Question

Calculate the mass of sodium acetate that must be added to \(500.0 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) acetic acid to form a \(\mathrm{pH}=5.00\) buffer solution.

Short answer

To create a buffer solution with pH=5.00 using 500.0 mL of 0.200M acetic acid, you need to add approximately 14.93 grams of sodium acetate. This is calculated using the Henderson-Hasselbalch equation in conjunction with the pKa of acetic acid and the desired [A-]/[HA] ratio.

Step-by-step solution

Find the pKa of the acetic acid

The pKa is the dissociation constant for the acid, which can be calculated using the formula:pKa = -log(Ka)The Ka value (acid dissociation constant) for acetic acid is \(1.8 × 10^{-5}\). We plug this value into the formula to find the pKa:pKa = -log(\(1.8 × 10^{-5}\)) ≈ 4.74

Find the ratio [A-]/[HA] using the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is: pH = pKa + log(\([A^-]/[HA]\)) We know the target pH is 5.00 and we found the pKa to be 4.74. We will now plug these values into the equation and solve for the [A-]/[HA] ratio: 5.00 = 4.74 + log(\([A^-]/[HA]\))

Solve for the [A-]/[HA] ratio

We now solve the equation for the ratio, following these steps: 1. Subtract pKa from pH: 5.00 - 4.74 = 0.26 2. Calculate the antilog of 0.26 (also known as the inverse of the logarithm), equal to 10^0.26: \([A^-]/[HA]\) = 10^0.26 ≈ 1.82

Calculate the moles of [HA] and [A-] needed

First, we find the initial moles of acetic acid [HA] in the solution: Given that the concentration of acetic acid in the solution is 0.200M and the total volume is 500.0 mL, we convert the volume to liters and multiply by the concentration: moles of [HA] = 0.5 L × 0.200 mol/L = 0.100 mol Now we find the moles of [A-] (sodium acetate) needed for the buffer solution: moles of [A-] = moles of [HA] × \([A^-]/[HA]\) ratio from Step 3 = 0.100 mol × 1.82 ≈ 0.182 mol

Calculate the mass of sodium acetate

Now, we can calculate the mass of sodium acetate required for a buffer solution with pH=5.00. The molar mass of sodium acetate (NaC₂H₃O₂) is approximately 82.03 g/mol. We will use the moles of sodium acetate found in step 4: mass of NaC₂H₃O₂ = moles × molar mass = 0.182 mol × 82.03 g/mol ≈ 14.93 g So, approximately 14.93 grams of sodium acetate should be added to the 500.0 mL of 0.200M acetic acid solution to create a buffer solution with pH=5.00.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a fundamental formula in chemistry used to calculate the pH of a buffer solution. This equation helps us understand the relationship between the pH of a solution, the pKa of the acid in the solution, and the ratio of the concentrations of the deprotonated form to the protonated form. The equation is given by:\[pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right) \]In this context, \([A^-]\) represents the concentration of the base form, typically the salt part, and \([HA]\) represents the concentration of the acid. This equation is essential when preparing buffer solutions as it allows us to achieve a specific pH by adjusting the concentrations of the acid and its conjugate base. It is a practical tool in lab settings for creating environments where pH stability is crucial.

acetic acid

Acetic acid (CH₃COOH) is a weak organic acid that is commonly found in vinegar and used in various industrial applications. It's known for its sour taste and pungent smell. In its dissociated form, acetic acid releases a proton (H⁺), which makes it acidic. The equilibrium involved in acetic acid dissociation is:\[CH_3COOH \rightleftharpoons CH_3COO^- + H^+\]In a buffer solution, acetic acid functions as the weak acid component. Its ability to partially dissociate makes it suitable for buffering because it can donate and accept protons as the pH shifts slightly. This makes acetic acid an excellent candidate for biological and chemical buffer systems where the maintenance of a stable pH is necessary.

sodium acetate

Sodium acetate (NaC₂H₃O₂) is the sodium salt of acetic acid, often used in chemical processes and buffer solutions. It dissolves in water to provide acetate ions, \(CH_3COO^-\), which can react with excess hydrogen ions in the solution. This reaction helps to neutralize changes in pH, maintaining the desired conditions for the buffer. The dissolution process is:\[NaC_2H_3O_2 \rightarrow Na^+ + CH_3COO^-\]In the buffer solution formation mentioned in the exercise, sodium acetate serves as the source of conjugate base (\([A^-]\)) which works alongside acetic acid to stabilize pH changes. The correct amount of sodium acetate is crucial to achieving the target pH, as seen in the step-by-step solution where its mass is meticulously calculated.

pKa

The \(pKa\) of a substance is a critical value that describes the strength of an acid in a solution. It is the negative logarithm of the acid dissociation constant, \(K_a\), illustrating how easily an acid releases a proton. \(pKa\) can be calculated using:\[pKa = -\log(K_a)\]For acetic acid, the \(pK_a\) is approximately 4.74, indicating its weak acidic nature due to its relatively small \(K_a\). This \(pKa\) plays a significant role in determining the pH of buffer solutions, using the Henderson-Hasselbalch equation. Knowing the \(pKa\) allows chemists to make specific pH calculations necessary for the maintenance of stable environments in various scientific and industrial applications.

acid dissociation constant

The acid dissociation constant, \(K_a\), measures the extent to which an acid dissociates in water. It is a crucial parameter that helps define the strength of an acid. The higher the \(K_a\), the stronger the acid, indicating a higher degree of ionization. For acetic acid:\[CH_3COOH \rightleftharpoons CH_3COO^- + H^+\]The equilibrium expression for \(K_a\) is:\[K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}\]For acetic acid, \(K_a\) is \(1.8 \times 10^{-5}\), highlighting its properties as a weak acid. Understanding \(K_a\) helps when tailoring buffer solutions to achieve desired pH levels. It provides insight into the dynamic equilibrium between the acid and its conjugate base, contributing to the efficiency and stability of buffer systems.