Calculate the volume of 1.00 M acetic acid solution and mass of sodium acetate needed to make 250 mL of a 0.450 M acetic acid/acetate buffer solution with a pH of 4.00. (The pKa is 4.74 for acetic acid)
*Please explain it in detail, don't leave a step out! Thank You!
I worked this below. I'll try to find it and give you a link.
I worked this below. I'll try to find it and give you a link.
http://www.jiskha.com/display.cgi?id=1415056292
Any questions?
To calculate the volume of the 1.00 M acetic acid solution needed, we can use the formula:
C₁V₁ = C₂V₂
Where:
C₁ = initial concentration of the acetic acid solution
V₁ = initial volume of the acetic acid solution
C₂ = final concentration of the acetic acid/acetate buffer solution
V₂ = final volume of the acetic acid/acetate buffer solution (given as 250 mL)
Let's plug in the values we know:
C₁ = 1.00 M
V₁ = ? (unknown)
C₂ = 0.450 M
V₂ = 250 mL
We can rearrange the formula to solve for V₁:
V₁ = (C₂V₂) / C₁
V₁ = (0.450 M * 250 mL) / 1.00 M = 112.5 mL
So, to make 250 mL of the 0.450 M acetic acid/acetate buffer solution, you will need 112.5 mL of the 1.00 M acetic acid solution.
Now, let's move on to calculating the mass of sodium acetate needed to make the buffer solution.
The Henderson-Hasselbalch equation can be used to relate the pH, pKa, and the ratio of the concentrations of the acid (acetic acid) and its conjugate base (acetate):
pH = pKa + log([acetate] / [acetic acid])
Given:
pH = 4.00
pKa = 4.74
Rearranging the formula, we get:
[acetate] / [acetic acid] = 10^(pH - pKa)
[acetate] / [acetic acid] = 10^(4.00 - 4.74) = 10^(-0.74) = 0.186
This ratio shows that for every 1 unit of acetic acid, we need 0.186 units of acetate.
Since we have 112.5 mL (or 0.1125 L) of the 1.00 M acetic acid solution, we can calculate the amount of acetic acid in moles:
moles of acetic acid = concentration * volume
moles of acetic acid = 1.00 M * 0.1125 L = 0.1125 mol
Using the ratio, we can calculate the moles of acetate needed:
moles of acetate = 0.186 * 0.1125 mol = 0.0209775 mol
The molar mass of sodium acetate is 82.03 g/mol. Therefore, the mass of sodium acetate needed can be calculated as:
mass = moles of acetate * molar mass
mass = 0.0209775 mol * 82.03 g/mol ≈ 1.72 g
Therefore, you would need approximately 1.72 grams of sodium acetate to make 250 mL of the 0.450 M acetic acid/acetate buffer solution with a pH of 4.00.