A buffered solution is made by adding 48.6 g C2H5NH3Cl to 1.00 L of a 0.77 M solution of C2H5NH2. Calculate the pH of the final solution. (Assume no volume change. Assume that all solutions are at 25°C.)
To calculate the pH of the final solution, we need to determine the concentrations of the C2H5NH3+ and C2H5NH2 species in the solution. The Henderson-Hasselbalch equation is used to relate the pH of a buffered solution to the concentrations of a weak acid and its conjugate base:
pH = pKa + log([A-]/[HA])
In this case, C2H5NH3Cl is the weak acid (HA) and C2H5NH2 is its conjugate base (A-). First, we need to determine the concentrations of C2H5NH3+ and C2H5NH2 in the final solution.
First, let's calculate the number of moles of C2H5NH3Cl:
moles of C2H5NH3Cl = mass / molar mass
moles of C2H5NH3Cl = 48.6 g / (46.07 g/mol + 35.45 g/mol)
moles of C2H5NH3Cl = 48.6 g / 81.52 g/mol
moles of C2H5NH3Cl = 0.596 mol
Since the volume of the solution is 1.00 L, the concentration of C2H5NH3Cl is:
concentration of C2H5NH3Cl = moles / volume
concentration of C2H5NH3Cl = 0.596 mol / 1.00 L
concentration of C2H5NH3Cl = 0.596 M
Next, let's determine the concentration of C2H5NH2:
concentration of C2H5NH2 = initial concentration - concentration of C2H5NH3Cl
concentration of C2H5NH2 = 0.77 M - 0.596 M
concentration of C2H5NH2 = 0.174 M
Now that we have the concentrations of C2H5NH3+ and C2H5NH2, we can calculate the pH using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
The pKa for the C2H5NH3+ / C2H5NH2 system is typically provided. Let's assume a pKa of 10.74.
pH = 10.74 + log(0.174/0.596)
pH = 10.74 + log(0.292)
pH = 10.74 + (-0.534)
pH = 10.21
Therefore, the pH of the final solution is approximately 10.21.