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
A. A
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.
Related: Chemistry — Ionic Equilibrium · All PYQ Banks