Answer:
(a) 13.64; (b) 8.04; (c) 2.25
Explanation:
AgI(s) ⇌ Ag⁺(aq) + I⁻(aq)
![K_{\text{sp}} = {\text{[Ag$^{+}$][I$^{-}$]} = 8.3\times 10^{-17}](https://tex.z-dn.net/?f=K_%7B%5Ctext%7Bsp%7D%7D%20%3D%20%7B%5Ctext%7B%5BAg%24%5E%7B%2B%7D%24%5D%5BI%24%5E%7B-%7D%24%5D%7D%20%3D%208.3%5Ctimes%2010%5E%7B-17%7D)
(a) pAg at 35.10 mL

AgI(s) ⇌ Ag⁺(aq) + I⁻(aq)
I/mol: 1.822 × 10⁻³ 2.040 × 10⁻³
C/mol: -1.822 × 10⁻³ -1.822 × 10⁻³
E/mol: 0 0.218 × 10⁻³
We have a saturated solution of AgI containing 0.218 × 10⁻³ mol of excess I⁻.
V = 25.00 mL + 35.10 mL = 60.10 mL
![\text{[I$^{-}$]} = \dfrac{0.218 \times 10^{-3}\text{ mol}}{\text{0.0610 L}} = 3.57 \times 10^{-3}\text{ mol/L}\\](https://tex.z-dn.net/?f=%5Ctext%7B%5BI%24%5E%7B-%7D%24%5D%7D%20%3D%20%5Cdfrac%7B0.218%20%5Ctimes%2010%5E%7B-3%7D%5Ctext%7B%20mol%7D%7D%7B%5Ctext%7B0.0610%20L%7D%7D%20%3D%203.57%20%5Ctimes%2010%5E%7B-3%7D%5Ctext%7B%20mol%2FL%7D%5C%5C)
AgI(s) ⇌ Ag⁺(aq) + I⁻(aq)
E/mol·L⁻¹: s 3.57 × 10⁻³ + s

Check for negligibility:
![\dfrac{3.57 \times 10^{-3}}{8.3\times 10^{-17}} = 4.3 \times 10^{13} > 400\\\\\therefore s \ll 3.63 \times 10^{-3}\\K_{\text{sp}} = s\times 3.63 \times 10^{-3}= 8.3\times 10^{-17}\\\\s = \text{[Ag$^{+}$]} = \dfrac{8.3\times 10^{-17}}{3.63 \times 10^{-3}} =2.29 \times 10^{-14}\\\\\text{pAg} = -\log \left (2.29\times 10^{-14} \right) = \mathbf{13.64}](https://tex.z-dn.net/?f=%5Cdfrac%7B3.57%20%5Ctimes%2010%5E%7B-3%7D%7D%7B8.3%5Ctimes%2010%5E%7B-17%7D%7D%20%3D%204.3%20%5Ctimes%2010%5E%7B13%7D%20%3E%20400%5C%5C%5C%5C%5Ctherefore%20s%20%5Cll%203.63%20%5Ctimes%2010%5E%7B-3%7D%5C%5CK_%7B%5Ctext%7Bsp%7D%7D%20%3D%20s%5Ctimes%203.63%20%5Ctimes%2010%5E%7B-3%7D%3D%208.3%5Ctimes%2010%5E%7B-17%7D%5C%5C%5C%5Cs%20%3D%20%5Ctext%7B%5BAg%24%5E%7B%2B%7D%24%5D%7D%20%3D%20%5Cdfrac%7B8.3%5Ctimes%2010%5E%7B-17%7D%7D%7B3.63%20%5Ctimes%2010%5E%7B-3%7D%7D%20%3D2.29%20%5Ctimes%2010%5E%7B-14%7D%5C%5C%5C%5C%5Ctext%7BpAg%7D%20%3D%20-%5Clog%20%5Cleft%20%282.29%5Ctimes%2010%5E%7B-14%7D%20%5Cright%29%20%3D%20%5Cmathbf%7B13.64%7D)
(b) At equilibrium
AgI(s) ⇌ Ag⁺(aq) + I⁻(aq)
E/mol·L⁻¹: s s

(c) At 47.10 mL

AgI(s) ⇌ Ag⁺(aq) + I⁻(aq)
I/mol: 2.444 × 10⁻³ 2.040 × 10⁻³
C/mol: -2.040 × 10⁻³ -2.040 × 10⁻³
E/mol: 0.404 × 10⁻³ 0
V = 25.00 mL + 47.10 mL = 72.10 mL
![\text{[Ag$^{+}$]} = \dfrac{0.404 \times 10^{-3}\text{ mol}}{\text{0.0721 L}} = 5.61 \times 10^{-3}\text{ mol/L}\\\text{pAg} = -\log(5.61 \times 10^{-3}) = \mathbf{2.25}](https://tex.z-dn.net/?f=%5Ctext%7B%5BAg%24%5E%7B%2B%7D%24%5D%7D%20%3D%20%5Cdfrac%7B0.404%20%5Ctimes%2010%5E%7B-3%7D%5Ctext%7B%20mol%7D%7D%7B%5Ctext%7B0.0721%20L%7D%7D%20%3D%205.61%20%5Ctimes%2010%5E%7B-3%7D%5Ctext%7B%20mol%2FL%7D%5C%5C%5Ctext%7BpAg%7D%20%3D%20-%5Clog%285.61%20%5Ctimes%2010%5E%7B-3%7D%29%20%3D%20%5Cmathbf%7B2.25%7D)