To find the pH of the final solution, we need to determine the concentration of the resulting solution after the reaction between hydrofluoric acid (HF) and lithium hydroxide (LiOH) has taken place.
First, let's write the balanced equation for the reaction:
HF + LiOH → LiF + H2O
We can see that the reaction between HF and LiOH will produce lithium fluoride (LiF) and water (H2O).
Since we are given the initial concentrations and volumes for HF and LiOH, we can use the concept of moles and stoichiometry to determine the concentration of the final solution.
Step 1: Calculate the number of moles of HF and LiOH initially:
n(HF) = C(HF) × V(HF) = 0.40 M × 0.100 L = 0.040 mol
n(LiOH) = C(LiOH) × V(LiOH) = 0.20 M × 0.100 L = 0.020 mol
Step 2: Determine the limiting reagent:
To determine the limiting reagent, we compare the moles of HF and LiOH. We can see that the stoichiometric ratio between HF and LiOH is 1:1. Since the moles of HF (0.040 mol) are greater than the moles of LiOH (0.020 mol), LiOH is the limiting reagent.
Step 3: Calculate the moles of LiF and H2O produced:
According to the balanced equation, 1 mole of LiOH produces 1 mole of LiF and 1 mole of H2O.
Therefore, the moles of LiF and H2O produced are both equal to the moles of LiOH, which is 0.020 mol.
Step 4: Calculate the volume of the final solution:
The volume of the final solution is the sum of the volumes of the initial solutions, which is 100 mL + 100.0 mL = 200.0 mL.
Step 5: Calculate the concentration of the final solution:
The concentration is given by:
C(final) = moles(final) / V(final)
Since the moles of LiF and H2O are equal to 0.020 mol each, the total moles of the final solution is 0.020 mol + 0.020 mol = 0.040 mol.
Converting the volume of the final solution to liters:
V(final) = 200.0 mL = 200.0 mL / 1000 mL/L = 0.200 L
Finally, we can calculate the concentration of the final solution:
C(final) = 0.040 mol / 0.200 L = 0.20 M
Step 6: Calculate the pH of the final solution:
To determine the pH, we need to use the pKa value of HF. The pKa for HF is given as 3.2.
The Henderson-Hasselbalch equation relates the pH of a solution to the pKa and the ratio of concentrations of the conjugate acid and base. The equation can be written as:
pH = pKa + log10([A-] / [HA])
In this case, we are dealing with weak acids and bases, so the concentration of the conjugate base ([A-]) is equal to the concentration of LiF, which is 0.020 M.
Using the Henderson-Hasselbalch equation:
pH = 3.2 + log10(0.020 M / 0.20 M)
Calculating the ratio of concentrations:
0.020 M / 0.20 M = 0.10
Taking the logarithm of the ratio:
log10(0.10) = -1
Adding the pKa and the logarithm value:
pH = 3.2 + (-1) = 2.2
Therefore, the pH of the final solution is 2.2.