Buffer capacity is a measure of a buffer solution\'s resistance to changes in pH as strong acid or base is added. Suppose that you have 165 mL of a buffer that is 0.360 M in both benzoic acid (C6H5COOH) and its conjugate base (C6H5COO–). Calculate the maximum volume of 0.250 M HCl that can be added to the buffer before its buffering capacity is lost.
165 mL x 0.360M = about 59.4 millimols base and 59.4 mmols acid.
..........base + HCl ==> acid
I........59.4.....0......59.4
add...............x...............
C........-x.....-x........+x
E.......59.4-x....0......59.4+x
pH = pKa + log (base)/(acid)
Look up the pKa for benzoic acid.
Subtract 1.0 from that (remember buffer capacity is acid/base that can be added and not make more than +/- 1 for change of pH) and substitute that for pH. Substitute 59.4-x and 59.4+x for base and acid and solve for x = millimols HCl that can be added to make that difference of pH = 1.
Then M = mmols/mL.
You know M HCl, mmols HCl, solve for mL HCl.
How do you solve for x? I keep getting a negative answer and I'm not sure that's right...
hmm i think you just did something wrong kpedenko ?
hmm I think you are something wrong
kpedenko, recall that it is an acid being added to a base therefore your ph/pka difference should be .1
To calculate the maximum volume of 0.250 M HCl that can be added to the buffer before its buffering capacity is lost, we need to use the Henderson-Hasselbalch equation and the concept of buffer capacity.
The Henderson-Hasselbalch equation is:
pH = pKa + log([A-]/[HA])
Where pH is the desired pH of the buffer, pKa is the dissociation constant of the acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
In this case, we have a buffer that is 0.360 M in both benzoic acid (C6H5COOH) and its conjugate base (C6H5COO–). The pKa of benzoic acid is 4.20.
To find the buffer capacity, we need to calculate the moles of the buffering species (benzoic acid and its conjugate base) and determine which one will be completely consumed first when adding HCl.
1. Calculate the moles of benzoic acid and its conjugate base:
Moles of benzoic acid = (0.360 M) * (0.165 L) = 0.0594 mol
Moles of conjugate base = (0.360 M) * (0.165 L) = 0.0594 mol
2. To determine which component will be consumed first, we compare the moles to the stoichiometry of the reaction between benzoic acid and HCl:
C6H5COOH + HCl → C6H5COOH2+ + Cl-
From the balanced equation, we can see that 1 mole of benzoic acid reacts with 1 mole of HCl.
3. Calculate the number of moles of HCl that can react with benzoic acid:
Moles of HCl = (0.250 M) * (V L)
4. Now we need to compare the moles of benzoic acid and HCl to determine which will be consumed first:
Benzoic acid: HCl = 0.0594 mol : Moles of HCl
The buffer capacity is determined by the limiting component of the reaction. In this case, we want to find the maximum volume of HCl that can be added, so we take the moles of benzoic acid as the limiting factor.
5. Set up an equation based on the ratio of moles:
0.0594 mol = (0.250 M) * (V L)
V = 0.0594 mol / (0.250 M)
V = 0.2376 L = 237.6 mL
So, the maximum volume of 0.250 M HCl that can be added to the buffer before its buffering capacity is lost is 237.6 mL.