In a chemical engineering process, water vapor (H2O) is heated to sufficiently high temperature that a significant portion of the water dissociates, or splits apart, to form oxygen (O2) and hydrogen (H2):
H2O → H2 + ½ O2
If it is assumed that this is the only reaction involved, the mole fraction x of H2O that dissociates can be represented by
K = x / 1 – x √2pt/2 + x
Where K = the reaction equilibrium constant and pt = the total pressure of the mixture. If pt = 3.5 atm and K = 0.04, determine the value of x that satisfies Eq. (P8.3).