Phosphate Buffer pH Calculation

To determine the pH of the phosphate buffer, we need to identify the acidic and basic components and use the Henderson-Hasselbalch equation.

The buffer is prepared using $Na_2HPO_4$ and $NaH_2PO_4$. The relevant acid-base conjugate pair for the given $pK_a$ (6.86) is $H_2PO_4^-$ (the acid) and $HPO_4^{2-}$ (the base).

• $NaH_2PO_4$ provides the acidic species $H_2PO_4^-$.
• $Na_2HPO_4$ provides the basic species $HPO_4^{2-}$.

Calculate Moles of Buffer Components

First, calculate the number of moles for each salt. Since the buffer volume is 1 litre, the moles calculated will directly correspond to the molar concentrations.

• Moles of $Na_2HPO_4$ (source of base $HPO_4^{2-}$): Mass = 208 g Molar mass = 142 g/mol Moles = $\frac{208 \text{ g}}{142 \text{ g/mol}} \approx 1.4648 \text{ mol}$ So, [Base] concentration $\approx 1.4648 \text{ M}$.
• Moles of $NaH_2PO_4$ (source of acid $H_2PO_4^-$): Mass = 71 g Molar mass = 120 g/mol Moles = $\frac{71 \text{ g}}{120 \text{ g/mol}} \approx 0.5917 \text{ mol}$ So, [Acid] concentration $\approx 0.5917 \text{ M}$.

Apply Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the $pK_a$ of the weak acid and the ratio of the concentrations of the conjugate base and the weak acid:

Substitute the calculated moles (which are equal to molar concentrations in 1 L) and the given $pK_a$:

• $pK_a = 6.86$
• [Base] $= [HPO_4^{2-}] \approx 1.4648 \text{ M}$
• [Acid] $= [H_2PO_4^-] \approx 0.5917 \text{ M}$

Calculation:

The calculated pH is approximately 7.25, which falls within the range of 7.2 to 7.3.