Acetate Buffer Ratio Calculation

To determine the molar ratio of salt ([A^-]) to acid ([HA]) needed for a specific buffer pH, we use the Henderson-Hasselbalch equation.

Henderson-Hasselbalch Equation

The equation is:

$ \text{pH} = \text{pKa} + \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) $

Here:

• Desired pH = 5.0
• Given pKa = 4.76
• We need to find the ratio $\frac{[\text{salt}]}{[\text{acid}]}$, which corresponds to $\frac{[\text{A}^-]}{[\text{HA}]}$.

Calculating the Molar Ratio

Substitute the known values into the equation:

$ 5.0 = 4.76 + \log_{10}\left(\frac{[\text{salt}]}{[\text{acid}]}\right) $

Rearrange the equation to solve for the logarithm of the ratio:

$ \log_{10}\left(\frac{[\text{salt}]}{[\text{acid}]}\right) = 5.0 - 4.76 $

$ \log_{10}\left(\frac{[\text{salt}]}{[\text{acid}]}\right) = 0.24 $

To find the ratio, take the antilogarithm (10 to the power of) of both sides:

$ \frac{[\text{salt}]}{[\text{acid}]} = 10^{0.24} $

$ \frac{[\text{salt}]}{[\text{acid}]} \approx 1.7378 $

Rounding to two decimal places, the required molar ratio is approximately 1.74.

Conclusion

The molar ratio [salt]/[acid] required to prepare an acetate buffer of pH 5.0 when the pKa is 4.76 is approximately 1.74.