Here is the hint I received on how to solve those tough pH problems I posted earlier:
Both of these can be solved using the H-H and doing the algebra. The math
itself is hard to type out, but in Q1 the values of [NaA] and [HA] are
0.04805 and 0.15195.
In Q2 you will have to set up two eqn's and 2 unknowns. For eqn 1 set up the
H-H for a pH of 7.45, and for eqn 2 set up the H-H for 7.35 with moles base
= initial moles base - 0.005 and moles acid = initial moles acid + 0.005.
You will then sub your eqn 1 value for one of the unknowns into your second
expression.
I have tried to solve the question using this formula but it is clear that I have not gotten far enough. Could anyone out there please try solving this for me?
(1) You wish to make a 0.200 mol/L PIPES buffer (PIPES:
1,4-Piperazine-N,N'-bis(2-ethane-sulfonic acid), C8H18N2O6S2, pKa = 6.80) at
a
pH of 6.300. Available to you is the disodium salt of PIPES
(Na2C8H16N2O6S2),
and a 2.00 F solution of HCl. Calculate
i)the mass of the disodium salt of PIPES,
ii) the volume of HCl,
that must be added to make 500.0 mL of this buffer.
I tried to initally use the Henderson Hasselbach equation to solve for the
ratio of weak base and its conjuate acid that would be needed to make the
buffer with the desired pH but this only gets me so far. I also set up a
second equation [A-] + [HA] = .200. I have then tried to set up a balanced
equation HA + H20 in equilibrium with A- + H3O+. However, I am stuck from
there and cannot seem to figure out the changes in moles.
2.
A chemist is following a hydrolysis reaction with an enzyme. The enzyme has
an
optimal working pH range of 7.40±0.05. It is known that H+ is evolved during
the hydrolysis reaction. The chemist does a quick calculation and determines
that the reaction she is following could generate up to 0.001 moles of H+
per
100.0 mL of solution. Describe how to make up 500.0 mL of the HEPES buffer
(HEPES: 4-(2-Hydroxyethyl)piperazine-1-ethanesulfonic acid, C8H18N2O4S, pKa
=
7.55) such that the reaction mixture will maintain a pH that is within the
optimal working range of the enzyme. Among the reagents in the lab are HEPES
as
the free acid form, and a 5.695 F solution of NaOH. What mass of HEPES and
what volume of NaOH should you use?
Note: while several solutions are possible, here you are asked to calculate
the
minimum amount of HEPES that could still maintain the pH within the desired
limits.
To solve the first problem, you can use the Henderson-Hasselbalch equation in combination with algebraic calculations. Let's break down the steps:
(1) i) Finding the mass of the disodium salt of PIPES:
First of all, calculate the moles of disodium salt needed. You have a 0.200 mol/L PIPES buffer, and since the disodium salt has a 2:1 ratio with PIPES, you will need a concentration of 0.100 mol/L of disodium salt. To find the moles, multiply the concentration by the volume: 0.100 mol/L * 0.500 L = 0.050 mol.
Next, determine the molar mass of the disodium salt of PIPES (Na2C8H16N2O6S2). Sum up the atomic masses:
2(Na) + 8(C) + 16(H) + 2(N) + 6(O) + 6(S) = 292 g/mol
Finally, calculate the mass using the moles and molar mass: mass = moles * molar mass = 0.050 mol * 292 g/mol = 14.6 g. Therefore, you will need 14.6 grams of the disodium salt of PIPES.
ii) Finding the volume of HCl:
To calculate the volume of HCl required, you need to consider its concentration and the fact that it will react with the disodium salt of PIPES. The reaction will consume the same amount of moles that were present in the disodium salt of PIPES.
Use the balanced equation between HCl and Na2C8H16N2O6S2:
2 Na2C8H16N2O6S2 + 8 HCl → 4 NaCl + 2 C8H18N2O6S2 + 16 H2O
Since the ratio is 2:8 between Na2C8H16N2O6S2 and HCl, and you determined you need 0.050 mol of Na2C8H16N2O6S2, you will need four times as much HCl: 4 * 0.050 mol = 0.200 mol.
Now, using the concentration of the HCl solution, you can calculate the volume needed following the equation C = n/V, where C is concentration, n is the number of moles, and V is the volume.
0.200 mol/L = 0.200 mol / V
V = 0.200 mol / 2 mol/L
V = 0.100 L = 100.0 mL
Therefore, you will need 100.0 mL of the 2.00 F solution of HCl.
For the second problem:
2) This problem also requires you to calculate the required amounts of reagents to prepare the HEPES buffer.
To maintain the pH within the optimal working range, you need to add a base (NaOH) to neutralize the H+ ions evolved during the hydrolysis reaction.
First, calculate the moles of H+ that could be generated per 100.0 mL of solution. You have 0.001 moles of H+ per 100.0 mL.
To calculate the moles of NaOH required for neutralization, use the balanced equation between H+ and NaOH:
H+ + OH- → H2O
Since the ratio between H+ and OH- is 1:1, you will need the same amount of moles of NaOH as H+. Therefore, you will need 0.001 moles of NaOH.
Now, calculate the volume of the 5.695 F solution of NaOH needed using the same equation as before, C = n/V:
5.695 mol/L = 0.001 mol / V
V = 0.001 mol / 5.695 mol/L
V = 0.000175 L = 0.175 mL
Therefore, you will need 0.175 mL of the 5.695 F solution of NaOH.
Next, calculate the moles of HEPES needed to buffer the system.
Use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
The optimal working pH range is 7.40±0.05, so the pH will be between 7.35 and 7.45.
Set up two equations:
Eqn 1: pH = 7.45 = 7.55 + log([A-]/[HA])
Eqn 2: pH = 7.35 = 7.55 + log(([A-] - 0.001) / ([HA] + 0.001))
From Eqn 2, solve for [A-] - 0.001:
7.35 - 7.55 = log(([A-] - 0.001) / ([HA] + 0.001))
-0.20 = log(([A-] - 0.001) / ([HA] + 0.001))
From Eqn 1, substitute the value of [A-] - 0.001 into the equation:
7.45 = 7.55 + log(([A-] - 0.001) / ([HA] + 0.001))
Solve this equation for [A-] to find the ratio between [HA] and [A-].
Given that [HA] + [A-] = 0.200, and using the values substituted into the equation, you can calculate [A-] and [HA].
Once you have the ratio, use the molar mass of HEPES (C8H18N2O4S) to calculate the mass required to achieve the desired buffer concentration. Also, note that the ratio between the moles of NaOH used and the moles of HEPES can help determine the limiting reagent.