PartA: What volume of 10.0M NaOH is needed to prepare a buffer with a pH of 7.79 using 31.52 g of TrisHCl? TrisHCl is a weak base and the molecular weight is 157.67 g/mol. I found the solution, it is 6.67 milliliters.
Part B: "The buffer from Part A is diluted to 1.00 L. To half of it (500.mL), you add 0.0150 mol of hydrogen ions without changing the volume. What is the resulting pH?
I cant figure out how to do part B
To solve Part B, we need to understand the concept of buffer capacity and the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is used to calculate the pH of a solution that contains a weak acid and its conjugate base or a weak base and its conjugate acid. The equation is as follows:
pH = pKa + log ([A-]/[HA])
Where:
pH = the pH value of the buffer solution
pKa = the acid dissociation constant of the weak acid or base
[A-] = concentration of the conjugate base
[HA] = concentration of the weak acid or base
In Part A, you have already prepared a buffer solution with a pH of 7.79. Let's assume the pKa of TrisHCl is known or can be determined. Based on the given information, the concentration of TrisHCl in the buffer can be calculated using its molar mass and mass:
Concentration (M) = (mass (g) / molar mass (g/mol)) / volume (L)
Once you have the concentration of TrisHCl, you can use the Henderson-Hasselbalch equation to calculate the concentration of the conjugate base ([A-]) and the weak acid ([HA]).
[HA] = concentration of TrisHCl
[A-] = concentration of the conjugate base
pH = 7.79 (given)
pKa = known or determined
Now, for Part B, we have a diluted buffer solution of 1.00 L, and we are adding 0.0150 mol of hydrogen ions (H+). Since the volume remains unchanged, we can assume no significant dilution of the original buffer solution.
To calculate the resulting pH, we need to determine the new concentration of the conjugate base ([A-]) and the weak acid ([HA]) in the buffer solution after adding the hydrogen ions.
First, we need to find the molar concentration of the hydrogen ions (H+):
[H+] = moles of hydrogen ions / volume of solution (L)
Now, apply the principle of conservation of mass in the buffer solution:
[A-](original) + [A-](added) = [A-](final)
[HA](original) = [HA](final)
Since we added hydrogen ions (H+), the concentration of the conjugate base will decrease, and the concentration of the weak acid will increase. Therefore, we can express the new concentrations as follows:
[A-](final) = [A-](original) - [H+]
[HA](final) = [HA](original) + [H+]
Now, we can substitute the values into the Henderson-Hasselbalch equation to calculate the new pH. Just remember to use the updated values for [A-] and [HA] after adding the hydrogen ions.
pH = pKa + log ([A-](final) / [HA](final))
Solving this equation will give you the resulting pH of the buffer solution after adding the hydrogen ions.
Note: It is important to know the pKa value of TrisHCl to calculate both Part A and Part B. If this information is not provided, you may need to consult a reference source or perform further experimentation to determine the pKa value.
To solve Part B, we will use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
where pKa is the dissociation constant of the weak acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. In this case, the weak acid is TrisHCl, and since it is a weak base, its conjugate acid is Tris+.
We know that the buffer solution is made up of TrisHCl and NaOH. The TrisHCl will act as the weak acid, providing [HA], and when it reacts with NaOH, it will produce Tris+ and water. Since the volume remains constant at 500 mL, we can assume that there's enough NaOH present to neutralize all the TrisHCl.
Given that the molecular weight of TrisHCl is 157.67 g/mol, we can find the number of moles of TrisHCl present in 31.52 g:
moles of TrisHCl = mass / molecular weight
moles of TrisHCl = 31.52 g / 157.67 g/mol
moles of TrisHCl = 0.20 mol
Since TrisHCl is a 1:1 ratio with Tris+, we have 0.20 mol of Tris+ in 500 mL. This gives us the concentration of Tris+:
concentration of Tris+ = moles of Tris+ / volume
concentration of Tris+ = 0.20 mol / 0.500 L
concentration of Tris+ = 0.40 M
Now, we need to add 0.0150 mol of hydrogen ions to the buffer solution. Since the volume remains constant, the new concentration of Tris+ will be:
new concentration of Tris+ = (initial moles of Tris+ + moles of additional hydrogen ions) / volume
new concentration of Tris+ = (0.20 mol + 0.0150 mol) / 0.500 L
new concentration of Tris+ = 0.43 M
Substituting the values into the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
pH = pKa + log (0.43 M / 0.40 M)
Now, we need the pKa value for TrisHCl. The pKa of TrisHCl is approximately 8.07. Substituting that value and solving the equation:
pH = 8.07 + log (0.43 M / 0.40 M)
pH = 8.07 + log (1.08)
Using a calculator, the logarithm evaluates to 0.033:
pH = 8.07 + 0.033
pH = 8.10
Therefore, the resulting pH after adding 0.0150 mol of hydrogen ions to the diluted buffer solution is approximately pH = 8.10.