Solved: The irreversible chemical reaction in which two molecules of solid potassium

Chapter 5, Problem 29

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The irreversible chemical reaction in which two molecules of solid potassium dichromate (K2Cr2O7), two molecules of water (H2O), and three atoms of solid sulfur (S) combine to yield three molecules of the gas sulfur dioxide (SO2), four molecules of solid potassium hydroxide (KOH), and two molecules of solid chromic oxide (Cr2O3) can be represented symbolically by the stoichiometric equation: 2K2Cr2O7 + 2H2O + 3S 4KOH + 2Cr2O3 + 3SO2. If n1 molecules of K2Cr2O7, n2 molecules of H2O, and n3 molecules of S are originally available, the following differential equation describes the amount x(t) of KOH after time t: dx dt = k n1 x 2 2 n2 x 2 2 n3 3x 4 3 , where k is the velocity constant of the reaction. If k = 6.22 1019, n1 = n2 = 2 103, and n3 = 3 103, use the Runge-Kutta method of order four to determine how many units of potassium hydroxide will have been formed after 0.2 s?