[roseandmirrors]

The question : Contain SO₂ 1 mole, O₂ 2 moles, SO₃ 0.5 mol in a close system size 5.0 dm³
Which occurs this reaction 2SO_2​ + O₂ 2SO₃ when the system is in equilibrium state, there are SO₃ 40% by moles. Find out equilibrium constant (k)

I try to solve it :
[SO₂] = 1 ÷ 5 = 0.2 M
[O₂]​ = 2 ÷ 5 = 0.4 M
[SO₃]​ = 0.5 ÷ 5 = 0.1 M

SO₃ 40% by mole = (1 + 2 + 0.5) × 40% = 1.4 mole
[SO₃]​ = 1.4 ÷ 5 = 0.28 M

so..
[SO₃] 0.1 + 0.18 = 0.28 M
[SO₂]​ 0.2 - 0.18 = 0.02 M
[O₂]​ 0.4 - 0.09 = 0.31 M

k = [SO₃]​² ÷ [So₂]​²[O₂]
  ​ = (0.28)​² ÷ (0.02)²(0.31) = 652.26

but my key book said that the answer is 76.9, what is wrong with my way to solve this question?

[AWK]

when the system is in equilibrium state, there are SO3 40% by moles

check oxygen in equlibrium!

[roseandmirrors]

I'm afraid that I still didn't quite get it but thank you so much, I'll try to think about this again in the morning

[AWK]

40% by mole = (1 + 2 + 0.5) × 40% = 1.4 mole

less than 2 moles

[roseandmirrors]

I understand it now. Thank you so much. You are life saver. 🙏