What molar ratio of acetic acid to sodium acetate is required to create a buffer solution at a pH of 4.89 at 25 degree C? Ka for acetic acid is

1.8 X 10-5

A. 2.9
B.0.56
C.1.4
D.0.72
E.0.2 ( I chose this and got is wrong)

I'm lost on how to do these problems, but I started out...

4.89=4.74 + log

got lost after that...

pH = pKa + log (base)/(acid)

4.89 = 4.74 + log(b)/(a)
Solve for base/acid ratio. That's the ratio they want.

To determine the molar ratio of acetic acid to sodium acetate required to create a buffer solution at a given pH, you need to use the Henderson-Hasselbalch equation. The equation is as follows:

pH = pKa + log ([A-]/[HA])

Where:
- pH is the desired pH of the buffer solution.
- pKa is the negative logarithm of the acid dissociation constant (Ka) for acetic acid.
- [A-] is the concentration of the conjugate base (in this case, sodium acetate).
- [HA] is the concentration of the weak acid (in this case, acetic acid).

Given:
- pH = 4.89
- pKa = -log(Ka) = -log(1.8 X 10^-5)

To find the molar ratio, we need to express [A-]/[HA] in terms of the ratio of moles of sodium acetate to moles of acetic acid. Let's set [A-]/[HA] equal to x.

x = [A-]/[HA]

Next, let's express [A-] and [HA] in terms of their respective concentrations and volumes:

[A-] = (moles of sodium acetate) / (total volume of buffer solution)
[HA] = (moles of acetic acid) / (total volume of buffer solution)

Since the molar concentration is given in terms of moles per liter (M), we can rewrite the concentrations:

[A-] = (moles of sodium acetate) / (total volume of buffer solution) = (CNaA) / V
[HA] = (moles of acetic acid) / (total volume of buffer solution) = (CHA) / V

Where:
- CNaA is the concentration of sodium acetate (in M).
- CHA is the concentration of acetic acid (in M).
- V is the total volume of the buffer solution (in liters).

By substituting these expressions into the Henderson-Hasselbalch equation, we get:

pH = pKa + log (x)

Rearranging the equation, we find:

log (x) = pH - pKa

Now, let's substitute the given values:

log (x) = 4.89 - (-log(1.8 X 10^-5))

Simplifying:

log (x) = 4.89 + 5 - log(1.8)

To solve for x, we need to get rid of the logarithm. We can do this by taking the antilog (inverse logarithm) of both sides:

x = antilog(4.89 + 5 - log(1.8))

Using a scientific calculator, evaluate the expression inside the antilog:

x ≈ 68.47

Therefore, the molar ratio of acetic acid to sodium acetate required to create the buffer solution is approximately 1:68.47.

Since none of the options provided exactly match this ratio, it's likely there was an error in the calculations.