What volumes of 50 mM #CH_3COOH# and 30 mM #NaCH_3COO# solutions are needed to prepare 2L of 20 mM acetate buffer pH 3.6? (#pK_a# for acetic acid is 4.74)

Question

Peyton Adams · Accepted Answer

WARNING! Long answer! You need to mix 750 mL of acetic acid with 90 mL of sodium acetate and add enough water to make 2 L of buffer.

The strategy to follow is 1) Write the chemical equation for the buffer. 2) Calculate the concentration ratio of #"CH"_3"COOH"# and #"CH"_3"COONa"#. 3) Calculate the molar ratio of #"CH"_3"COOH"# and #"CH"_3"COONa"# . 4) Calculate the moles of #"CH"_3"COOH"# and #"CH"_3"COONa"#. 4) Calculate the volumes of #"CH"_3"COOH"# and #"CH"_3"COONa"#. 1) Chemical equation #"HA" + "H"_2"O" ⇌ "H"_3"O"^(+) + "A"^"-"#; #"p"K_text(a) = 4.74# 2) Calculate the concentration ratio We use the Henderson-Hasselbalch equation to calculate the concentration ratio. #"pH" = "p"K_"a" + log(("[A"^"-""]")/"[HA]")# #3.6 = 4.74 + log(("[A"^"-""]")/"[HA]")# #log(("[A"^"-""]")/"[HA]") = "3.6 - 4.74" = -1.14# #log(("[HA]")/("[A"^"-""]")) = 1.14# #("[HA]")/("[A"^"-""]") = 10^1.14 = 13.8# #"[HA]" = "13.8[A"^"-""]"# 3) Calculate the molar ratio Since both the acetic acid and the sodium acetate are in the same solution, the ratio of their concentrations is the same as the ratio of their moles. That is, #n_"HA" = 13.8n_"A⁻"# 4) Calculate the moles #"Total moles" = 2 "L" × "20 mmol"/(1 "L") = "40 mmol"# #n_"HA" + n_"A⁻" = 13.8n_"A⁻" + n_"A⁻" = 14.8n_"A⁻" = "40 mmol"# #n_"A⁻" = "40 mmol"/14.8 = "2.70 mmol"# ∴ #n_"HA" = ("40-2.70) mmol" = "37.3 mmol"# 5) Calculate the volumes #V_"HA" = 37.3 color(red)(cancel(color(black)("mmol HA"))) × "1 L HA"/(50 color(red)(cancel(color(black)("mmol HA")))) = "0.75 L HA" = "750 mL HA"# #V_"HA" = 2.70 color(red)(cancel(color(black)("mmol A⁻"))) × "1 L A⁻"/(30 color(red)(cancel(color(black)("mmol A⁻")))) = "0.090 L A⁻" = "90 mL A⁻"# Thus, you mix 750 mL of the acetic acid with 90 mL of the sodium acetate and add enough water to make 2 L of pH 3.6 buffer.

Naomi Aronson · Answer

undefined To prepare the buffer solution, you would need 1.6 liters of the 50 mM CH3COOH solution and 0.4 liters of the 30 mM NaCH3COO solution.