Question

What is the pH of a 0.18 M solution of trimethylamine?

Question 1 options:

	11.53
	2.47
	3.46
	10.54
	11.93

Answer 1

Trimethylamine (CH₃)₃N which is a Weak Base with theoritical calculated ( K_b = 6.4x10^-5 ) when dissolved in water produces Conjugate Acid Trimethyl ammonium cation [(CH₃)₃NH⁺] and hydroxyl anion(OH^-).

So, we can use ICE table to determine the equilibrium concentration of hydroxyl anions (OH^-). So an ICE table looks like this given below :

	(CH3)3N(aq)	H2O(l) ⇌	(CH3)3NH+(aq)	OH-(aq)
I	0.18	-	0	0
C	-X	-	+X	+X
E	0.18-X	-	X	X

Therefore,

K_b = [(CH₃)₃NH⁺(aq)][OH^-(aq)] / [(CH₃)₃N(aq)] ( 6.4x10^-5 )= X * X / (0.18-X)

As, K_b has a very small value when compared with the initial concentration of the Base , so we can use the approximation ( 0.18 - X ≈ 0.18)

( 6.4x10^-5 )= X * X / 0.18

X² = 1.152 x 10^-5

X = (1.152 x 10^-5)^(1/2)

X = 3.39 x 10^-3

So, [OH^-] = X = 3.39 x 10^-3

As we have got the got concentration of OH^- now we calculate the pOH and then Ccalculate the pH of the solution

pOH = - log [OH^-]

pOH = - log(3.39 x 10^-3)

pOH  = 2.47

We know,

pK_w= pH + pOH (pK_w=14 , as K_w=1.0 x 10^-14)

Therefore,

pH = pK_w - pOH = 14 - 2.47 =11.53

Hence the pH of a 0.18 M solution of trimethylamine is option (a) 11.53