Final answer:
To find the pH of the solution after 50.0 mL of base has been added, calculate the moles of HCl and NaOH that have reacted. At the equivalence point, the moles of HCl and NaOH react in a 1:1 stoichiometric ratio.
Step-by-step explanation:
1) To find the pH of the solution after 50.0 mL of base has been added, we need to calculate the moles of HCl and NaOH that have reacted. The moles of HCl can be determined using the volume and molarity of HCl, and the moles of NaOH can be determined using the volume and molarity of NaOH. Next, we need to determine which is the limiting reagent. Once we know the limiting reagent, we can use the moles of that reagent to calculate the moles of the other reagent that have reacted. Finally, we can calculate the concentration of HCl and NaOH remaining in the solution and use that to calculate the pH of the solution.
2) At the equivalence point, the moles of HCl and NaOH react in a 1:1 stoichiometric ratio. Therefore, the moles of HCl and NaOH will be equal at the equivalence point. We can use this information to calculate the concentration of HCl and NaOH at the equivalence point, and then calculate the pH of the solution.