Calculate the pH of a 1.60 mol L^-1 CH₃NH₃Cl solution. K_b for methylamine, CH₃NH₂, is 3.7 × 10^-4. A)1.61 B)5.18 C)8.82 D)12.39

Question

Quizplus · Accepted Answer

First, we should identify the acid-base reaction in the solution. The lone pair on the nitrogen in CH3NH2 (methylamine) can act as a Lewis base and accept a proton from water, resulting in the formation of CH3NH3+ and OH-. The equilibrium constant for this reaction is given by: 
Kb = ([CH3NH3+][OH-])/[CH3NH2]

Since Kb is small, we can simplify the equation: 
[OH-] = Kb[CH3NH2]/[CH3NH3+]

We are given the concentration of CH3NH2 as 1.60 M. To find the concentration of CH3NH3+, we need to use the fact that it is formed by the reaction of CH3NH2 with HCl. Assuming complete dissociation of HCl, we can calculate the concentration of H+ as 1.60 M. Since there is a 1:1 stoichiometry between H+ and CH3NH3+, the concentration of CH3NH3+ is also 1.60 M.

Plugging in these values, we get:
[OH-] = (3.7 x 10^-4)(1.60)/(1.60) = 3.7 x 10^-4

Since the solution is neutral, we have:
[H+] = [OH-] = 3.7 x 10^-4 M

Taking the negative logarithm of both sides, we get:
pH = -log[H+] = -log(3.7 x 10^-4) = 5.18

Therefore, the answer is choice B.

Calculate the PH of a 1