Try this
..........SO2 + NO2 ==> SO3 + NO
I.........2.53...0.......0.....0
C..........-x....x.......1.1...1.1
E.........2.53-x..x......1.1....1.1
Total mols = 2.53-x_x_1,1+1.1 = 4.73-x
XSO2 = (2.53-x)/(4.73-x)
XNO2 = x/(4.73-x)
XSO3 = 1.1/(4.73-x)
XNO = 1.1(4.73-x)
Then partial pressures are
pSO2 = (2.53-x)/(4.73-x)]*Ptotal
pNO2 = [x/(4.73-x)]*Ptotal
pSO3 = [1.1/(4.73-x)]*Ptotal
pNO = [1.1/4.73-x)]*Ptotal
I won't finish but here is what you do.
Substitute partial pressures from above into K expression. Solve for x = mols NO2 and you have it. Don't worry about all of this extraneous stuff; it cancels and you are left with a simple quadratic to solve.