You wish to prepare a pH 4.76 acetic acid sodium acetate buffer with a buffer intensity of 1 M per pH. What concentrations of acetic acid and sodium acetate are needed?
I assume 1 M/pH means 1 mol in a liter for a pH of 1.0
First, determine the ratio of base(b) to acid(a).
4.76 = 4.76 + log (b/a)
b/a = 1 or b=a initially. You should confirm that.
Than make an ICE table. We will work this backwards since we want to know how much to start with. We will call the amount we start with x. Since b = a then both will be x
....HAc + OH^- ==> Ac^- + H2O
I....x....0........x......
add.......1................
C...-1...-1........+1
E...x-1...0.......x+1
Now plug the E line into the HH equation and solve for x. The pH will be 5.76 (for the pH change of 1)
5.76 = 4.76 + log[(x+1)/(x-1)]
x = ? I calculated 1.22 mols/L but you should confirm that AND you should make an ICE table starting with 1.22 M with HAc and Ac^- and see if that gives you a 5.76. If it does that means that amount of HAc and Ac^- will provide enough material to allow 1 mol/L NaOH to be added and the pH will not rise above 5.76.
To prepare a pH 4.76 acetic acid sodium acetate buffer, we need to calculate the concentrations of acetic acid and sodium acetate needed.
First, let's understand the role of acetic acid and sodium acetate in a buffer system. Acetic acid (CH3COOH) acts as a weak acid, and its conjugate base, acetate (CH3COO-), which is obtained from sodium acetate (CH3COONa), acts as a weak base. Together, they form a buffer system.
The Henderson-Hasselbalch equation is commonly used to calculate the pH and composition of a buffer solution:
pH = pKa + log ([A-]/[HA])
In this case, acetic acid (HA) is the weak acid, and acetate (A-) is the conjugate base. The pKa is the logarithmic measure of the acid dissociation constant, which represents the strength of an acid. For acetic acid, its pKa is 4.76.
The buffer intensity is defined as the change in the concentration of the acid or base per unit change in pH. In this case, the buffer intensity is 1 M per pH.
Let's calculate the concentrations of acetic acid and sodium acetate:
1. Determine the concentration of the weak acid (acetic acid):
We know that [A-]/[HA] = 1, as the buffer intensity is 1 M per pH.
Since [A-]/[HA] = 1, [A-] = [HA]
Let x be the concentration of acetic acid.
Therefore, x = [A-] = [HA].
2. Use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
4.76 = 4.76 + log(x/x)
0 = log(1)
The logarithm of 1 is 0, so the equation simplifies to:
0 = 0
This equation is true for any value of x.
Therefore, the concentrations of acetic acid and sodium acetate can be any equal concentration, as long as the total concentration is 1 M. For example, you can choose a 0.5 M concentration each for acetic acid and sodium acetate.
In summary, to prepare a pH 4.76 acetic acid sodium acetate buffer with a buffer intensity of 1 M per pH, you can use equal concentrations of acetic acid and sodium acetate, such as 0.5 M each.