Calculate the amount of Na2HPO4 and NaH2PO4 needed to make a 100 mL of 0.1 M sodium phosphate buffer solution that has pH 6.5 and a pka =6.8.
To calculate the amount of Na2HPO4 and NaH2PO4 needed to make a 100 mL of 0.1 M sodium phosphate buffer solution with a pH of 6.5 and a pKa of 6.8, we can use the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is as follows:
pH = pKa + log([A-]/[HA])
In this equation, [A-] represents the concentration of the dissociated form of the buffer (Na2HPO4) and [HA] represents the concentration of the undissociated form of the buffer (NaH2PO4).
We need to rearrange this equation to solve for the ratio of [A-]/[HA]:
[A-]/[HA] = 10^(pH - pKa)
Now, let's substitute the given values into the equation:
[A-]/[HA] = 10^(6.5 - 6.8)
= 10^(-0.3)
Solving the exponent, we have:
[A-]/[HA] = 0.501187
Since the sum of the concentrations of [A-] and [HA] is 0.1 M (the desired concentration of the buffer solution), we can set up the following equation:
[A-] + [HA] = 0.1
To solve this equation, we can use the ratio obtained earlier:
[A-] = 0.501187 * [HA]
Substituting this into the above equation:
0.501187 * [HA] + [HA] = 0.1
Combining like terms:
1.501187 * [HA] = 0.1
Simplifying:
[HA] = 0.1 / 1.501187
= 0.066601 M
Now, we can calculate the concentration of [A-]:
[A-] = 0.501187 * [HA]
= 0.501187 * 0.066601
= 0.033349 M
To find the amount of Na2HPO4 and NaH2PO4 needed, we need to multiply the concentrations by the volume of the solution:
Amount of Na2HPO4 = [A-] * Volume
= 0.033349 M * 100 mL
= 3.3349 moles
Amount of NaH2PO4 = [HA] * Volume
= 0.066601 M * 100 mL
= 6.6601 moles
Therefore, to make a 100 mL of 0.1 M sodium phosphate buffer solution with a pH of 6.5 and a pKa of 6.8, you would need approximately 3.3349 moles of Na2HPO4 and 6.6601 moles of NaH2PO4.