Question

Describe how to prepare a buffer solution from \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\) and \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) to have a \(\mathrm{pH}\) of 7.5

Short answer

Mix \(\mathrm{NaH}_2\mathrm{PO}_4\) and \(\mathrm{Na}_2\mathrm{HPO}_4\) in a 1:2 ratio by concentration, then adjust the pH if needed.

Step-by-step solution

Identify the Buffer Components

To create a buffer solution with a pH of 7.5 using sodium dihydrogen phosphate \(\mathrm{NaH}_2\mathrm{PO}_4\) and disodium hydrogen phosphate \(\mathrm{Na}_2\mathrm{HPO}_4\), we first identify them as our acid (\(\mathrm{NaH}_2\mathrm{PO}_4\)) and base (\(\mathrm{Na}_2\mathrm{HPO}_4\)). This combination can effectively buffer the solution around the desired pH because their pKa is near the target pH.

Use the Henderson-Hasselbalch Equation

Apply the Henderson-Hasselbalch equation: \[\mathrm{pH = pKa + \log \left(\frac{[\mathrm{A}^-]}{[\mathrm{HA}]}\right)}\]where \([\mathrm{A}^-]\) is the concentration of the base (\(\mathrm{Na}_2\mathrm{HPO}_4\)), and \([\mathrm{HA}]\) is the concentration of the acid (\(\mathrm{NaH}_2\mathrm{PO}_4\)). For this system, the pKa is approximately 7.2.

Calculate the Required Ratio

Rearrange the formula to solve for the ratio:\[\frac{[\mathrm{A}^-]}{[\mathrm{HA}]} = 10^{(\mathrm{pH} - \mathrm{pKa})}\]Substitute the values: \[\frac{[\mathrm{A}^-]}{[\mathrm{HA}]} = 10^{(7.5 - 7.2)} = 10^{0.3} \approx 2.0\]This means you need roughly twice as much \(\mathrm{Na}_2\mathrm{HPO}_4\) as \(\mathrm{NaH}_2\mathrm{PO}_4\).

Prepare the Solution

To prepare the buffer, decide on the total concentration of phosphate you want. Let's assume you choose a total concentration of 0.2 M. Allocating this according to the 2:1 ratio,\[\mathrm{[A]^-] = 2 \times [HA] = \frac{2}{3} \times 0.2 \ M = 0.133 \ M}\] \[\mathrm{[HA] = \frac{1}{3} \times 0.2 \ M = 0.067 \ M}\] Mix these concentrations of \(\mathrm{Na}_2\mathrm{HPO}_4\) and \(\mathrm{NaH}_2\mathrm{PO}_4\) in distilled water.

Adjust and Verify pH

After mixing, measure the pH of your solution using a pH meter. If necessary, adjust the pH slightly by adding small amounts of NaOH (to increase pH) or HCl (to decrease pH) until it is exactly 7.5. This final adjustment accounts for any small deviations or impurities in the chemicals.

Key concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a useful tool in chemistry for calculating the pH of a buffer solution. It provides a link between pH, pKa, and the concentrations of acid and base in a solution.

This equation is especially helpful when you're trying to prepare a buffer solution with a specific pH.

• The equation is expressed as: \[ \mathrm{pH = pKa + \log \left(\frac{[A^-]}{[HA]}\right)} \]
• In this equation, \([A^-]\) is the concentration of the conjugate base, and \([HA]\) is the concentration of the weak acid.
• To use this equation correctly, you need to know the pKa value of your buffering system, which is the pH at which half of the acid is dissociated.

With this formula, you can calculate the necessary ratio of the base and acid forms to achieve your desired pH. Typically, accurate pH calculations require the pKa to be near the target pH, ensuring the buffer is effective over that range.

Phosphate Buffer

Phosphate buffers are commonly used in laboratories due to their ability to maintain a stable pH environment.

These buffering solutions typically involve combinations of either mono- and di-basic sodium phosphate or other similar compounds.

• Phosphate buffers are ideal for many biological processes because they closely mimic the pH of the human body.
• Sodium dihydrogen phosphate (\(\mathrm{NaH}_2\mathrm{PO}_4\)) and disodium hydrogen phosphate (\(\mathrm{Na}_2\mathrm{HPO}_4\)) are typical components of phosphate buffers.
• By mixing these components in the right proportions, you can achieve a buffer with your specified pH, such as 7.5.
• The phosphate system is chosen because its pKa of approximately 7.2 is close to the desired buffer pH. This proximity is crucial for effective buffering.

This type of buffer is widely used in procedures that require a confirmation of internal pH stability, such as enzyme reactions or tissue studies.

pH Adjustment

Adjusting the pH of your buffer solution is a crucial step after initially mixing your components. While proportions calculated through the Henderson-Hasselbalch equation give a good approximation, exact pH measurement and correction is key.

Using a pH meter, the exact pH can be measured:

• If the pH is higher than desired, add a small amount of a strong acid like hydrochloric acid (\(\mathrm{HCl}\)) to lower it.
• If the pH is too low, adding a base like sodium hydroxide (\(\mathrm{NaOH}\)) will increase it.
• Make minute adjustments to avoid overshooting the target pH. This ensures that the buffer maintains its ability to resist pH changes effectively over time.

By carefully adjusting the pH, you ensure your buffer is set to the precise pH required for your experimental needs, guaranteeing the best possible conditions for your studies or reactions.