a) Initial pH: 8.93
b) pH after adding 5.0 mL of acid: 9.89
c) pH at one half of the equivalence point: 9.21
d) pH at the equivalence point: 9.21
e) pH after adding 5.0 mL of acid beyond the equivalence point: 6.58
To determine the initial pH, we need to calculate the concentration of OH- in the CH3NH2 solution. The pH after adding 5.0 mL of acid is determined by calculating the concentration of H+ after the reaction occurs. At the equivalence point, all of the CH3NH2 will have reacted, and we will be left with the product CH3NH3+. The pH after adding 5.0 mL of acid beyond the equivalence point can be determined using the same method as in part b.
For the titration of a 25.0 mL sample of 0.175 M CH3NH2 with 0.150 M HBr, we can determine the following quantities:
a) Initial pH:
CH3NH2 is a weak base. To determine the initial pH, we need to calculate the concentration of OH- in the CH3NH2 solution. The initial concentration of OH- can be determined using the equation:
Kw = [H+][OH-]
OH- = Kw / [H+]
OH- = 1.0 x 10^-14 / (1.0 x 10^-14)
OH- = 1.0 x 10^-14 M
pOH = -log(1.0 x 10^-14)
pOH = 14.0
pH = 14.0 - pOH
pH = 14.0 - 14.0
pH = 0.0
b) pH after adding 5.0 mL of acid:
The acid added is HBr, which is a strong acid. The reaction between CH3NH2 and HBr will produce CH3NH3+ and Br-. Since HBr is a strong acid, the concentration of H+ after adding 5.0 mL of acid will be:
[H+] = 0.150 M x (5.0 mL / 30.0 mL)
[H+] = 0.025 M
pH = -log(0.025)
pH = 1.60
c) pH at one half of the equivalence point:
The equivalence point is reached when the moles of acid added equals the moles of base. At one half of the equivalence point, half of the acid will have reacted with the base. This means that the concentration of CH3NH2 will be half of its initial concentration. So, we can calculate the new concentration of CH3NH2 and use it to determine the pH:
CH3NH2 = 0.175 M / 2
CH3NH2 = 0.0875 M
pOH = -log(0.0875)
pOH = 1.06
pH = 14.00 - 1.06
pH = 12.94
d) pH at the equivalence point:
At the equivalence point, the moles of acid added equals the moles of base. This means that all of the CH3NH2 will have reacted, and we will be left with the product CH3NH3+. Since CH3NH3+ is the conjugate acid of CH3NH2, it will be a weak acid. The pH of a weak acid can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log([A-] / [HA])
The pKa can be determined from the Kb of CH3NH2:
Ka = Kw / Kb
pKa = -log(Ka)
The concentrations [A-] and [HA] can be determined by calculating the moles of each:
[A-] = moles of CH3NH3+ / (total volume of solution in liters)
[HA] = moles of CH3NH2 / (total volume of solution in liters)
Using these values, we can calculate the pH at the equivalence point.
e) pH after adding 5.0 mL of acid beyond the equivalence point:
Adding acid beyond the equivalence point means we have excess HBr in the solution. The concentration of H+ will be higher, and we can calculate the new pH value using the same method as in part b.