Strong base is dissolved in 535 mL of 0.200 M weak acid (Ka = 3.16 × 10-5) to make a buffer with a pH of 4.04. Assume that the volume remains constant when the base is added.
HA (aq)+ OH^-(aq) -> H2O(l) + A^-(aq)
Calculate the pKa value of the acid and determine the number of moles of acid initially present.
When the reaction is complete, what is the concentration ratio of conjugate base to acid?
How many moles of strong base were initially added?
For the first question, I got:
pKa: 4.44
mol HA: 0.107
Which the system says is ok, but for the second and third question I got:
[A^-]/[HA]= 0.3981
mol OH^-: 0.03046
I don't know what is wrong, I am doing this:
pH = pKa + log ([A^-]/[HA])
4.04 = 4.44 + log ([A^-]/[HA])
-0.4 = log ([A^-]/[HA])
inv log (-.4) = ([A^-]/[HA])
0.39810 = ([A^-]/[HA])
And then
0.39810 = ([A^-]/[HA])
x / (0.107 - x) = 0.39810
x= 0.0304
First, you transposed 3.16E-5 to 3.61E-5 to come up with pKa = 4.44. It won't change that much but pKa is 4.5 using 3.16E-5 for Ka.
Then working with millimoles, x/(107-x) = 0.347 and x = about 27.5 millimols. That isn't that far from you 30.4 but probably far enough that the key counted it wrong. I think all you need to do is to adjust the pKa value.
Many thanks for showing your work. It makes it easy to catch mistakes like this.
Thanks you!!
To determine the pKa value of the acid, you correctly used the Henderson-Hasselbalch equation:
pH = pKa + log ([A^-]/[HA])
To solve for pKa, rearrange the equation:
pKa = pH - log ([A^-]/[HA])
Plugging in the given values:
pKa = 4.04 - log ([A^-]/[HA])
To calculate the number of moles of acid initially present, you can use the formula for concentration:
Molarity = moles/volume
0.200 M = moles/(535 mL)
Moles of acid = 0.200 M x 535 mL = 0.107 mol
For the concentration ratio of the conjugate base to acid, you properly used the equation [A^-]/[HA] = 0.3981.
However, to calculate the number of moles of strong base initially added, you need to use the fact that the strong base OH^- reacts stoichiometrically with the weak acid HA in a 1:1 ratio.
The number of moles of strong base added is equal to the number of moles of weak acid that reacted:
moles of strong base = moles of weak acid
Therefore, you can use the moles of acid initially present (0.107 mol) as the answer for the moles of strong base initially added.
Overall, your calculation for the pKa value and moles of acid initially present is correct. The issue seems to be with the calculation for the number of moles of strong base initially added.