Question

Given, 1 "mole of" \[{{N}_{2}}\]"and" 3 "moles of ${{H}_{2}}$ are placed in 1L vessels. Find the concentration of \[N{{H}_{3}}\] at equilibrium, if the equilibrium constant \[\left( {{K}_{c}} \right)\] at 400K "is" $\dfrac{4}{27}$

Answer 1

Hint: A chemical reaction's equilibrium constant is the value of its reaction quotient at chemical equilibrium, a condition reached by a dynamic chemical system after a period of time has passed in which its composition shows no discernible tendency to change. The equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture for a particular set of reaction circumstances.

Complete answer:
As a result, established equilibrium constant values may be used to calculate the composition of a system at equilibrium, given its beginning composition. The value of the equilibrium constant can, however, be influenced by reaction factors such as temperature, solvent, and ionic strength. Many chemical systems, as well as physiological processes like oxygen transport by haemoglobin in blood and acid–base balance in the human body, need an understanding of equilibrium constants.
For our question
\[{{N}_{2}}+3{{H}_{2}}\to 2N{{H}_{3}}\quad \Delta {{H}^{{}^\circ }}=-91.8~\text{kJ/mol}\]
The equilibrium constant is written as
\[K=\dfrac{[{{A}_{p}}{{B}_{q}}]}{{{[A]}^{p}}{{[B]}^{q}}}\]
Volume = 1 L
Temperature = 400 K
Equilibrium constant, ${{K}_{c}}=\dfrac{4}{27}$
The net balanced chemical reactions
\[{{N}_{2}}+3{{H}_{2}}\to 2N{{H}_{3}}\quad \]

Initial Concentration	1	2	0
At equilibrium	1-x	3-3x	2x

The equilibrium constant \[{{K}_{c}}=\dfrac{{{[N{{H}_{3}}]}^{2}}}{{{[{{N}_{2}}]}^{1}}{{[{{H}_{2}}]}^{3}}}\]
Now from the question
\[{{K}_{c}}=\dfrac{{{[N{{H}_{3}}]}^{2}}}{{{[{{N}_{2}}]}^{1}}{{[{{H}_{2}}]}^{3}}}=\dfrac{4}{27}=\dfrac{{{(2x)}^{2}}}{(1-x){{(3-3x)}^{2}}}\]
Find the value of x
\[\dfrac{4}{27}=\dfrac{{{(2x)}^{2}}}{(1-x){{(3-3x)}^{2}}}\]
$x=0.381M$
Concentration of $N{{H}_{3}}$=$2x=2(0.381)M$
Concentration of $N{{H}_{3}}$=$=0.762M$

Note:
The determination of stability constant values beyond the usual range for a specific procedure is one application of a stepwise constant. Many metal EDTA complexes, for example, are outside the potentiometric method's range. Competition with a weaker ligand dictated the stability constants for such complexes.