Calculate the volume (in mL) of 0.170 M NaOH that must be added to 361 mL of 0.0491 M 3-(N-Morpholino)propanesulfonic acid (MOPS) to give the solution a pH of 7.55. The pKa of MOPS = 7.18.
To solve this question, we can use the Henderson-Hasselbalch equation, which relates the pH of a solution to the pKa and the concentrations of the acid and its conjugate base. The equation is given by:
pH = pKa + log ([A-]/[HA])
In this equation, [A-] represents the concentration of the conjugate base, and [HA] represents the concentration of the acid.
1. First, we need to find the ratio of [A-] to [HA] that will give us a pH of 7.55. Rearranging the Henderson-Hasselbalch equation, we have:
log ([A-]/[HA]) = pH - pKa
Substituting the values we know, we get:
log ([A-]/[HA]) = 7.55 - 7.18
Taking the antilog of both sides, we have:
[A-]/[HA] = 10^(7.55 - 7.18)
2. Next, we need to calculate the concentration of [HA] in the original solution. We know that the concentration of MOPS is 0.0491 M, which is equal to [HA]. Let's call the volume of MOPS as V1.
V1 * 0.0491 = moles of MOPS
Since the molarity of MOPS and the volume of MOPS are given, we can calculate the number of moles of MOPS from the given values.
3. Now, let's calculate the concentration of [A-]. We are given a 0.170 M NaOH solution that will be added to the original solution. Let's call the volume of NaOH as V2.
V2 * 0.170 = moles of NaOH
Since the molarity of NaOH and the volume of NaOH are given, we can calculate the number of moles of NaOH from the given values.
4. Since NaOH is a strong base, it will fully react with MOPS to form the conjugate base (A-). This means that the number of moles of NaOH added to the solution will be equal to the number of moles of [A-] formed.
5. From step 1, we know the ratio of [A-]/[HA], and from step 3, we know the number of moles of [A-]. By multiplying the number of moles of [A-] by the ratio, we can calculate the number of moles of [HA]:
moles of [HA] = number of moles of [A-] * ([HA]/[A-])
6. Finally, we can calculate the volume of [HA] using the concentration and the number of moles of [HA]:
Volume of [HA] = moles of [HA] / concentration of [HA]
This will give us the volume of [HA] required to achieve a pH of 7.55.
Please note that the equation above assumes that the volumes of MOPS and NaOH solutions are additive, and the volume of the final solution is the sum of the volumes of the individual solutions.