[zach81210]

Hi all,

I'm really confused on this buffer problem that I've been trying to solve. I used to solving for pH, but using the Henderson-Hasselbach formula to solve for volume has got me all sorts of confused.

Here is the example problem they provided in order to solve problems of this format:

How would you make 100mL of 0.1M acetate buffer, pH 4.0 from 0.1M sodium acetate and 0.1M acetic acid? The pKa of acetic acid is 4.76.

Step 1: Determine the ratio of A- to HA using the Henderson-Hasselbalch equation

pH= pKa + log A-/HA

4.0= 4.76 + log A-/HA

0.174= A-/HA

Step 2: Write an equation representing the final concentration of the buffer

Final concentration of buffer= HA- A-
0.1M=HA+A-

Step 3: Represent the concentration of A- in terms of HA and substitute into Equation 1 and solve for HA

0.174=A-/HA
A-=0.174[HA]
Thus, 0.1M=HA + A-
0.1M= HA +0.174[HA]

Now here is where I get very confused, as the next parts of this step are:
0.1M= 1.174[HA]

[HA]=0.085M, final concentration of acetic acid in buffer

I'm really confused as to how they get the last two figures provided (1.174[HA] and 0.085M respectively). Could you guys please help me out here? I would greatly appreciate it.

[AWK]

In my opinion, the problem is ambiguous, and the calculations are also unfinished. You should calculate solution volumes, not concentrations. It is recommended that the results should be rounded off at the last stage of the calculation. If you round the intermediate results, it should be done fairly safely for calculations: in intermediate results, I would advise leaving at least two significant numbers more.
If we assume that the input data are inaccurate, then we have one significant digit in concentration and in input pH 4.0, pKa is certainly the experimental data and has two significant digits (why?), and the volume of the solution has 3 significant digits if we write it as 100. . The accuracy of calculations with one significant digit does not make sense, so we assume that all input data except pKa are accurate. The calculated volumes, in our case, will have two significant digits (after the final rounding).

[Borek]

0.1M= HA +0.174[HA]

Now here is where I get very confused, as the next parts of this step are:
0.1M= 1.174[HA]

This is trivial algebra. x+2x=3x, doesn't it?

[HA]=0.085M, final concentration of acetic acid in buffer

I'm really confused as to how they get the last two figures provided (1.174[HA] and 0.085M respectively). Could you guys please help me out here? I would greatly appreciate it.

Again trivial algebra, just solve 0.1M= 1.174[HA] for [HA].

As AWK suggested, you don't need to go the concentration route, you are mixing two 0.1M solutions so the final buffer solution will be 0.1M no matter what. You can deal directly with the volumes. Doesn't mean going through concentrations is wrong, just takes longer.

[Babcock_Hall]

@OP, In general I suggest checking your answer for reasonableness.  When pH < pK_a, [HA] > [A^-].  Do your two concentrations fulfill this expectation?  Do they sum to 0.100 M?  Students often generate unreasonable answers without realizing it.