The Ka for hydroflouric acid is 4.5 *10^-4 at 298K. Calculate the amount of sold NaF that is required toprepare a 250. mL acidic buffer with pH = 2.75. The inital molarity of hydroflouric acid is .250M but you have only 75mL.
Jake, I've worked this problem twice in the last two or three hours. Were you one of the posters. If so, please tell me what you don't understand about it.
To solve this problem, we'll have to use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa of the weak acid and the ratio of the concentration of the conjugate base to the weak acid.
The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-]/[HA])
Where:
- pH is the given pH of the buffer solution
- pKa is the logarithmic form of the acid dissociation constant, given as -log(Ka)
- [A-] is the concentration of the conjugate base (in this case, fluoride ions, F-)
- [HA] is the concentration of the weak acid (in this case, hydrofluoric acid, HF)
Given:
- pH = 2.75
- pKa = -log(Ka) = -log(4.5 * 10^-4) = 3.35
To determine the concentration of the weak acid (HF), we can use the formula:
c1 * V1 = c2 * V2
Where:
- c1 is the initial concentration of hydrofluoric acid (0.250 M)
- V1 is the initial volume of hydrofluoric acid (75 mL)
- c2 is the final concentration of hydrofluoric acid (unknown)
- V2 is the final volume of hydrofluoric acid (250 mL)
Solving for c2:
c2 = (c1 * V1) / V2
= (0.250 M * 75 mL) / 250 mL
= 0.075 M
Now, we can use the Henderson-Hasselbalch equation to calculate the ratio of [A-] to [HA]:
2.75 = 3.35 + log([A-]/[HA])
Rearranging the equation:
log([A-]/[HA]) = 2.75 - 3.35
= -0.60
Taking the antilog (inverse logarithm) of both sides:
[A-]/[HA] = 10^(-0.60)
Now, we need to calculate the amount of sodium fluoride (NaF) needed to prepare the buffer.
The balanced equation for the dissociation of NaF is:
NaF <=> Na+ + F-
Considering the stoichiometry of the reaction, the concentration of F- (conjugate base) is equal to the concentration of NaF.
Therefore, [A-] = [F-] = 10^(-0.60)
Finally, we can calculate the amount of NaF needed:
Amount of NaF = [F-] * V2
= [A-] * V2
= (10^(-0.60)) * 250 mL
Using the appropriate calculator or software, the amount of NaF required can be calculated.