Question

1. One way to solve chemical equilibrium problems is to write n equations with n unknowns, and then to eliminate unknowns from equations until you have one equation of order n. To solve such an equation involves something like using the quadratic formula (if n = 2) or some other algorithm if n > 2. One such algorithm is the Newton Raphson technique. Let’s pretend that you are solving an equilibrium problem and you have derived the following equation which is of order 3, where x is concentration of some species. Solve for x in this equation using the Newton Raphson equation. Show all work.

0 = x³ +2.6x² +3.3 x -12

Answer 1

solving the chemical equilibrium equation using newton Raphson's iterative method XnH = Rn- f (an) where an is the initial guess general form. x²+2 6x² +3.3x+2) Xnt - an- Taking 372 +590 + 3.3 Iteration (1) (1) initial guess x=0 after first iteration , x = 3636 after using the value of first iteration x=2 303 x = 1.610 a=1399 x = 1371 a = 1.371 So, after the 6th iteration the value of a becomes equal to 1371