initial [S

_{2}] is 0.008M (0.004 mole/0.5L)

At equilibirum, there is 2*10

^{-11} moles of S - so [ S ] is 4*10

^{-11}M.

If 2*10

^{-11} moles of S is formed, that means 1*10

^{-11} moles of S

_{2} reacted - this is a negligible amount so effectively [S

_{2}] at equilibirum is still 0.008M.

So K

_{c} = (4*10

^{-11})

^{2}/0.008 = 2*10

^{-19}