Diethylamine (C2H5)2NH, is a weak base that ionizes in water,a 0.600 M solution of (C2H5)2NH is 4.65% ionized at 25 degrees Celsius.
-Calculate the pH of the solution.
-Calculate the Kb for diethylamine.
Let's call diethylamine simply BNH.
.......BNH + HOH ==> BNH2^+ + OH^-
I.....0.600...........0........0
C........-x............x........x
E......0.600-x........x.........x
%ionization = 4.65%; therefore,
x = (BNH^+) = (OH^-) = 0.600 x 0.0465
pOH = -log(OH^-) and yo have OH^-
Then pH + pOH = pKw = 14. You have pOH and 14, solve for pH.
Then substitute the values in the E line into Kb expression and solve for Kb.
To calculate the pH of the solution and the Kb for diethylamine, we first need to determine the concentration of the hydroxide ions (OH-) produced by the ionization of the diethylamine.
1. Calculate the concentration of hydroxide ions (OH-) from the percentage ionization:
Since the solution is 4.65% ionized, we can calculate the concentration of OH- using the formula:
[OH-] = (Percentage of ionization / 100) * initial concentration
[OH-] = (4.65 / 100) * 0.600 M
2. Calculate the concentration of the remaining unreacted diethylamine (C2H5)2NH:
The amount of diethylamine that ionizes is equal to the amount of OH- produced. Therefore, the remaining concentration of (C2H5)2NH is equal to the initial concentration minus the concentration of OH- ions.
[C2H5)2NH] = initial concentration - [OH-]
3. Calculate the pOH:
pOH = -log10[OH-]
4. Calculate the pH:
Since pH + pOH = 14 (at 25 degrees Celsius), we can find the pH by subtracting the pOH value from 14.
Now, let's calculate the values:
1. [OH-] = (4.65 / 100) * 0.600 M
[OH-] = 0.0279 M
2. [C2H5)2NH] = 0.600 M - 0.0279 M
[C2H5)2NH] = 0.572 M
3. pOH = -log10[OH-]
pOH = -log10(0.0279)
pOH ≈ 1.554
4. pH = 14 - pOH
pH ≈ 14 - 1.554
pH ≈ 12.446
Therefore, the pH of the diethylamine solution is approximately 12.446.
To calculate the Kb for diethylamine, we can use the equation:
Kw = Ka x Kb
Kw is the ion product of water and has a constant value of 1.0 x 10^-14 at 25 degrees Celsius.
Ka is the acid dissociation constant of the conjugate acid of diethylamine. Since diethylamine is a weak base, its conjugate acid is a weak acid.
1. Calculate Kw:
Kw = 1.0 x 10^-14
2. Determine Ka:
Since diethylamine is a weak base, its conjugate acid will be a weak acid. The Ka value is not given directly, but we can assume it is very small.
Therefore, we can approximate Ka as "x" and Kb as "x" as well.
3. Calculate Kb using the equation:
Kw = Ka x Kb
1.0 x 10^-14 = x * x
x^2 = 1.0 x 10^-14
x = √(1.0 x 10^-14)
Therefore, the Kb value for diethylamine is approximately √(1.0 x 10^-14).
Please note that the exact value may have to be calculated using a calculator or scientific notation.