At 25^ C , the concentration of H ⁺ ions in 1.00 10⁻³ M aqueous solution of a weak monobasic acid having acid dissociation constant (K_a )=4.00 10⁻¹¹ is X 10⁻⁷ M . The value of X is _____ . Use: Ionic product of water (K_w )=1.00 10⁻¹⁴ at 25^ C

Step-by-step solution

Because concentration of H + from weak acid is less we need to consider self ionization of H ₂ O also. array rl HX ( aq ) & H ⁺+ X ⁻( aq ) 10⁻³- x & x + y x H ₂ O (l) & H ⁺( aq )+ OH ⁻( aq ) & x + y y array Approximation : (10⁻³- x ) 10⁻³ aligned & x(x+y) 10⁻³ =K_a=4 10⁻¹¹....(1) & y(x+y)=K w=10⁻¹⁴.....(2) aligned array ll Add (1)+(2) array array ll & ( x + y )^2=5 10⁻¹⁴ & x + y = [ H ⁺ ]= 5 10⁻⁷ & x = 5 =2.236 array Answer 2.23 or 2.24.