How many moles of hydrochloric acid (pKa of HF=3.14) must be added to 500.0 mL of 0.30M sodium fluoride (NaF) to give a buffer of pH 3.50? Ignore the volume change due to the addition of hdrofluoric acid
500 mL x 0.30M NaF = 150 millimols NaF.
3.50 = 3.14 + log (base)/(acid)
3.50 = 3.14 + log (150/x)
Solve for x = millimoles HCl, then change to mols.
0.662moles
To determine the number of moles of hydrochloric acid (HCl) needed to create a buffer solution, we need to apply the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa of its conjugate acid-base pair.
The Henderson-Hasselbalch equation is:
pH = pKa + log([A-]/[HA])
Where:
- pH is the desired pH of the buffer solution
- pKa is the pKa value of the conjugate acid (HF in this case)
- [A-] is the concentration of the conjugate base (F-) in the buffer solution
- [HA] is the concentration of the acid (HF) in the buffer solution
We are given:
- pH = 3.50
- pKa = 3.14
- [A-] = concentration of fluoride ion (NaF) = 0.30 M
- [HA] = concentration of the acid (HF) we want to calculate
Rearranging the Henderson-Hasselbalch equation, we have:
[HCl] = (10^(pH - pKa)) * [A-] / (1 + 10^(pH - pKa))
Substituting the given values, we can find the concentration of HCl needed to achieve the desired pH:
[HCl] = (10^(3.50 - 3.14)) * 0.30 M / (1 + 10^(3.50 - 3.14))
Simplifying the equation, we get:
[HCl] = 0.0434 M
Finally, to find the number of moles of HCl, we need to multiply the concentration by the volume (in liters) of the NaF solution.
Volume NaF solution = 500.0 mL = 0.500 L
Number of moles HCl = concentration HCl * volume NaF solution
= 0.0434 M * 0.500 L
= 0.0217 moles
Therefore, approximately 0.0217 moles of hydrochloric acid (HCl) must be added to 500.0 mL of 0.30 M sodium fluoride (NaF) to create a buffer solution with a pH of 3.50, considering the volume change.