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 26.0 mol of water at 23.8°C. (a) Use the ideal gas law to find the pressure needed in each tank.

___ atm H2

____ atm O2

B. Use the van der Waals equation to find the pressure needed in each tank.

____ atm H2

____atm O2

Answer 1

For Ideal gas;

PV = nRT

we have reaction equation

2H₂ + O₂ -----> 2H₂O

to make 26 mol H₂O we need 26 mol H₂ and 26/2 mol O₂ = 13 mol O₂

T = 23.8 ^oC = 23.8 + 273 = 296.8 K

(A)

P_H2 = 26 mol x 0.08206 atm.L/mol.K x 296.6K / 20.0L = 31.66 atm

P_O2 = 13 mol x 0.08206 atm.L/mol.K x 296.6K / 20.0L = 15.83 atm

(B)

{P+a(n/V)²}{V/n-b} = RT

P = RT/{V/n-b} - a(n/V)²

vanderwalls constant for H₂

a = 0.2453 bar L²/mol²

b = 0.02651 L/mol

P = 0.08206 atm.L/mol.K.296.6 K/{(20 L / 26mol-0.02651 L/mol) - 0.2453 bar L²/mol²(26mol / 20 L)²}

P = 74.16 bar

= 73.19 atm

for O₂

a = 1.382 bar L²/mol²

b = 0.03186 L/mol

P_O2 = 26.37 bar

= 26 atm