A chemical engineer studying this reaction fills a flask at with of nitrogen dioxide gas. he then raises the temperature considerably, and when the mixture has come to equilibrium determines that it contains of nitrogen dioxide gas. the engineer then adds another of nitrogen dioxide, and allows the mixture to come to equilibrium again.

Nitrogen dioxide is one of the many oxides of nitrogen (often collectively called "NOx") that are of interest to atmospheric chemistry. It can react with itself to form another form of NOx, dinitrogen tetroxide. A chemical engineer studying this reaction fills a 25.0 L tank at 19. °C with 10. mol of nitrogen dioxide gas. He then raises the temperature considerably, and when the mixture has come to equilibrium determines that it contains 3.9 mol of nitrogen dioxide gas. The engineer then adds another 3.3 mol of nitrogen dioxide, and allows the mixture to come to equilibrium again. Calculate the moles of dinitrogen tetroxide after equilibrium is reached the second time. Round your answer to 2 significant digits.

Explanation:

                                                                         2NO₂ →   N₂O₄

Molarity of NO₂ = 10/25 = 0.4M                     Ф 0.4              0 → I

Equilibrium = 3.9 / 25 = 0.16M                       -2x                  +x→ c

 Adding NO₂ = 3.3 / 25 = 0.132M                  0.4 - 2x             x→ E

                                                                         0.4 - 2x = 0.16

                                                                                    x = 0.12

Kc =  [N₂O₄]   =   (0.12 )

        [NO₂]²         (0.16)²

kc = 4.69

N total = NO₂ = 0.4 + 0.132 = 0.532M

                      2NO₂ → N₂O₄

               0.532 - 2x              0.12 + x

                4.69 =  x + 0.12

                         ( 0.532 - 2x )²

  (4 x¬ + 0.283 - 2.128 x ) 4.69 = x + 0.12

   18.76 x¬ - 10.98 x  + 1.23 = 0

          x = 0.414 , 0.171 ,    0.147

            [ N₂O₄ ] =  0.12 + 0.147 = 0.267M

              Moles of N₂O₄ = 0.267 ₓ 25 = 6.68  ⇒ Moles of N₂O₄ = 6.7