The gas substance consist of nitrogen oxide and oxygen. Find the oxygen concentration when nitrogen oxide oxides with maximal rate.
We have the following equation of chemical reaction: 2NO + O_2 = 2NO_2 The speed of this reaction can be calculated as: V = kx^2 * y, where x - concentration of NO, y - concentration of O_2, k - constant, depends only on temperature.
Let's substitute y = 100 - x: V = kx^2 * (100 - x) = k(100x^2 - x^3). The derivative is: dV / dx = k(200x - 3x^2) = 0. Then x1 = 0 and x2 = 66.7%. The first root cannot be the solution of the problem. So, x = 66.7% and finally: y = 100 - 66.7 = 33.3% - concentration of O_2.