Calculating the Ratio of Conjugate Base to Weak Acid

Oct 13, 2025 by wbrum.org 21 views

A buffer solution is a mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid. It is designed to resist changes in pH when small amounts of acid or base are added to it. Buffer solutions are commonly used in various applications, including medical, industrial, and laboratory settings.

The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is given by:

pH = pKa + log10([A-]/[HA])

where:

pH is the pH of the buffer solution
pKa is the acid dissociation constant of the weak acid
[A-] is the concentration of the conjugate base
[HA] is the concentration of the weak acid

Given Values

In this problem, we are given the following values:

pH = 5
pKa (CH₃COOH) = 4.7
The buffer solution consists of CH₃COOH (acetic acid) and CH₃COONa (sodium acetate)

Calculating the Ratio of Conjugate Base to Weak Acid

We can use the Henderson-Hasselbalch equation to calculate the ratio of [CH₃COO⁻] to [CH₃COOH]. Rearranging the equation to solve for the ratio, we get:

[CH₃COO⁻]/[CH₃COOH] = 10^(pH - pKa)

Substituting the given values, we get:

[CH₃COO⁻]/[CH₃COOH] = 10^(5 - 4.7) [CH₃COO⁻]/[CH₃COOH] = 10^0.3

Evaluating the Result

To evaluate the result, we can use the fact that 10^0.3 is approximately equal to 2. Therefore, the ratio of [CH₃COO⁻] to [CH₃COOH] is approximately 2.

Conclusion

In conclusion, the ratio of [CH₃COO⁻] to [CH₃COOH] in a buffer solution consisting of CH₃COOH and CH₃COONa with a pH of 5 is approximately 2.

Answer

The correct answer is (C) 2.

Additional Information

The Henderson-Hasselbalch equation is a powerful tool for calculating the pH of buffer solutions. It is widely used in various applications, including medical, industrial, and laboratory settings. The equation is based on the principle that a buffer solution resists changes in pH when small amounts of acid or base are added to it.

Understanding the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is given by:

pH = pKa + log10([A-]/[HA])

where:

pH is the pH of the buffer solution
pKa is the acid dissociation constant of the weak acid
[A-] is the concentration of the conjugate base
[HA] is the concentration of the weak acid

Using the Henderson-Hasselbalch Equation

To use the Henderson-Hasselbalch equation, we need to know the pH of the buffer solution, the pKa of the weak acid, and the concentrations of the conjugate base and weak acid. We can then plug these values into the equation to calculate the pH of the buffer solution.

Example Problem

Suppose we have a buffer solution consisting of CH₃COOH and CH₃COONa with a pH of 5. We want to calculate the ratio of [CH₃COO⁻] to [CH₃COOH]. We can use the Henderson-Hasselbalch equation to solve this problem.

Step 1: Write Down the Henderson-Hasselbalch Equation

pH = pKa + log10([A-]/[HA])

Step 2: Plug in the Values

pH = 5 pKa (CH₃COOH) = 4.7 [CH₃COO⁻] = x [CH₃COOH] = y

Step 3: Rearrange the Equation

[CH₃COO⁻]/[CH₃COOH] = 10^(pH - pKa) [CH₃COO⁻]/[CH₃COOH] = 10^(5 - 4.7) [CH₃COO⁻]/[CH₃COOH] = 10^0.3

Step 4: Evaluate the Result

To evaluate the result, we can use the fact that 10^0.3 is approximately equal to 2. Therefore, the ratio of [CH₃COO⁻] to [CH₃COOH] is approximately 2.

Conclusion

In conclusion, the ratio of [CH₃COO⁻] to [CH₃COOH] in a buffer solution consisting of CH₃COOH and CH₃COONa with a pH of 5 is approximately 2.

Answer

The correct answer is (C) 2.