A 100 mL sample of 0.10M HCl is mixed with 50mL of 0.10M NH3 (Kb=1.8x10^-5). What is the resulting pH?
To determine the resulting pH of the solution after mixing HCl and NH3, we need to consider the reaction between these two compounds. HCl is a strong acid and fully dissociates in water, while NH3 is a weak base and partially dissociates. The reaction between HCl and NH3 can be represented as:
HCl + NH3 ↔ NH4+ + Cl-
To solve this problem, we need to follow these steps:
1. Calculate the moles of HCl and NH3.
2. Determine which reactant is limiting, i.e., which one will be fully consumed in the reaction.
3. Calculate the concentration of the excess reactant.
4. Determine the concentration of the products NH4+ and Cl- after the reaction.
5. Calculate the concentration of OH- ions formed from NH4+.
6. Determine the concentration of H3O+ ions present in the solution.
7. Calculate the pH using the concentration of H3O+.
Let's now go through these steps step by step.
1. Calculate the moles of HCl and NH3:
Moles of HCl = concentration (M) × volume (L) = 0.10 M × 0.100 L = 0.010 mol
Moles of NH3 = concentration (M) × volume (L) = 0.10 M × 0.050 L = 0.005 mol
2. Determine the limiting reactant:
To determine the limiting reactant, we compare the mole ratios of HCl and NH3 in the balanced chemical equation. The balanced equation shows that the ratio of HCl to NH3 is 1:1. Since both HCl and NH3 are present in a 1:1 mole ratio, neither is in excess, and the limiting reactant is NH3.
3. Calculate the concentration of the excess reactant:
Since HCl is not in excess and is fully consumed in the reaction, its concentration after the reaction is zero.
4. Determine the concentration of the products NH4+ and Cl-:
The concentration of NH4+ and Cl- ions after the reaction will be equal to the concentration of NH3 initially added since NH3 is the limiting reactant.
Concentration of NH4+ = concentration of NH3 = 0.10 M
Concentration of Cl- = concentration of NH3 = 0.10 M
5. Calculate the concentration of OH- ions formed from NH4+:
The Kb value is given as 1.8 × 10^-5. Since NH4+ is a weak acid, it will partially dissociate, and OH- ions will be formed. Using the Kb expression for this reaction, we can determine the concentration of OH- ions:
Kb = [NH4+][OH-] / [NH3]
1.8 × 10^-5 = [0.10][OH-] / [0.10]
[OH-] = (1.8 × 10^-5) M
6. Determine the concentration of H3O+ ions:
Since this is a neutralization reaction between a strong acid (HCl) and a weak base (NH3), the concentration of H3O+ ions formed will be equal to the concentration of OH- ions.
[H3O+] = (1.8 × 10^-5) M
7. Calculate the pH:
pH = -log10[H3O+]
pH = -log10[(1.8 × 10^-5) M]
Calculating the value from step 7, we get pH = 4.74 as the resulting pH of the solution.