For the reaction $ NH_{2}^{{}}+3{{H}_{2}}\underset{{}}{\leftrightarrows}2N{{H}_{3}} $ in a vessel, after the addition of equal number of moles of $ {{N}_{2}} $ and $ {{H}_{2}} $ ​ ​ equilibrium state is achieved. Which of the following is correct?
(A) $ \left[ {{H}_{2}} \right]=\left[ {{N}_{2}} \right]. $
(B) $ \left[ {{H}_{2}} \right]<\left[ {{N}_{2}} \right]. $
(C) $ \left[ {{H}_{2}} \right]>\left[ {{N}_{2}} \right]. $
(D) $ \left[ {{H}_{2}} \right]<\left[ N{{H}_{3}} \right]. $

Hint : The equilibrium constant is a constant which is specific for each reaction because it depends on certain conditions such as temperature. The formula of the equilibrium constant is the ratio of the concentration of the product to the concentration of the reactant.

Complete Step By Step Answer:
In the given question we have to find the equilibrium constant for the synthesis of ammonia at $ {{450}^{{}^\circ }}C $ . It is given that the moles of ammonia are one when one mole of nitrogen and two moles of hydrogen are combined. - Firstly, we know the balance reaction will be: $ NH_{2}^{{}}+3{{H}_{2}}\underset{{}}{\leftrightarrows}2N{{H}_{3}} $
At time $ =0 $ , the no. of moles of nitrogen is one mole and no. of moles of hydrogen is two moles whereas the no. of moles of ammonia will be zero because they didn't react. Now, at a time $ t $ let the $ x $ moles be used in the reaction. So, the no. of moles of nitrogen will be and no. of moles of hydrogen will be $ 2-3x $
Number of moles of $ {{N}_{2}} $ and $ {{H}_{2}} $ ​ equilibrium state is achieved. Then $ \left[ {{H}_{2}} \right]<\left[ {{N}_{2}} \right] $ Assume total volume is $ 1L $ So number of moles is equal to molar concentration. Assume that four moles of $ {{N}_{2}} $ ​ and four moles of $ {{H}_{2}} $ ​ are mixed. As per reaction stoichiometry, if one mole of $ {{N}_{2}} $ ​ will react with three moles of $ {{H}_{2}} $ to reach equilibrium, then
 $ \Rightarrow 4-1=3~ $ moles of $ {{N}_{2}} $ and $ 4-3=1~ $ mole of $ {{H}_{2}} $ ​ will remain unreacted. Hence, $ \left[ {{H}_{2}} \right]<\left[ {{N}_{2}} \right] $
Therefore, correct answer is option B i.e. $ \left[ {{H}_{2}} \right]<\left[ {{N}_{2}} \right] $

Note :
Before writing the expression for equilibrium constant one must write a balanced equation. The value of equilibrium constant tells about the concentration of reactant and product in the reaction such as if the value of is more than $ 1000, $ then it means that the concentration of the product is high.