What is the magnitude of the change in pH when 0.005 moles of HCl is added to 0.100 L of a buffer solution that is 0.100 M in CH₃CO₂H and 0.100 M NaCH₃CO₂? The K_a for acetic acid is 1.8 × 10^-5. A)0.00 B)0.20 C)0.47 D)1.30

Question

Quizplus · Accepted Answer

First, we need to calculate the pH of the buffer solution before adding the HCl. 
Using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

where pKa is the acid dissociation constant, [A-] is the concentration of the conjugate base (in this case, CH3COO-), and [HA] is the concentration of the acid (in this case, CH3COOH).

From the given information, we know that: 
pKa = 4.74 
[A-] = [CH3COO-] = 0.100 M 
[HA] = [CH3COOH] = 0.100 M

Substituting these values into the Henderson-Hasselbalch equation:

pH = 4.74 + log(0.100/0.100)

pH = 4.74

So the pH of the buffer solution before adding the HCl is 4.74.

Next, we need to calculate the new concentrations of CH3COO- and CH3COOH after adding the HCl.

The HCl will react with the CH3COO- to form CH3COOH:

HCl + CH3COO- -> CH3COOH + Cl-

Since the HCl is a strong acid, it will completely dissociate in water:

HCl -> H+ + Cl-

So the H+ ions from the HCl will react with the CH3COO- ions to form CH3COOH, thus decreasing the concentration of CH3COO- and increasing the concentration of CH3COOH.

The amount of H+ ions produced from 0.005 moles of HCl is:

0.005 mol HCl x (1 mol H+ / 1 mol HCl) = 0.005 mol H+

Since the buffer solution has equal concentrations of CH3COO- and CH3COOH, we can assume that half of the H+ ions (0.0025 mol H+) will react with the CH3COO- ions to form CH3COOH.

The new concentration of CH3COOH will be:

[CH3COOH] = 0.100 M + 0.0025 mol / 0.100 L = 0.1025 M

The new concentration of CH3COO- will be:

[CH3COO-] = 0.100 M - 0.0025 mol / 0.100 L = 0.0975 M

Now we can calculate the new pH of the buffer solution using the Henderson-Hasselbalch equation:

pH = 4.74 + log(0.0975/0.1025)

pH = 4.27

The magnitude of the change in pH is:

ΔpH = pH after - pH before = 4.27 - 4.74 = 0.47

Therefore, the answer is C.

What Is the Magnitude of the Change in PH When