Nitrogen and oxygen react together to form nitric oxide, which decomposes to give back the reactants. In a container of one litre capacity, two moles of nitrogen, two moles of oxygen and four moles of niric oxide were injected. What will be the concentration of nitric oxide at equilibrium at 1,727o C? The equilibrium constant for the reaction, at 1,727o C, is 4.1:
(A) 6.01 mol/L
(B) 3.54 mol/L
(C) 4.71 mol/L
(D) 5.84 mol/L

Dear Student,

N2 + O2   2NO 2        2             4                ..initially2-x   2-x      4+2x equilibrium Kc=4.1We know that, Kc =[NO]2[O2][N2]     =(4+2x1)(2-x1)(2-x1)                       (since concentration=MolesVolume)or, 4.1=(4+2x)(2-x)(2-x)since x<<2Therefore, 2-x2So, 4.1(2-x)2=4+2x4.1(4+x2-4x)=4+2x16.4+4.1x2-16.4x=4+2xor, 4.1x2-18.4x+12.4=0or, x2-4.48x+3.02=0or, x=-(-4.48)±(4.48)2-4(1)(3.02)2(1)       =4.48±20.07-12.082       =4.48±2.832       =3.65 or 0.79x 3.65 as x cannot be greater than 2   (this will make [N2] and [O2] at equilibrium negative)x=0.79[NO]=4+2×0.79        =5.58 mol/LHence,correct answer is (D)

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