Calculating Buffer Solution Volumes for pH 4.6 using Titration Virtual Lab

[westdavi]

I really need help. I am a teacher and can't seem to figure out this problem, although I know I did it once before. I have used a virtual lab and know that you need 71 ml of acetic acid and 29 ml of NaOH, but don't know how to calculate it. Can someone tell me? I know the concentration of H in the solution from the pH and I know the percent ionisation using the K=1.85 X 10^-5. I am pretty sure that you use the ratio of CH3COO- concentration,which is related to the OH- concentration,and CH3COOH concentration, but can't seem to figure it out. Anyway, I hope someone can help me
You have two bottles, one filled with 1M HAc (HAc = acetic acid) and one filled with 1M NaOH. You want to make 100ml of a buffer with pH=4.6 by mixing together appropriate amounts of these solutions. How much of each solution do you use?

 

[siddharth]

You can use Henderson's equation to find the amount of each solution.

$$pH = pK_a + \log\frac{[Salt]}{[Acid]}$$

Let the two unknowns (amount of each solution added) be x,y.
One equation is the Henderson's equation and the other is the total volume of the solution is 100ml.

In a bit more detail,
Because you are preparing an acid buffer, you need an excess of the acid.

Now 1ml of Acetic acid reacts with 1ml of NaOH. So If $x$ml of acetic acid and $y$ml of NaOH were added to prepare the buffer, what will be the final concentration of the acid present?It will be the total amount of acid initially minus the amount of acid which reacts with NaOH to form the salt. From this you can find the final concentrations of the acid and the salt after the reaction.Plug those into the equation above. Also, since the total volume of the buffer is 100ml, you have $x + y = 100$. Solve for x and y to get your required answer

 

[Moonbear]

westdavi, please only start one thread on a topic.

 

[GCT]

adding to what siddharth said, you can determine the ratio of the concentrations (and assuming that the pKa of acetic acid is not too far from the desired pH) by solving for the ratio of concentrations in the H-H equation.

This will be the respective concentrations of acid and its conjugate salt required, that is it defines a quantitative relationship between them.

$$C[HA]=[A-]$$, where C is a constant

Its good that you have equimolar solutions of the weak acid and the strong base.

Next you can use employ the Ka equation, intially, the acid will be in equilibrium, that is it'll have an initial pH

$$Ka= \frac{[H30+][A-]}{[HA]}~=~ \frac{x^2 }{[HA]-x}$$

From this you can find the intial acid concentration at equilibrium, the 1M is the formal concentration, not the equilibrium concentration.

$$C {(V_{acid}[HA_{initial}]-V_{base}1M)}=V_{base}$$

now you have a ratio of the volume to be employed, if "R" is the ratio Vbase/Vacid, then Vacid + R/Vacid = .1L. Solve for Vacid, then subtract this quantity from .1L to find the volume of the base needed...mix the two volumes and you'll have your buffer.