A student needs 1.0L of buffer solution with a PH =10.0 .She selects the HCO3^-
>CO3^2- buffer system. The K(HCO3^-) =5.6x10^-11 .
what is the [HCO3^-]/[CO3^2-]ratio for the buffer?
pH = pKa + log[(CO3^-2)/(HCO3^-)]
I would solve for base/acid, then take the reciprocal.
To find the [HCO3^-]/[CO3^2-] ratio for the buffer, we need to determine the ratio of the concentrations of these ions in the solution. The pH value of the buffer will guide us in calculating this ratio.
First, we need to understand that the HCO3^-/CO3^2- buffer system acts as an acid-base pair, where HCO3^- acts as a weak acid and CO3^2- acts as its conjugate base.
In a buffer solution, the pH is determined by the ratio of the concentrations of the weak acid and its conjugate base, as well as their acid dissociation constants (pKa). The Henderson-Hasselbalch equation can be used to calculate the pH of a buffer solution:
pH = pKa + log([A-]/[HA])
Where:
pH = the desired pH (in this case, pH = 10.0)
pKa = the negative logarithm of the acid dissociation constant (pKa = -log(Ka))
In this case, we have the K(HCO3^-) = 5.6 x 10^-11, which is the Ka of HCO3^-. To find the pKa, we need to take the negative logarithm of the Ka:
pKa = -log(K(HCO3^-))
Now, we can plug in the values into the Henderson-Hasselbalch equation:
10.0 = pKa + log([CO3^2-]/[HCO3^-])
Since we want to find the [HCO3^-]/[CO3^2-] ratio, we can rearrange the equation:
log([CO3^2-]/[HCO3^-]) = 10.0 - pKa
To find the ratio, we can use the antilog function:
[CO3^2-]/[HCO3^-] = antilog(10.0 - pKa)
Using the given pKa value, we can calculate the ratio:
pKa = -log(5.6 x 10^-11)
= 10.25
[CO3^2-]/[HCO3^-] = antilog(10.0 - 10.25)
Now, using the antilog function, we can determine the ratio:
[CO3^2-]/[HCO3^-] = antilog(-0.25)
To find the antilog of -0.25, we need to raise 10 to the power of -0.25:
[CO3^2-]/[HCO3^-] = 10^(-0.25)
Using a calculator, we can find that 10^(-0.25) is approximately 0.5623.
Therefore, the [HCO3^-]/[CO3^2-] ratio for the buffer is approximately 0.5623.