating unit in Alaska uses propane combustion is th......
A space heating unit in Alaska uses propane combustion is the heat supply. Liquid propane comes from an outside tank at -44°C and the air supply is also taken in from the outside at -44°C. The airflow regulator is misadjusted, such that only 90% of the theoretical air enters the combustion chamber resulting in incomplete combustion. The products exit at 1000 K as a chemical equilibrium gas mixture including only CO _2, CO , H _2 O , H _2 \text {, and } N _2. Find the composition of the products. Hint: use the water gas reaction in Example 16.4.
Propane: Liquid, T _1=-44^{\circ} C =229.2 \,K
Air: T _2=-44^{\circ} C =229.2 \,K, 90% Theoretical Air
Products: T _3=1000 \,K , CO _2, CO , H _2 O , H _2, N _2
Theoretical Air: C _3 H _8+5 O _2+18.8 N _2 \Rightarrow 3 CO _2+4 H _2 O +18.8 N _2
90% Theoretical Air:
C _3 H _8+4.5 O _2+16.92 N _2 \Rightarrow aCO _2+ bCO + cH _2 O + dH _2+16.92 N _2
Carbon: a + b = 3
Oxygen: 2a + b + c = 9 Where: 2 ≤ a ≤ 3
Hydrogen: c + d = 4
\begin{array}{cllcc}\text { Reaction: } & CO + & H _2 O & \leftrightarrow CO _2 & + H _2 \\\text { Initial: } & b & c & a & d \\\text { Change: } & – x & – x & x & x \\\text { Equil: } & b – x & c – x & a + x & d + x\end{array}
Chose an Initial guess such as: a = 2, b = 1, c = 4, d = 0
Note: A different initial choice of constants will produce a different value for x, but will result in the same number of moles for each product.
n _{ CO 2}=2+ x , \quad n _{ CO }=1- x , \quad n _{ H 2 O }=4- x , \quad n _{ H 2}= x , \quad n _{ N 2}=16.92
The reaction can be broken down into two known reactions to find K
\text { (1) } \quad 2 CO _2 \leftrightarrow 2 CO + O _2 @ 1000 K \ln \left( K _1\right)=-47.052
\text { (2) }\quad 2 H _2 O \leftrightarrow 2 H _2+ O _2 @ 1000 K \ln \left( K _2\right)=-46.321
For the overall reaction: \ln K =\left(\ln \left( K _2\right)-\ln \left( K _1\right)\right) / 2=0.3655 ; K =1.4412