Q.2-2-16P - Organic Chemistry (Mcmurry)

Question

Question: What is the K_a of HCN if its pK_a = 9.31?

Step-by-Step Solution

Answer

Answer

The  K_a of HCN is $4.9\times {10}^{-10}$if its pK_a= 9.31.

Step 1:Acid and base strength

Acids differ in their ability to donate H⁺. Stronger acids, such as HCl, react almost completely with water, whereas weaker acids, such as acetic acid (CH₃COOH), react only slightly. The exact strength of a given acid HA in water solution is described using the acidity constant (k_a)for the acid-dissociation equilibrium.

Example:

                                               $$\begin{gathered} {\text{HA+H}}_2{\text{O⇄A}}^{-}{\text{H}}_3\text{O} \\ {K}_a=\frac{\left[H_3{O}^{+}\right]\left[A^{-}\right]}{\left[HA\right]} \end{gathered}$$

Acid strengths normally pk_a  uses values rather than k_a  values, where the pk_a  is the negative common logarithm of k_a :

                           pk_a =-log k_a 

The stronger acid has a smaller pk_a  and a weaker acid has a larger pk_a  .

Step 2: Calculate of HCN

As we know from above step,

   pk_a =-log k_a   --------eq(1)

 

Taking antilog on both sides of eq(1),

Antilog (pk_a )= -k_a 

Antilog (-9.31) = k_a

 10^-9.31            = k_a 

4.9 x 10^-10      = k_a 

The k_a  of HCN is 4.9 x 10^-10   if its pk_a = 9.31.