Question 1
1.1. In a chemical engineering process, water vapor (H₂O) is heated to sufficiently
high temperatures that a significant portion of the water dissociated, or splits
apart to form oxygen (O₂) and hydrogen (H₂):
$$H_2O \rightleftharpoons H_2 + \frac{1}{2}O_2$$
If it assumed that this is the only reaction involved, the mole fraction x of H₂O
that dissociates can be represented by
$$K = \frac{x}{1-x} \sqrt{\frac{2P}{2+x}}$$
Where K is the reaction equilibrium constant and P is the total pressure of the
mixture. If P = 3.5 atm and K = 0.04; determine the value of x that satisfies
the above equation.
[Hint: use the fzero function]
(5)
1.2. A reversible chemical reaction
$$2A + B \rightleftharpoons C$$
can be characterized by the equilibrium relationship
$$K = \frac{C_c}{C_a^2C_b}$$
where the nomenclature cᵢ represents the concentration of constituent i. Suppose that
we define a variable x as representing the number of moles of C that are produced.
Conservation of mass can be used to reformulate the equilibrium relationship as
$$K = \frac{(C_{c,0} + x)}{(C_{a,0} - 2x)^2 (C_{b,0} - x)}$$
where the subscript 0 designates the initial concentration of each constituent. If K =
0.016, Cₐ₀ = 42, Cʙ₀ = 28 and Cᴄ₀ = 4, determine the value of x.
1.2.1. Used the bisection rule (create an m-file) to find the roots with the initial
guesses of x₁ = 0 and xᵤ = 20 and an absolute error of 0.5%.
[Hint: simplify the equation]
(10)