Moles of a conjugate base in a buffer solution

[alr1014]

Homework Statement

You need to produce a buffer solution that has a pH of 5.70. You already have a solution that contains 0.0200 moles of acetic acid. Using the Henderson-Hasselbalch equation calculate the moles of sodium acetate needed to create a buffer with the desired pH? The Ka of acetic acid is 1.8 × 10^-5.

Homework Equations

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

The Attempt at a Solution

pKa= -log (1.8 × 10^-5) = 4.74
5.70 = 4.74 + log (base/acid)
Unfortunately, I have been staring at this problem for about an hour and am unsure how to find the concentration of the acid to discover the consent ration of the base. I am not sure how to proceed since the problem does not give a volume to find the molarity.
Any help with this would be greatly appreciated!

 

[Borek]

Hint: you don't need the acid concentration.

$$C_A = \frac {n_A} {V}$$
$$C_B = \frac {n_B} {V}$$

$$\frac {C_A}{C_B} = ...$$

 

[alr1014]

I appreciate your responce, any responce really. Although, your equation set seems to need a volume as well, and the problem I am to work out does not include one. That is a big area I am being messed up. As well as the problem states to use that particular equation to find the moles of base needed.

 

[Borek]

Although, your equation set seems to need a volume as well

Plug concentrations into ratio and see what happens. V/V = ?

 

[alr1014]

Hint: you don't need the acid concentration.

$$C_A = \frac {n_A} {V}$$
$$C_B = \frac {n_B} {V}$$

$$\frac {C_A}{C_B} = ...$$

Since the problem called for using the henderson-hasselbalch equation, and that entails using the concentration of the acid, I used the volume used in the lab for the titration (25 mL). Not sure if that is right... but I got an answer. I will check with a few of my class mates before lab in the morning. Thank you for your help.

 

[Borek]

You don't need any specific volume.

V/V = 1 - volume cancels out. Ratio of concentrations (if these are concentrations in the same solution) is identical to the ratio of numbers of moles.

 

[alr1014]

You don't any specific volume.

V/V = 1 - volume cancels out. Ratio of concentrations (if these are concentrations in the same solution) is identical to the ratio of numbers of moles.

That very simple answer was probably the best answer you could have given me! Tha k you so very much for having the patience for dealing with slightly dense people like me!

 

[Borek]

That very simple answer was probably the best answer you could have given me!

I hoped you will see it by yourself. You will learn much more when you put an effort and find such things by yourself, than when they are presented on a silver plate.