And combine at a given temperature to produce

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

\text{N}_2

and

\text{O}_2

combine at a given temperature to produce

\text{NO}

. At equilibrium the yield of

\text{NO}

is '

x

' per cent by volume. If

x = \sqrt{K \cdot a \cdot b} - \frac{K(a+b)}{4}

where

K

is the equilibrium constant of the given reaction at the given temperature and

a

and

b

are the volume percentage of

\text{N}_2

and

\text{O}_2

respectively in the initial pure mixture, what should be the initial composition of the reacting mixture in order that maximum yield of

\text{NO}

is ensured? Also report the maximum value of

K

at which '

x

' is maximum.