If K_a of weak acid HA is 1 10⁻⁷ , calculate the [ H ₃ O ^+] of 0.1 M solution at equilibrium.

Step-by-step solution

For a weak acid HA, the dissociation reaction is: HA + H ₂ O H ₃ O ^+ + A ^- The dissociation constant is given by K_a = [ H ₃ O ^+][ A ^-] [ HA ] . Since K_a is very small, the degree of dissociation is much less than 1 , and the concentration of hydronium ions can be approximated as: [ H ₃ O ^+] = K_a C Substituting the given values K_a = 1 10⁻⁷ and C = 0.1 M : [ H ₃ O ^+] = 1 10⁻⁷ 0.1 [ H ₃ O ^+] = 10⁻⁸ [ H ₃ O ^+] = 1 10⁻⁴ M Answer: 1 10⁻⁴ M