Calculate the ratio of the concentration of CO3-2 & HCO3- ions needed to achieve buffering at pH= 9.50. The PkA2 of H2CO3 is 10.25.
To calculate the ratio of the concentration of CO3-2 and HCO3- ions needed to achieve buffering at pH 9.50, we will need to use the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-]/[HA])
Where:
pH is the given pH (9.50 in this case)
pKa is the acid dissociation constant (pKa2 of H2CO3 is 10.25)
[A-] is the concentration of the conjugate base (CO3-2)
[HA] is the concentration of the acid (HCO3-)
First, let's rearrange the equation:
pH - pKa = log([A-]/[HA])
Now, substitute the given values and solve for the ratio:
9.50 - 10.25 = log([CO3-2]/[HCO3-])
-0.75 = log([CO3-2]/[HCO3-])
To remove the logarithm, we need to convert from log scale to exponential form:
10^(-0.75) = [CO3-2]/[HCO3-]
Solving the exponential:
0.1778 = [CO3-2]/[HCO3-]
Therefore, the ratio of the concentration of CO3-2 to HCO3- ions needed to achieve buffering at pH 9.50 is approximately 0.1778:1.
To calculate the ratio of the concentration of CO3^2- and HCO3^- ions needed to achieve buffering at pH= 9.50, we need to use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa of the weak acid and the ratio of its conjugate acid and base. The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-]/[HA])
In this case, CO3^2- is the conjugate base (A^-) and HCO3^- is the weak acid (HA). We are given the pKa2 of H2CO3, which is the diprotic acid that dissociates into HCO3^- and CO3^2-.
Let's first calculate the value of [A-]/[HA] using the Henderson-Hasselbalch equation:
9.50 = 10.25 + log([CO3^2-]/[HCO3^-])
Rearranging the equation, we have:
log([CO3^2-]/[HCO3^-]) = 9.50 - 10.25
log([CO3^2-]/[HCO3^-]) = -0.75
To simplify the calculation, we can convert the log expression into an exponential form:
[CO3^2-]/[HCO3^-] = 10^(-0.75)
[CO3^2-]/[HCO3^-] = 0.1778
Therefore, the ratio of the concentration of CO3^2- to HCO3^- ions needed to achieve buffering at pH = 9.50 is approximately 0.1778.
Plug into the Henderson-Hasselbalch equation and solve for the ratio you want.
Post your work if you get stuck.