A buffered solution is made by adding 50.0 g NH4Cl to 1.00 L of a 0.70 M solution of NH3. Calculate the pH of the final solution. (Assume no volume change.)
Use the Henderson-Hasselbalch equation.
Moles
To calculate the pH of the final solution, we need to consider the reaction between NH4Cl and NH3.
First, let's write down the balanced equation:
NH4Cl + NH3 -> NH4+ + Cl-
NH4+ is the conjugate acid of NH3, and Cl- is a spectator ion. We can ignore Cl- in the calculation.
Now, let's analyze the solution composition:
NH3 is the weak base and NH4+ is a weak acid. When they are present together in a solution, they form a buffer system that resists changes in pH.
To determine the pH, we need to calculate the concentration of NH4+ in the solution. We know that we added 50.0 g of NH4Cl, so we need to convert this mass to moles:
molar mass of NH4Cl = 14.01 g/mol (atomic mass of N) + 4 * 1.01 g/mol (atomic mass of H) + 35.45 g/mol (atomic mass of Cl) = 53.46 g/mol
moles of NH4Cl = mass / molar mass = 50.0 g / 53.46 g/mol
Next, we need to determine the concentration of NH4+ in the solution. Since we added 50.0 g of NH4Cl to 1.00 L of solution, the concentration of NH4+ can be calculated using the formula:
concentration = moles / volume
For NH4+, the moles are the same as NH4Cl, so the concentration of NH4+ is:
concentration of NH4+ = moles of NH4+ / volume of solution
Now, let's calculate the concentration of NH4+:
volume of solution = 1.00 L
concentration of NH4+ = moles of NH4+ / volume of solution
Next, we calculate the moles of NH4+:
moles of NH4+ = moles of NH4Cl = 50.0 g / 53.46 g/mol
Finally, we calculate the concentration of NH4+:
concentration of NH4+ = (50.0 g / 53.46 g/mol) / 1.00 L
Now that we have the concentration of NH4+, we can use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log10(concentration of NH3 / concentration of NH4+)
The pKa value for NH3/NH4+ pair is typically given as 9.25.
Substituting the values into the Henderson-Hasselbalch equation, we get:
pH = 9.25 + log10(concentration of NH3 / concentration of NH4+)
Finally, calculate the pH by substituting the values into the equation and solving:
pH = 9.25 + log10(0.70 / concentration of NH4+)
By calculating the concentration of NH4+ and plugging it into the equation, you can determine the pH of the final solution.