Given : Initial Moles of SO2 = 2.86
Let initial moles of NO2 = x
The chemical equilibrium is
                          Â
SO2(g)Â Â +Â Â Â
NO2(g)Â Â Â Â ---> SO3(g) + NO(g)
Initial
moles        Â
2.86Â Â Â Â Â Â Â Â Â Â Â Â Â Â
x                   Â
0Â Â Â Â Â Â Â Â Â Â Â Â
0
Change                  Â
-y            Â
-y                  Â
+y          Â
+y
Equilibrium      Â
2.86-y            Â
x-y                 Â
y             Â
y
Given : mole sof SO3 at equilibrium = 1.30 so y = 1.30
Now Keq = [SO3][NO] / [SO2][NO2]
2.50 = 1.30 X 1.30 / (2.86-1.30) (x-1.30)
1.48 = 1 / 1.56 X (x-1.30)
(x-1.30) = 0.433
x = 1.733 moles
so number of moles of NO2 that must be added = 1.733 moles