Question

heat of formation

Fuel cells can be powered by the reaction between formic acid and oxygen as following HCOOH + 12 02 → CO2 + H2O As formic acid and oxygen react together inside the fuel cell, it produced both electrical power and heat. While there is no shaft work produced by the fuel cells, this electrical power produced by the fuel cells can be considered as the shaft work term when you perform the energy balance. A fuel cell is being supplied with 100. liters per minute of pure formic acid at 1 atm and 25 °C. Air is also fed to the fuel cell to supply the oxygen. The air is fed at 1 atm and 25 °C and at 100% excess. The fuel cell operates at 70 °C so that the gas stream leaving the fuel cell is also at 70 °C. The gas stream leaving the fuel cell contains no formic acid. The fuel cell transfers heat to the surroundings at a rate of 1.50 x 103 kW. How much electrical power does the fuel cell generate?

Answer 1

The reaction occuring is

$HCOOH(L) + \frac{1}{2}O_{2}(g)\rightarrow CO_{2}(g) + H_{2}O(g)$

Formic acid is fed at 25°C and 1 atm

At T = 25°C formic acid is liquid

V = 100 L/min = 0.1 m³/min

T = 25°C = 298 K

Density of formic acid at T = 25°C = 1220 Kg/m3

Formic acid at inlet = (0.1) (1220) = 122 Kg/min

M. W of formic acid = 46 Kg/kmol

Moles of formic acid = 122/46 =

2.65217 kmol/min

formic acid is in outlet so all formic acid reacts

Air supllied is 100% excess

Oxygen required according to stiochiometry = (2.65217) (0.5) = 1.326085 moles

But o2 supplied = 1.326085(2) = 2.65217 mol/min

Air supplied = 2.65217/(0.21) =

12.6293 kgmol/min

The products leave at 70°C

Cp of products is taken at average temperature of (25+70) /2 = 47.5°C = 320.65 K

Reference enthaply is at T= 25°C

So ∆H(reactants) = 0

Product analysis

Component	kmol/min	Cp(KJ/mol°C)	H(KJ/min)
CO2	2.65217	38.070	4543.565
H2O	2.65217	33.693	4021.18
O2	1.326085	29.536	762.52
N2	12.6293(0.79) = 9.9772	29.146	13085.796
Total	25.6029		22413.061

H(products) = 22413.061 KJ/min

From handbook at T = 25°C

∆Hf(CO2) (g) = -393. 5 KJ/mol

∆Hf(H2O) (g) = -241. 83 KJ/mol

∆Hf(HCOOH) (L) = -425. 5 KJ/mol

∆H_r = ∆H_products - ∆H_reactants

∆H_r = (-241.83) +(-393.5) -(-425.5) =

-209. 83 KJ/mol

Moles of formic acid reacted =2.65217 kmol/min

∆Hr = -209. 83(1000) (2.65217) =

-556504. 8311 KJ/min

Total energy

Q = ∆Hr + H(products)

Q = -556504. 8311 + 22413.061

Q = -534091. 7701 KJ/min = -8901. 529 KW

Fuel cell transfers to the surroundings 1.50(1000) KW of heat = 1500 KW

Doing energy balance electrical energy produced = 8901.529 - 1500 = 7401.529 KW

Electrical power = 7401.529 KW

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