Question #1809d
1 Answer
Explanation:
Start by using the known pH of the solution to find the molarity of the hydrogen ions,
So, you know that quinine's conjugate acid,
#"OH"_text((aq])^(+) -> "Q"_text((aq]) + "H"_text((aq])^(+)#
The concentration of the conjugate acid is simply the ratio between the number of moles you have and the volume of the solution
#["QH"^(+)] = "0.23 moles"/"1.0 L" = "0.23 M"#
The concentration of
#["H"^(+)] = 10^(-"pH") = 10^(-4.58) = 2.63 * 10^(-5)"M"#
Since the dissociation reactrion produces equal numbers of moles of
#["Q"] = ["H"^(+)] = 2.63 * 10^(-5)"M"#
The acid dissociation constant for this equilibrium will thus be
#K_a = (["Q"] * ["H"^(+)])/(["QH"^(+)])#
#K_a = (2.63 * 10^(-5) * 2.63 * 10^(-5))/0.23 = 2.7 * 10^(-9)#
Finally, to get the base dissociation constant,
#K_a * K_b = K_W" "# , where
This means that
#K_b = K_W/K_a = 10^(-14)/(2.7 * 10^(-9)) = color(green)(3.7 * 10^(-6))#