Question

To study a key fuel-cell reaction, a chemical engineer has 20.0-L tanks of H₂ and of O₂ and wants to use up both tanks to form 28.0 mol of water at 23.8°C. (b) Use the van der Waals equation to find the pressure needed in each tank.

Answer 1

the pressure needed on H2 tank is 34.9477319atm and the pressure needed in O2 tanks is 16.7690007atm .

Given , to study a key fuel-cell reaction , a chemical engineer has 20.0L tanks of H2 and O2 and wants to use up both tanks to form 28.0mol of water at 23.8°C .

the reaction of the fuel cell is given by ,

H2(g) +1/2 O2 ( g) →H2O

Moles of H2 required = 28 mol

moles of O2 required = 14mol

Now according to van der waals equation ,

p= (nRT/ V-nb)  - an^2 / V^2

for H2 , a = 0.2453L^2bar /mol^2 , b= 0.02651L/mol

P for H2

= (28×0.0821×296.8/20-28×0.02651 ) -(0.2456 ×28×28/20×20)

P for H2 = 35.4291079-0.481376 = 34.9477319 atm

for O2 ,  a = 1.38L^2bar/mol^2 , b = 0.03186L/mol

P for O2 = (14×0.0821×296.8 /20-14×0.03186) - (1.382×14×14/20×20)

P for O2 = 17.4461807 - 0.67718 =16.7690007 atm

Hence , the pressure needed on H2 tank is 34.9477319atm and the pressure needed in O2 tanks is 16.7690007atm .

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