Answer
Kc = 281.03
Work Step by Step
$ Kp = Kc(RT)^{\Delta n} $
If we have Kp = 3.423 then we need to find the value of $\Delta n$
2SO$_2$(g) + O$_2$(g) 2SO$_3$(g)
Sicne we have 3 moles on the left and 2 moles on the right, it means we have a $\Delta n$ of -1. Therefore, we have:
$ 3.423 = Kc(RT)^-1 $
R = 0.0821 and T = 1000K so we have RT = 82.1 and then
Kc = 281.03
