Calculate the ratio of conjugate base to acid at a pH of 8.36.
Recall the fundamental properties of the logarithm
+log(ab)
is the same as
−log(ba)
so Henderson Hasselbach can have plus or minus signs. The correct equation is
pH=pKa+log(conjugate baseacid)
or
pH=pKa−log(acidconjugate base)
Now sort out whether the textbook solution is right or not.
Also;
Important is the knowledge how Ka is defined:
Ka=[H+][A−][HA]
If we perform logarithmization, we get:
logKa=log[H+]+log[A−][HA]
If we apply the operator pX=−logX:
pKa=pH−log[A−][HA]
respectively
pH=pKa+log[A−][HA]
In our case, HA=H2CO3 and A−=HCO3−.
This problem can't be solved until you know the pKa. When you do then
pH = pKa + log [(base)/(acid)] and then you solve for (base)/(acid) to give you the ratio.
@ Helper. I'm confused about what you have written for two reasons.
1. You talk about H2CO3 and HCO3^- but I don't see these compounds/ions anywhere in the problem. Perhaps this is a carry over from a previous problem posted by Steve; however, I looked for that and couldn't find it.
2. The second reason, and perhaps more importantly, is that the division sign (/) has been omitted from each of the equations. They would be correct if the / sign had been included. Technically, they are wrong without the / sign. This is not a big deal since this answer doesn't answer the question but I'm just pointing it out for your information. You may not be aware that the / sign is missing. Have I missed something something?
To calculate the ratio of the conjugate base to acid at a specific pH, you need to know the pKa (acid dissociation constant) value of the acid in question.
The pKa is a measure of the strength of an acid. For a weak acid, pKa values are usually provided in chemistry references or textbooks. Once you have the pKa, you can use it to calculate the ratio of conjugate base to acid using the Henderson-Hasselbalch equation:
pH = pKa + log([conjugate base]/[acid])
In this case, the pH is given as 8.36. To find the ratio, we first need to determine the pKa value for the acid in question.
Assuming you have the pKa value, let's say it is 4.75. Now we can substitute the values into the Henderson-Hasselbalch equation:
8.36 = 4.75 + log([conjugate base]/[acid])
Rearranging the equation, we get:
log([conjugate base]/[acid]) = 8.36 - 4.75
log([conjugate base]/[acid]) = 3.61
Now, to find the actual ratio, we need to eliminate the logarithm by taking the antilog of both sides:
10^(log([conjugate base]/[acid])) = 10^3.61
[conjugate base]/[acid] = 10^3.61
Using a calculator, we find:
[conjugate base]/[acid] ≈ 4159.74
So, at a pH of 8.36, the ratio of the conjugate base to acid is approximately 4159.74:1.