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JEE MainChemistryIonic Equilibrium

An aqueous solution of a weak monobasic acid HA has a measured pH of 3.0 . If the acid dissociation constant ( pK_a ) of HA is 4.0 , what is the exact degree of dissociation ( ) of the acid in this solution?

Options

  1. A1 10
  2. B10 11
  3. C1 11
  4. D1 9

Correct answer

C. 1 11

Step-by-step solution

For a weak monobasic acid HA, the exact relationship between its dissociation constant K_a , hydrogen ion concentration [ H ^+] , and degree of dissociation is: K_a = [ H ^+] 1- Taking the negative logarithm on both sides: - K_a = - [ H ^+] - ( 1- ) pK _a = pH - ( 1- ) Rearranging the equation to solve for the logarithmic term: ( 1- ) = pH - pK _a Substitute the given values ( pH = 3.0 and pK _a = 4.0 ): ( 1- ) = 3.0 - 4.0 = -1.0 Taking the antilogarithm of both sides: 1- = 10⁻¹ = 0.1 Solving for : = 0.1(1 - ) = 0.

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