a. According to the Henderson-Hasselbalch equation, how many grams of sodium acetate will you need to add to 125 mL of 0.100 M acetic acid to make a pH=4.74 buffer? (I found this to be 1.025g) I need help with the rest
b. What is the actual pH of the resulting buffer when you add that many grams of sodium acetate to 125 mL of 0.100 M acetic acid?
c. If I want to make the buffer by adding 0.100 M NaOH instead of sodium acetate, how many milliliters of NaOH are needed to reach pH=4.74?
d. If I add enough water to the above buffer to make the total volume 1.00 L, what's the new pH?
e. How many milliliters of 0.25 M HCl will be needed to change the pH of the dilute buffer by 1 pH unit?
a. You already found that 1.025g of sodium acetate is needed.
b. To find the actual pH of the resulting buffer, we can use the Henderson-Hasselbalch equation since it is a buffer solution:
pH = pKa + log ([A-] / [HA])
Here, pKa of acetic acid is 4.74, and we need to find the concentrations of acetate ion (A-) and acetic acid (HA).
First, calculate the moles of acetic acid:
Moles of acetic acid = 0.100 mol/L * 0.125 L = 0.0125 mol
Next, calculate the moles of sodium acetate:
Moles of sodium acetate = 1.025g / (82.03 g/mol) = 0.0125 mol
Now, calculate the concentrations of acetate ion and acetic acid:
[A-] = moles of sodium acetate / (0.125 L) = 0.0125 mol / 0.125 L = 0.1 M
[HA] = moles of acetic acid / (0.125 L) = 0.0125 mol / 0.125 L = 0.1 M
Substitute the values into the Henderson-Hasselbalch equation:
pH = 4.74 + log (0.1 / 0.1) = 4.74 + log (1) = 4.74
So, the actual pH is 4.74.
c. To find the volume of 0.100 M NaOH needed to reach pH = 4.74, we can set up an equation for the moles of NaOH added:
Moles of NaOH = moles of sodium acetate
Since we already calculated that 0.0125 moles of sodium acetate is needed:
0.0125 mol = (0.100 mol/L) * volume in L
Volume in L = 0.0125 mol / 0.100 mol/L = 0.125 L
Therefore, 125 mL of 0.100 M NaOH is needed.
d. When the buffer solution is diluted to 1.00 L, the ratio of acetate ion to acetic acid remains constant, as both concentrations will be diluted by the same factor. Therefore, the pH of the diluted buffer will still be 4.74, according to the Henderson-Hasselbalch equation.
e. To change the pH of the buffer by 1 pH unit, we use the buffer capacity formula:
Buffer capacity = (Δ moles of H+ or OH-) / (ΔpH * volume)
In this case, we want to find the amount of 0.25 M HCl needed to change the pH by 1 unit. First, convert the buffer capacity formula to moles of added HCl:
Δ moles of H+ = ΔpH * volume * buffer capacity
We assume that the buffer capacity remains approximately constant upon dilution. For an acetate buffer system (acetic acid and sodium acetate), the approximate buffer capacity is 0.058.
Now, we can calculate the moles of HCl needed:
Δ moles of H+ = 1 * 1 * 0.058 = 0.058 mol
To find the volume of 0.25 M HCl, use the definition of molarity:
0.058 mol = (0.25 mol/L) * volume in L
Volume in L = 0.058 mol / 0.25 mol/L = 0.232 L
Therefore, 232 mL of 0.25 M HCl is needed to change the pH of the dilute buffer by 1 pH unit.