A reference calls for the use of "one litre of 0.1 molar acetate buffer pH 5.2” Calculate the amounts of sodium acetate and acetic acid required to make up this buffer, given that for acetic acid Ka = 1.8 x 10-5
To calculate the amounts of sodium acetate and acetic acid required to make up the buffer, we can use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
Where:
- pH is the desired pH of the buffer (pH 5.2 in this case)
- pKa is the dissociation constant of the acid (given as Ka = 1.8 x 10^-5)
- [A-] is the concentration of the conjugate base (sodium acetate)
- [HA] is the concentration of the acid (acetic acid)
Step 1: Calculate the ratio of the conjugate base to acid
Since the pH is 5.2 and pKa is -log(Ka) = -log(1.8 x 10^-5), we can substitute the values and solve for the ratio:
5.2 = -log(1.8 x 10^-5) + log([A-]/[HA])
5.2 + log([HA]/[A-]) = -log(1.8 x 10^-5)
log([HA]/[A-]) = -log(1.8 x 10^-5) - 5.2
Now, let's calculate the concentration ratio using the antilog function:
([HA]/[A-]) = antilog[ -log(1.8 x 10^-5) - 5.2 ]
Step 2: Calculate the individual concentrations of sodium acetate and acetic acid
Let's assume x represents the concentration of sodium acetate ([A-]) and 0.1 - x represents the concentration of acetic acid ([HA]). The total volume is given as 1 liter.
Using the ratio calculated in step 1, we have:
([HA]/[A-]) = (0.1 - x) / x
Since we know ([HA]/[A-]) = antilog[ -log(1.8 x 10^-5) - 5.2 ], we can substitute this in the above equation and solve for x:
antilog[ -log(1.8 x 10^-5) - 5.2 ] = (0.1 - x) / x
Solve for x:
x = (0.1) / (1 + antilog[ -log(1.8 x 10^-5) - 5.2 ])
The concentration of sodium acetate ([A-]) is x, while the concentration of acetic acid ([HA]) is 0.1 - x.
Using the calculated value of x, you can find the amounts of sodium acetate and acetic acid required by multiplying the concentration by the total volume (1 liter).
To calculate the amounts of sodium acetate and acetic acid required to make up the 0.1 Molar acetate buffer at pH 5.2, we need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is as follows:
pH = pKa + log([A-]/[HA])
Where:
pH = desired pH of the buffer (5.2 in this case)
pKa = -log(Ka)
[A-] = concentration of the conjugate base (sodium acetate in this case)
[HA] = concentration of the weak acid (acetic acid in this case)
First, we need to find the pKa value from the given Ka value:
Ka = [A-][H+]/[HA]
1.8 x 10^(-5) = ([A-][H+])/[HA]
Since we are dealing with acetic acid, [HA] is the initial concentration of acetic acid, which is equal to the concentration of sodium acetate, since they are in a 1:1 ratio.
Now, let's solve for pKa:
pKa = -log(1.8 x 10^(-5))
Next, substitute the pKa and pH values into the Henderson-Hasselbalch equation:
5.2 = pKa + log([A-]/[HA])
Solving for log([A-]/[HA]):
log([A-]/[HA]) = 5.2 - pKa
Now, calculate the concentration ratio [A-]/[HA]:
[A-]/[HA] = 10^(5.2 - pKa)
Since the acetic acid and sodium acetate are in a 1:1 ratio, the concentration of sodium acetate and acetic acid will be the same.
Finally, calculate the amount of substance needed by multiplying the concentration ratio by the final volume of the buffer:
Amount of sodium acetate = 0.1 M × [A-] × volume of the buffer (in liters)
Amount of acetic acid = 0.1 M × [HA] × volume of the buffer (in liters)
By following these calculations, you can determine the amounts of sodium acetate and acetic acid required to create the 0.1 Molar acetate buffer at pH 5.2.