Answer to Question #14966 in Calculus for Julia

Question

The gas substance consist of nitrogen oxide and oxygen. Find the oxygen concentration when nitrogen oxide oxides with maximal rate.

Answer 1

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.