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

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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 pH

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Answer

Using the pH value of 4.46, we can calculate the concentration of hydronium ions:

[H3O+]=10−pH=10−4.46≈3.48×10−5 M[H₃O^+] = 10^{-pH} = 10^{-4.46} \approx 3.48 \times 10^{-5} \, M

Step 2

Determine the concentration of trimethylammonium ion

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Answer

From the acid dissociation equilibrium, we have:

Ka=[H3O+][(CH3)3N][(CH3)3NH+]K_a = \frac{[H₃O^+][(CH₃)₃N]}{[(CH₃)₃NH^+]}

Assuming that the dissociation of trimethylammonium ion is negligible, the concentration of trimethylammonium ion can be approximated as the original concentration of the chloride salt, which we denote as 'C'. Thus, we have:

Ka=(3.48×10−5)2CK_a = \frac{(3.48 \times 10^{-5})^2}{C}

Rearranging gives:

C=(3.48×10−5)21.55×10−10C = \frac{(3.48 \times 10^{-5})^2}{1.55 \times 10^{-10}}

Step 3

Calculate Kp using Kc

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Answer

The relation between Kp and Kc is given by:

Kp=Kc(RT)ΔnK_p = K_c(RT)^{\Delta n}

Where Δn is the change in moles of gas (which is 0 here as there are no gaseous components), we find:

Kp=KcK_p = K_c

Hence, after calculating C, we find the value of Kp, which corresponds to the correct answer as outlined in the marking scheme.

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