I need major help with this problem! especially with the first equation that is used...

A buffer is prepared by adding 115 mL of 0.20M NH3 to 145 mL of .15M NH4NO3. What is the pH of the final solution?

Use the Henderson-Hasslebalch equation.

To solve this problem, we need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is defined as:

pH = pKa + log ([A-]/[HA])

In this case, NH4+ (from NH4NO3) acts as HA (acid) and NH3 acts as A- (conjugate base).

Let's break down the steps to solve the problem:

Step 1: Find the pKa value
The pKa is a measure of the acidity of the acid-conjugate base pair. In this case, the NH4+/NH3 pair acts as the acid-conjugate base pair. The pKa value of NH4+/NH3 can be found in a reference book or online, and it is approximately 9.25.

Step 2: Calculate the concentrations of NH4+ and NH3
We are given the volumes and concentrations of NH3 and NH4NO3. To calculate the concentrations, we need to divide the moles of solute by the total volume of the solution.

For NH3:
Concentration (NH3) = moles / volume
Moles of NH3 = volume x molarity = 115 mL x 0.20 M = 23 moles
Volume (total solution) = 115 mL + 145 mL = 260 mL = 0.260 L
Concentration (NH3) = 23 moles / 0.260 L = 0.088 M

For NH4NO3:
Concentration (NH4NO3) = moles / volume
Moles of NH4NO3 = volume x molarity = 145 mL x 0.15 M = 21.75 moles
Volume (total solution) = 115 mL + 145 mL = 260 mL = 0.260 L
Concentration (NH4NO3) = 21.75 moles / 0.260 L = 0.084 M

Step 3: Substitute the values into the Henderson-Hasselbalch equation
pH = pKa + log ([A-]/[HA])

pH = 9.25 + log ([0.088]/[0.084])

Step 4: Solve for pH using logarithm properties
pH = 9.25 + log (1.0476)

Step 5: Use a calculator to find the logarithm and calculate the pH value
pH = 9.25 + 0.0202
pH ≈ 9.27

Therefore, the pH of the final solution is approximately 9.27.