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\( \mathrm{N}_{2} \) and \( \mathrm{O}_{2} \) combine at a given temperature to produce \( \mathrm{NO} \). At equilibrium the yield of \( \mathrm{NO} \) is ' \( x \) ' percent by volume. If \( x=\sqrt{(k \cdot a \cdot b)-[K(a+b) / 4]} \), where \( K \) is the equilibrium constant of the given reaction at the given temperature and \( a \) and \( b \) are the volume percentage of \( \mathrm{N}_{2} \) and \( \mathrm{O}_{2} \) respectively in the initial pure mixture, what should be the initial composition of the reacting mixture inorder that maximum yield of \( \mathrm{NO} \) is ensured? Also report the maximum value of \( K \) at which ' \( x \) ' is maximum.
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