Question #90a90
1 Answer
Explanation:
First thing first, I think that you have some incorrect data in your question.
For example, if you use the information provided by the question, the molar conductivity of the chloroacetic solution will have different value than what you list here,
I assume that this value was supposed to be the molar conductivity at infinite dilution,
More specifically, this value should either be
#Lamda_0 = 362 * 10^(-4)"S m"^2"mol"^(-1)#
or
#Lamda_0 = "362 S cm"^2"mol"^(-1)#
With this being said, the equation that establishes a relationship between conductivity,
#color(blue)(Lamda = k/c)" "# , where
This is where things usually get a little tricky. You need to make sure that you use the right units. For example, molar concentration must be used in moles per cubic meter, which means that you must convert the given moles per liter
#0.0625"moles"/color(red)(cancel(color(black)("liter"))) * (10^3color(red)(cancel(color(black)("liters"))))/"1 m"^3 = 0.0625 * 10^(3)"mol m"^(-3)#
Likewise, notice that the conductivity uses
#3.319 * 10^(-3)"S"/color(red)(cancel(color(black)("cm"))) * (10^2color(red)(cancel(color(black)("cm"))))/"1 m" = 3.319 * 10^(-1)"S m"^(-1)#
The molar conductivity of the solution will thus be
#Lamda = (3.319 * 10^(-1)"S m"^(-1))/(0.0625 * 10^3"m"^(-3)) = 5.3104 * 10^(-3) "S m"^(-2)"mol"^(-1)#
Now, the equation that connects the degree of ionization of a weak electrolyte,
#alpha = Lamda/Lamda_0#
In your case, the degree of dissociation for chloroacetic acid will be - keep in mind that
#alpha = (5.3104 * 10^(-3)color(red)(cancel(color(black)("S m"^(-2)"mol"^(-1)))))/(362 * 10^(-4)color(red)(cancel(color(black)("S m"^(-2)"mol"^(-1))))) = color(green)(0.147)#
The acid dissociation constant,
#color(blue)(K_a = alpha^2/(1 - alpha) * c)#
In your case, the value of
#K_a = (0.147^2)/(1-0.147)^2 * "0.0625 M" = color(green)(1.86 * 10^(-3)"M")#
The listed value for the acid dissociation constant of chloroacetic acid is
You can check this result by using the molar conductivity
#color(blue)(K_a = Lamda^2/((Lamda_0 - Lamda) * Lamda_0) * c)#
This calculation will give you
#K_a = 1.58 * 10^(-3)"M"#