Answer

A typical equilibrium problem: write the relevant reactions, write the mass action expression, set up an ICE table, and then solve for the unknown.

Let [NH₃]_init = C_am = 4^th5^th/100 and [NH₄Cl]_init = 1^st2^nd/100 = 0.10 M for all students

NH₄⁺(aq) + Cl^–(aq) ← NH₄Cl(aq)

NH₄⁺(aq) + H₂O(l) → ← H₃O⁺(aq) + NH₃(aq)

K_a = [H₃O⁺]_e[NH₃]_e                         [NH₄⁺]_e = 5.6×10^–10

Initial0.10 0 C_am

Change– x +x – x

Initial0.10 – x x C_am + x

Approximate? 0.10/5.6×10^–10 = 1.8×10⁸ > 100, Yes

5.6×10^–10 = (x)(C_am)/(0.10)

x = [H₃O⁺]_e = (5.6×10^–10)(0.10)/(C_am)

pH = –log[H₃O⁺]_e, all to two places past the decimal.

 

a) Add 1.0 g of HCl(g) so the concentration of HCl is 1 mol/(1.0 g + 35.5 g)(1.0 L) = 0.027 M

NH₄⁺(aq) + Cl^–(aq) ← NH₄Cl(aq)

NH₄⁺(aq) + H₂O(l) → ← H₃O⁺(aq) + NH₃(aq)

A/B reaction:NH₄⁺(aq) + Cl^–(aq) ← HCl(aq) + NH₃(aq)

K_a = [H₃O⁺]_e[NH₃]_e                         [NH₄⁺]_e = 5.6×10^–10

Initial0.10 0 C_am

A/B reaction+0.027 0 – 0.027

Change– x +x – x

Equilibrium0.127 – x x C_am – 0.027 + x

Approximate? 0.10/5.6×10^–10 = 1.8×10⁸ > 100, Yes

5.6×10^–10 = (x)(C_am – 0.027)/(0.127)

x = [H₃O⁺]_e = (5.6×10^–10)(0.10)/(C_am)

pH = –log[H₃O⁺]_e, all to two places past the decimal.

 

b) Add 1.0 g of NaOH(s) so the concentration of NaOH is 1 mol/(23.0 g + 16.0 g + 1.0 g)(1.0 L) = 0.025 M

NH₄⁺(aq) + Cl^–(aq) ← NH₄Cl(aq)

NH₄⁺(aq) + H₂O(l) → ← H₃O⁺(aq) + NH₃(aq)

A/B reaction:NH₄⁺(aq) + NaOH(s) → Na⁺(aq) + NH₃(aq) + H₂O(l)

K_a = [H₃O⁺]_e[NH₃]_e                         [NH₄⁺]_e = 5.6×10^–10

Initial0.10 0 C_am

A/B reaction– 0.025 0 + 0.025

Change– x +x – x

Equilibrium0.075 – x x C_am – 0.025 + x

Approximate? 0.10/5.6×10^–10 = 1.8×10⁸ > 100, Yes

5.6×10^–10 = (x)(C_am – 0.025)/(0.075)

x = [H₃O⁺]_e = (5.6×10^–10)(0.10)/(C_am)

pH = –log[H₃O⁺]_e, all to two places past the decimal.

Specific Answers:

[NH₃]_init (M) [NH₄Cl]_init (M) pH pH after HCl pH after NaOH

0.50 0.10 9.95 9.82 10.10

0.52 0.10 9.97 9.84 10.11

0.54 0.10 9.98 9.86 10.13

0.55 0.10 9.99 9.87 10.14

0.56 0.10 10.00 9.87 10.14

0.57 0.10 10.01 9.88 10.15

0.58 0.10 10.02 9.89 10.16

0.59 0.10 10.02 9.90 10.17

0.60 0.10 10.03 9.91 10.17

0.61 0.10 10.04 9.91 10.18

0.62 0.10 10.04 9.92 10.19

0.63 0.10 10.05 9.93 10.19

0.65 0.10 10.06 9.94 10.21