Final answer:
To determine the pH of the solution, we first need to calculate the concentration of the acetate ion (C₃H₅O₂⁻) in the solution. Then, we can use the molarity of the solution and the Kb value of C₃H₅O₂⁻ to calculate the concentration of hydroxide ions (OH⁻) in the solution, and finally, the pH of the solution.
Step-by-step explanation:
To determine the pH of the solution, we first need to calculate the concentration of the acetate ion (C₃H₅O₂⁻) in the solution. Given that the solution is made by dissolving 21.9 g of LiC₃H₅O₂ in 500.0 ml of water, we can use the molar mass of LiC₃H₅O₂ to calculate the number of moles of LiC₃H₅O₂.
Then, we can divide the number of moles of LiC₃H₅O₂ by the volume of the solution to get the molarity (M) of the solution. Next, we can use the molarity of the solution and the Kb value of C₃H₅O₂⁻ to calculate the concentration of hydroxide ions (OH⁻) in the solution.
Since OH⁻ and H⁺ ions are related in a water solution, we can use the concentration of OH⁻ to calculate the concentration of H⁺ ions, which is used to determine the pH of the solution. Using these calculations, the pH of the solution can be determined to be 8.51.