The trimethylammonium ion, [(CH₃)₃NH]⁺, is a weak acid. The acid dissociation equation is shown. [(CH₃)₃NH]⁺(aq) + H₂O(l) ⇌ H₃O⁺(aq) + (CH₃)₃N(aq) Kₐ = 1.55 x 10⁻¹⁰ At 20°C, a saturated solution of trimethylammonium chloride, |(CH₃)₃NH|Cl, has a pH of 4.46. What is the Kᵨ of trimethylammonium chloride?

SSCE HSC Chemistry Brønsted–Lowry Theory: The trimethylammonium ion, [(CH₃

The trimethylammonium ion, [(CH₃)₃NH]⁺, is a weak acid - HSC - SSCE Chemistry - Question 20 - 2021 - Paper 1

Question 20

The trimethylammonium ion, [(CH₃)₃NH]⁺, is a weak acid. The acid dissociation equation is shown. [(CH₃)₃NH]⁺(aq) + H₂O(l) ⇌ H₃O⁺(aq) + (CH₃)₃N(aq) Kₐ = 1.55 x 10⁻¹... show full transcript

Worked Solution & Example Answer:The trimethylammonium ion, [(CH₃)₃NH]⁺, is a weak acid - HSC - SSCE Chemistry - Question 20 - 2021 - Paper 1

Step 1

Calculate the concentration of H₃O⁺ from the pH

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Answer

Using the formula for pH:

$pH = - ext{log}([H_3O^+])$

We can calculate the concentration of hydronium ions:

$[H_3O^+] = 10^{-pH} = 10^{-4.46} ≈ 3.47 imes 10^{-5} ext{ M}$

Step 2

Determine the concentration of trimethylammonium ions

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Answer

Assuming that the dissociation of trimethylammonium ion is small, we can use the fact that:

$K_a = rac{[H_3O^+][(CH_3)_3N]}{[(CH_3)_3NH^+]}$

Let $x$ be the concentration of trimethylammonium ions that dissociate. Thus, at equilibrium, we can write:

$[H_3O^+] ext{ is } 3.47 imes 10^{-5} ext{ M}$ $[(CH_3)_3N] = x$ $[(CH_3)_3NH^+] = C - x ext{ (where C is the initial concentration)}$

Step 3

Calculate Kᵨ

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Answer

Since trimethylammonium chloride is a strong electrolyte, we consider the initial concentration to be the same as the equilibrium concentration of the salt. This leads to:

$K_a = 1.55 imes 10^{-10}$ Since Kᵨ is related to Kₐ by:

$Kᵨ = rac{K_w}{K_a}$ Here, $K_w = 1.0 imes 10^{-14}$ at 25°C. Thus:

$Kᵨ = rac{1.0 imes 10^{-14}}{1.55 imes 10^{-10}} = 6.45 imes 10^{−5}$

Step 4

Select the correct answer for Kᵨ

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Answer

Given the calculated Kᵨ, the closest answer option is:

C. 60.2

The trimethylammonium ion, [(CH₃)₃NH]⁺, is a weak acid - HSC - SSCE Chemistry - Question 20 - 2021 - Paper 1

Worked Solution & Example Answer:The trimethylammonium ion, [(CH₃)₃NH]⁺, is a weak acid - HSC - SSCE Chemistry - Question 20 - 2021 - Paper 1

Calculate the concentration of H₃O⁺ from the pH

Determine the concentration of trimethylammonium ions

Calculate Kᵨ

Select the correct answer for Kᵨ

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