the value of the kc for the reaction 2hi gives h2 +i2 is 1*10^-4. at a given time the composition of reaction mixture is [hi] = 2*10^-5 mol , h2 = 1*10^-5mol i2 = 1*10^-5mol in which direction the reaction will proceed??

Dear student

       2HI    <==> H₂ + I₂   Kc = 1*10^-4

After time t, [HI] = 2*10^-5 mol, $H_2$ = 1*10^-5 mol,  [I₂] = 1*10^-5 mol.
So after time t,  Kc = $\frac{ \left[H_2\right] \left[I_2\right]}{{\left[HI\right]}^2}$
                          Kc =  (  1*10^-5) (  1*10^-5) /  ( 2*10^-5 )²
                          Kc = 0.25

The value of the equilibrium constant is increases, so the reaction will shift in the backward direction to achieve the equilibrium state.

Regards