Question

Use of Molar Concentrations to Calculate \(\mathrm{pHI}\) What is the \(\mathrm{pH}\) of a solution that contains \(0.20 \mathrm{~m}\) sodium acetate and \(0.60\) m acetic acid \(\left(\mathrm{p} K_{\mathrm{n}}=4.76\right)\) ?

Short answer

The pH of the solution is approximately 4.28.

Step-by-step solution

Identify Components

Determine which components of the solution will affect the pH. The solution contains acetic acid (a weak acid) and sodium acetate (its conjugate base). This is a buffer solution.

Apply Henderson-Hasselbalch Equation

Use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution: \[pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)\]Where \([A^-]\) is the concentration of acetate ions and \([HA]\) is the concentration of acetic acid.

Substitute Values

Substitute the given concentrations and the \( pK_a \) value into the Henderson-Hasselbalch equation:\[pH = 4.76 + \log\left(\frac{0.20}{0.60}\right)\]

Calculate Ratio

Calculate the ratio of sodium acetate to acetic acid: \[ \log\left(\frac{0.20}{0.60}\right) = \log\left(\frac{1}{3}\right) \approx -0.477 \]

Compute the pH

Add the calculated value of the logarithmic ratio to the \( pK_a \):\[ 4.76 - 0.477 = 4.28 \]Thus, the pH of the solution is approximately 4.28.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is an important formula used to calculate the pH of a buffer solution, which consists of a weak acid and its conjugate base. Although it may seem complex at first, it's actually quite straightforward: \[ pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right) \]Here:

• \([A^-]\) represents the concentration of the conjugate base, which is the anionic part of the weak acid after it donates a proton.
• \([HA]\) symbolizes the concentration of the weak acid itself.
• \(pK_a\) is the acid dissociation constant, indicating the strength of the weak acid in aqueous solution. In this case, it's 4.76 for acetic acid.

The equation is derived from the equilibrium constant expression for a weak acid. It provides a simple method to estimate the pH based on the ratio of these concentrations. Understanding this equation is essential for managing buffer systems in various chemical and biological applications.

buffer solution

A buffer solution is a special type of solution designed to resist significant changes in pH upon the addition of small amounts of acids or bases. The key to maintaining this stability is its composition:

• It includes a weak acid and its conjugate base in appreciable amounts.
• This combination allows the solution to neutralize added hydroxide ions or protons, thereby maintaining a nearly constant pH.

In our example, the buffer consists of acetic acid (weak acid) and sodium acetate (conjugate base). This system can counteract pH changes effectively, making buffer solutions crucial in many chemical reactions and biological systems, like blood, where maintaining a specific pH range is vital. It's this balancing act of neutralizing acids and bases that defines the functionality and utility of buffer solutions.

acetic acid

Acetic acid is a common weak acid, often recognized as the main component of vinegar. Its chemical formula is \(CH_3COOH\), and it's known by its characteristic sour taste and pungent smell.

• Being a weak acid, it does not completely dissociate in water, meaning not all acetic acid molecules donate protons to form acetate ions \(CH_3COO^-\) and hydronium ions \(H_3O^+\).
• The constant \(pK_a\) for acetic acid is 4.76, which indicates its acid strength.

In buffer solutions, the acetic acid part can donate protons to neutralize added bases, which aligns perfectly with our exercise of calculating the pH of buffer solutions. Understanding acetic acid's behavior in solutions is important for grasping how buffer systems work in neutralizing added bases.

sodium acetate

Sodium acetate is the salt of acetic acid and is often used as the conjugate base component in buffer solutions. It forms when acetic acid is neutralized by sodium hydroxide. Here's what you should know about it:

• Its chemical formula is \(CH_3COONa\), indicating that it's composed of sodium ions \(Na^+\) and acetate ions \(CH_3COO^-\).
• In solution, sodium acetate dissociates completely, providing a steady supply of acetate ions.
• These acetate ions play a crucial role in buffering, as they can react with any added protons, mitigating pH changes.

In the pH calculation scenario, the role of sodium acetate is vital as it contributes the conjugate base \([A^-]\) in the Henderson-Hasselbalch equation. This ensures that the system can respond to added acids, confirming the buffer's effectiveness in maintaining a stable pH level.