Answer:
8.4g of NH₄Br the student need to dissolve into the solution.
Step-by-step explanation:
Full question is:
A chemistry graduate student is given 300 mL of a 0.20 M ammonia (NH3) solution. Ammonia is a weak base with Kb = 1.8 x10^-5. What mass of NH4Br should the student dissolve in the NH3 solution to turn it into a buffer with pH = 9.10?
Using H-H expression for weak bases, you can find pH of a buffer thus:
pOH = pKb + log [BH⁺] / [B]
Where pKb is -log Kb =4.744, [BH⁺] concentration of of conjugate acid, NH₄Br and [B] concentration of weak base, NH₃ (It is possible to take the moles of both compounds and not its concentration).
As pH the student wants is 9.10, pOH is:
pOH = 14 - pH = 14 - 9.10 = 4.90
Replacing this information in H-H equation:
4.90 = 4.744 + log [NH₄Br] / [NH₃]
Moles of NH₃ in the solution are:
300mL = 0.300L × (0.20mol / L) = 0.060mol NH₃
Knowing this:
4.90 = 4.744 + log [NH₄Br] / [0.06mol]
0.156 = log[NH₄Br] / [0.06mol]
1.4322 = [NH₄Br] / [0.06mol]
0.08593 moles = [NH₄Br]
To create the buffer of pH = 9.10, you need 0.08593 moles of NH₄Br
As molar mass of NH₄Br is 97.94g/mol, mass of 0.08593 moles are:
0.08593 moles NH₄Br × (97.94g / mol) =
8.4g of NH₄Br the student need to dissolve into the solution.