The irreversible chemical reaction in which two molecules ofsolid potassium dichromate (K^C^O?), two molecules ofwater (HaO), and three atoms ofsolid sulfur (S) combine to yield three molecules of the gas sulfur dioxide (SO2), four molecules ofsolid potassium hydroxide (KOH), and two molecules ofsolid chromic oxide (CnCU) can be represented symbolically by the stoichiometric equation: 2X^07 + 2H2O + 3S ^ 4KOH + 2^03 + 3802. If! molecules ofI^C^O?, 112 molecules of H2O, and molecules ofS are originally available, the following differential equation describes the amount x(t) of KOH after time t: |= - I) ("" " I) ("3 " T) ' where k is the velocity constant of the reaction. If A: = 6.22 x I0-19 , n\ = n2 = 2 x 103 , and R3 = 3 x ID3 , use the Runge-Kutta method of order four to determine how many units of potassium hydroxide will have been formed after 0.2 s.
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