The osmotic pressure of a 0.19 M aqueous solution of a weak monoprotic acid HA is found to be 5 % higher than that of a 0.19 M aqueous solution of a non-electrolyte at the same temperature. The dissociation constant K_a of the acid is x 10⁻⁵ . The value of x is _______.

Step-by-step solution

Let the concentration of the solutions be C = 0.19 M . For a non-electrolyte, the van 't Hoff factor i = 1 . Its osmotic pressure is _ non-electrolyte = C R T . For the weak acid HA , the osmotic pressure is _ HA = i C R T . Given that _ HA is 5 % higher than _ non-electrolyte , we have: _ HA = 1.05 _ non-electrolyte i C R T = 1.05 C R T i = 1.05 For a weak monoprotic acid dissociating as HA H ^+ + A ^- , the van 't Hoff factor is related to the degree of dissociation by: i = 1 + 1.05 = 1 + = 0.05 The dissociation