Consider the following equilibrium, ( CO ( g )+2 H ₂( g ) CH ₃ OH ( g ) ) 0.1 mol of CO along with a catalyst is present in a (2 dm ^3 ) flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of ( CH ₃ OH ) is formed. The ( K _ p ^0 ) is ______ ( 10⁻³ ) (nearest integer). Given : ( R =0.08 dm ^3 ) bar ( K ⁻¹ ~mol ⁻¹ ) Assume only methanol is formed as the product and

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( array llll & CO ( g ) & + & 2 H ₂( g ) & & CH ₃ OH ( g ) t =0 & 0.1 ~mol & & a ~mol & & - t _ eq & 0.1- x & & a -2 x & & x =0.04 & =0.06 & & = a -0.08 & & & & =0.23-0.08 & & & =0.15 ~mole array ) ( aligned & V =2 ~L & ~T =500 ~K & P _ total =5 bar & n _ Total =0.25= 1 4 ~mol & P _ total = n _ total RT V & 5=(0.06+ a -0.08+0.04) 0.08 500 2 & 10=(0.02+ a ) 0.08 500 aligned ) ( a =0.25-0.02=0.23 ~mol . ) ( aligned & K _ P = X _ CH ₃ OH X _ CO X _ H ₂ ^2 1 ( P _ T )^2 = 0.04 0.06 (0.15)^2 [ 1 / 4 5 ]^2 & = 4 6 (0.15)