If one added 130 mL of 2 M NaOH to 1 L of a buffer composed of 2.3 M NH3 and 3.2 M NH4Cl, what would be the pH of the resulting solution? The Kb of NH3 is 1.8 × 10−5.
pH=~9.2
To find the pH of the resulting solution, we need to calculate the concentration of NH3 (ammonia) and NH4+ (ammonium ion) after adding NaOH. We can then use the Henderson-Hasselbalch equation to determine the pH.
Here's how you can solve this problem step by step:
Step 1: Determine the change in concentrations of NH3 and NH4+ after adding NaOH.
- NaOH is a strong base and reacts with NH4+ to form NH3 and water. The reaction is as follows:
NaOH + NH4+ → NH3 + H2O
- Since NaOH is in excess, NH4+ will be fully converted into NH3. Therefore, the change in concentration of NH4+ is equal to -130 mL.
- The change in concentration of NH3 will be equal to the concentration of NH4+ that reacted since stoichiometry is 1:1.
Step 2: Calculate the concentrations of NH3 and NH4+ after the reaction.
- Given that the initial concentration of NH3 is 2.3 M and NH4+ is 3.2 M, the final concentration of NH3 will be:
Final [NH3] = Initial [NH3] + Change [NH3]
= 2.3 M + (130 mL/1000 mL/L) M
- The final concentration of NH4+ will be:
Final [NH4+] = Initial [NH4+] + Change [NH4+]
= 3.2 M + (-130 mL/1000 mL/L) M
Step 3: Calculate the ratio of [NH3]/[NH4+] (which is the ratio needed for Henderson-Hasselbalch equation).
- Calculate the concentration of NH3 in moles:
[NH3] (mol/L) = Final [NH3] Molarity * Volume (L)
- Calculate the concentration of NH4+ in moles:
[NH4+] (mol/L) = Final [NH4+] Molarity * Volume (L)
- Take the ratio of [NH3] to [NH4+] to get the ratio needed for the Henderson-Hasselbalch equation.
Step 4: Use the Henderson-Hasselbalch equation to calculate the pH of the resulting solution.
- The Henderson-Hasselbalch equation is given as:
pH = pKa + log([NH3]/[NH4+])
- The pKa value can be calculated using the Kb value:
pKa = 14 - pKb
- Substitute the values into the Henderson-Hasselbalch equation to find the pH.
By following these steps, you should be able to calculate the pH of the resulting solution.