How many moles of NaOH must be added to 1.0 L of 1.4 M HC2H3O2 to produce a solution buffered at each pH?
(a) pH = pKa mol
(b) pH = 3.07 mol
(c) pH = 5.15 mol
Use the Henderson-Hasselbalch equation.
First find moles acetic acid. M x L = moles.
.......CH3COOH + OH^- ==>CH3COONa + H2O
start...moles.... 0.......0
change..-x........+x........+x
final..moles-x.....0......0+x
Then substitute into the HH equation and solve for x. After, I always like to check it by calculating the moles acetate and moles acetic acid remaining, plug into the HH equation and see if it gives the correct pH.
To determine how many moles of NaOH must be added to achieve a specific pH in a buffered solution, we need to consider the Henderson-Hasselbalch equation. This equation relates the pH of a solution with the pKa (the negative logarithm of the acid dissociation constant) and the ratio of the concentration of the conjugate base to the concentration of the acid.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Where pH is the desired pH, pKa is the acid dissociation constant of the weak acid (HC2H3O2 in this case), [A-] is the concentration of the conjugate base (C2H3O2-), and [HA] is the concentration of the weak acid (HC2H3O2).
Let's calculate the number of moles of NaOH needed for each given pH:
(a) pH = pKa mol
For this case, we can see that the desired pH is equal to the pKa. This means that the ratio [A-]/[HA] should be 1. By adding 1 mole of NaOH, we can neutralize 1 mole of HC2H3O2 and produce 1 mole of C2H3O2-. Therefore, 1 mole of NaOH is needed.
(b) pH = 3.07 mol
In this case, we have a specific pH value that is not equal to the pKa. Using the Henderson-Hasselbalch equation, we can solve for the required concentration ratio [A-]/[HA]. Rearranging the equation, we have:
log([A-]/[HA]) = pH - pKa
Substituting the given values, we get:
log([A-]/[HA]) = 3.07 - pKa
To find [A-]/[HA], we need to take the antilogarithm (10 raised to the power) of both sides:
[A-]/[HA] = 10^(3.07 - pKa)
Now, we need to determine the concentration of HC2H3O2 (assuming it's the same as the initial concentration) as well as the concentration of C2H3O2- needed to achieve the desired ratio. Once we have those concentrations, we can calculate the number of moles of NaOH needed.
(c) pH = 5.15 mol
Similarly to case (b), we need to use the Henderson-Hasselbalch equation and follow the same steps to calculate the number of moles of NaOH required.
The overall process involves solving the Henderson-Hasselbalch equation to determine the ratio of the concentrations of the conjugate base and weak acid, and then using that ratio to find the number of moles of NaOH needed to achieve the desired pH.