On itre of a buffer solution containing 0.02 mol of proponoic acid and sodium proponate has PH =4.75.what will be the dissolved in the above buffer solution?(Dissociation constant oofvproponoic acid at 25 degree is 1.34·10^-5)

To determine the concentration of hydrogen ions dissolved in the buffer solution containing propanoic acid and sodium propanoate, we can use the Henderson-Hasselbalch equation. This equation is particularly useful for buffer solutions, as it relates the pH of the solution to the pKa of the weak acid and the ratio of the concentrations of the acid and its conjugate base.

Understanding the Components

In your buffer solution, we have:

• Propanoic acid (C₂H₅COOH), which acts as the weak acid.
• Sodium propanoate (C₂H₅COONa), which serves as the conjugate base.

Given Data

From your question, we know:

• Concentration of propanoic acid = 0.02 mol
• pH of the solution = 4.75
• Dissociation constant (K_a) of propanoic acid = 1.34 × 10^-5

Calculating pKa

First, we need to find the pKa of propanoic acid. The relationship between pKa and Ka is given by:

pKa = -log(K_a)

Substituting the given value:

pKa = -log(1.34 × 10^-5) ≈ 4.87

Applying the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is expressed as:

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

Where [A^-] is the concentration of the conjugate base (sodium propanoate) and [HA] is the concentration of the weak acid (propanoic acid).

Rearranging the Equation

We can rearrange the equation to solve for the ratio of the concentrations:

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

Substituting the known values:

log([A^-]/[HA]) = 4.75 - 4.87 = -0.12

Now, we can exponentiate to find the ratio:

[A^-]/[HA] = 10^-0.12 ≈ 0.76

Finding the Concentration of the Conjugate Base

Let’s denote the concentration of sodium propanoate as [A^-] and the concentration of propanoic acid as [HA]. We know [HA] = 0.02 mol. Using the ratio we found:

[A^-] = 0.76 × [HA] = 0.76 × 0.02 mol = 0.0152 mol

Calculating the Concentration of Hydrogen Ions

Now, we can find the concentration of hydrogen ions [H⁺] in the solution. The dissociation of propanoic acid can be represented as:

HA ⇌ H⁺ + A^-

Using the expression for the dissociation constant:

K_a = [H⁺][A^-]/[HA]

We can rearrange this to find [H⁺]:

[H⁺] = K_a × [HA]/[A^-]

Substituting the known values:

[H⁺] = (1.34 × 10^-5) × (0.02) / (0.0152)

[H⁺] ≈ 1.76 × 10^-5 mol/L

Final Thoughts

In summary, the concentration of hydrogen ions dissolved in the buffer solution is approximately 1.76 × 10^-5 mol/L. This calculation illustrates how the components of a buffer solution interact to maintain a stable pH, even when acids or bases are added. Understanding these relationships is crucial for applications in chemistry, biology, and environmental science.