Question

A chemistry graduate student is given 125 mL of a 0.10M dimethylamine ((CH₃)₂NH) solution. Dimethylamine is a weak base with Kb = 5.4 x 10⁻¹¹. What mass of (CH₃)₂NH₄Cl should the student dissolve in the (CH₃)₂NH solution to turn it into a buffer with pH = 10.38? (CH₃)₂NH₄Cl is dissolved in it. Be sure your answer has a unit. You may assume that the volume of the solution doesn't change when the symbol, and round it to 2 significant digits.

a) 7.5 g b) 15.0 g c) 22.5 g d) 30.0 g

Answer 1

The mass of (CH₃)₂NH₄Cl required is calculated by converting the desired pH to pOH, determining the hydroxide ion concentration, the dimethylammonium ion concentration, and finally calculating the mass of the conjugate salt needed to create the buffer.

Step-by-step explanation:

To determine the mass of (CH₃)₂NH₄Cl needed to create a buffer solution with a pH of 10.38, we first need to calculate the pOH using the formula pH + pOH = 14. This gives us a pOH of 3.62. Next, we use the formula pOH = -log[OH-], calculate the hydroxide ion concentration, and subsequently the dimethylammonium ion concentration using Kb for dimethylamine and the given concentration of the base solution.

With the ion concentration, we can calculate the moles of dimethylammonium ions we need and convert this to moles of (CH₃)₂NH₄Cl using the 1:1 stoichiometry between the base and its conjugate salt. Finally, we can find the mass of (CH₃)₂NH₄Cl using its molar mass. After performing the calculations, we can compare the result with the given options (a) 7.5 g, (b) 15.0 g, (c) 22.5 g, and (d) 30.0 g to find the correct answer.