# Answer to Question #14966 in Calculus for Julia

Question #14966

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

Expert's answer

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.

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.

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