Question

Which one is incorrect with regard to pK$_a$?

• A. In pK\(_a\), K\(_a\) is acid dissociation constant
• B. pK\(_a\) is measurement of the concentration of hydrogen ions in a solution
• C. Higher the K\(_a\) the stronger the acid
• D. pK\(_a\) is used to show the strength of an acid

Hint:

• \(K_a\): Acid dissociation constant. Larger \(K_a \implies\) stronger acid.
• pK\(_a = -\log_{10}K_a\). Smaller pK\(_a \implies\) stronger acid.
• pH = \(-\log_{10}[\text{H}^+]\). Measures hydrogen ion concentration (acidity/basicity of a solution).
• Henderson-Hasselbalch equation relates pH, pK\(_a\), and the ratio of conjugate base to acid: pH = pK\(_a\) + \(\log_{10}(\frac{[\text{A}^-]}{[\text{HA}]})\).

Answer 1

The Correct Option is B

Let's analyze each statement regarding pK\(_a\): (a) "In pK\(_a\), K\(_a\) is acid dissociation constant": TRUE. K\(_a\) is the equilibrium constant for the dissociation of an acid HA \(\rightleftharpoons\) H\(^+\) + A\(^-\). \(K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}\). (b) "pK\(_a\) is measurement of the concentration of hydrogen ions in a solution": FALSE. The measurement of the concentration of hydrogen ions in a solution is pH, where pH = \(-\log_{10}[\text{H}^+]\). pK\(_a\) is defined as \(-\log_{10}K_a\). It is a measure of the acid's strength (its tendency to dissociate), not directly the [H\(^+\)] in a particular solution (though it's related via the Henderson-Hasselbalch equation). (c) "Higher the K\(_a\) the stronger the acid": TRUE. A larger K\(_a\) value means the acid dissociates more completely, producing more H\(^+\) ions, hence it is a stronger acid. (d) "pK\(_a\) is used to show the strength of an acid": TRUE. Since pK\(_a\) = \(-\log_{10}K_a\), there is an inverse relationship between pK\(_a\) and K\(_a\). A stronger acid has a larger K\(_a\) and therefore a *smaller* pK\(_a\). So, pK\(_a\) values are indeed used to indicate acid strength (lower pK\(_a\) = stronger acid). The incorrect statement is (b). \[ \boxed{\text{pK}_a \text{ is measurement of the concentration of hydrogen ions in a solution}} \]