A buffer system contains 0.25M NH4+ and 0.19M NH3. pka of NH4 is 9.25.
How many moles of NaOH must be added to 1.00L of this solution to increase the pH to 9.25?
mol NH3 = M x L = 0.19*1 = 0.190
mol NH4^+ = 0.25*1 = 0.250
-----------------
........NH4^+ + OH^- ==> NH3 + H2O
I.....0.250.....0......0.190
add..............x............
C.......-x......-x.......+x
E.....0.250-x.....0......0.190+x
Substitute into the Henderson-Hasselbalch equation and solve for x = mol NaOH added to 1L buffer to make pH = 9.25
To solve this problem, we need to understand the principles behind buffer solutions and how they resist changes in pH. A buffer solution is a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid). In this case, the weak acid is NH4+ and its conjugate base is NH3.
The reaction that occurs in this buffer solution is:
NH4+ + H2O ⇌ NH3 + H3O+
In a buffer solution, these reactants and products are present in equilibrium. When hydroxide ions (OH-) are added to the solution (such as in the form of NaOH), they react with the hydronium ions (H3O+) to form water:
OH- + H3O+ ⇌ 2H2O
This reaction reduces the concentration of H3O+ ions in the solution and increases the concentration of water. As a result, the pH of the solution increases.
Now, let's calculate the number of moles of NaOH needed to increase the pH to 9.25.
Given:
Initial concentration of NH4+ = 0.25 M
Initial concentration of NH3 = 0.19 M
pKa of NH4+ = 9.25
Volume of solution = 1.00 L
To calculate the number of moles of NaOH needed, we can use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the concentrations of the acid and conjugate base:
pH = pKa + log([conjugate base] / [weak acid])
First, we need to determine the concentrations of the weak acid (NH4+) and the conjugate base (NH3).
Initially, the concentration of NH4+ is 0.25 M, and the concentration of NH3 is 0.19 M. We can assume that the dissociation of NH4+ is negligible compared to its concentration, so we can consider 0.25 M as the concentration of the weak acid.
Now, let's substitute the given values into the Henderson-Hasselbalch equation to find the pH:
9.25 = pKa + log([NH3] / [NH4+])
9.25 = 9.25 + log(0.19 / 0.25)
Simplifying this equation, we have:
log(0.19 / 0.25) = 0
To increase the pH to 9.25, the concentration of NH3 should equal the concentration of NH4+. This means we need to consume all the NH4+ present and convert it to NH3.
Now, let's calculate the moles of NH4+ in the solution:
moles of NH4+ = concentration of NH4+ × volume of solution
moles of NH4+ = 0.25 M × 1.00 L = 0.25 mol
Since we need to convert all the NH4+ to NH3, the number of moles of NaOH required is equal to the number of moles of NH4+:
moles of NaOH = 0.25 mol
Therefore, we need to add 0.25 moles of NaOH to 1.00 L of the solution to increase the pH to 9.25.