The pH of the solution containing 50 mL each of 0.10 M sodium acetate and 0.01 M acetic acid is [Given pK_a of CH₃ COOH = 4.57]

Concept:

pH of acidic buffer - 

• Buffer solution - Buffer solution is a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. It is a solution highly known for maintaining its pH on dilution with a small amount of strong acid or strong base by maintaining the H⁺ ion concentration inside it. 
• Two types of buffer solutions are there
• Acidic buffer - Highly specific for pH<7 and is a mixture of a weak acid and its conjugate base.
• Weak buffer - Highly specific for pH>7 and is a mixture of a weak base and its conjugate acid.
• pH of the acidic buffer is given by the formula -

pH = pKa + log ([salt]/[acid])

where pK_a = negative logarithms of the acid dissociation constant.

As acetic acid is a weak acid and sodium acetate is its conjugate salt with a strong base(NaOH), they form an acidic buffer whose pH is calculated by the formula -

pH = pKa + log ([salt]/[acid])

Chemical reaction - CH₃COOH + NaOH \(\rightarrow\) CH₃COONa +H₂O

Calculation -

Given,

• pKa = 4.57 (negative logarithms of the acid dissociation constant of acetic acid)
• [acid] = 0.01 M (concentration of acetic acid)
• [salt] = 0.10 M (concentration of salt)

Put all these values in the formula,

pH = pKa + log ([salt]/[acid])

=4.57 + log(0.10 / 0.01)

=4.57 + log(10)

= 4.57 + 1   -- (∵ log10 = 1)

=5.57

So, the pH of the buffer solution is = 5.57

Hence, the correct answer is option 2.