The much-abused drug cocaine is an alkaloid. Alkaloids are noted for their bitter taste, an indication their basic properties. Cocaine C17H21O4N, is soluble in water the the extent of 0.17g/100 mL solution, and a saturated solution has a PH = 10.08. What is the value of Kb for cocaine?

C17H21O4N + H2O --> <--- C17H21O4NH+ + OH- Kb = ?

I would appreciate if someone would do this problem without skipping any steps, I need to understand it completely for an exam. With the data 0.17g/100 mL how do I find M (concentration)? Thanks.

kb=2,6 x 10^-6

is it correct?

pH + pOH = 14

pOH = 14-10.08 = 3.92
[OH-]=-log^-1(3.92)=1.2002x10^-4
---------
Kb = [BH+][OH-] / [B], with B = base
here,
Kb = [C17H21O4NH+][OH-] / [C17H21O4N]
since [C17H21O4NH+]=[OH-]
Kb = [OH-]^2 / {[C17H21O4N]-[OH-]}
Since [OH-] is much smaller than the overall concentration of the base, we can approximate:
Kb = [OH-]^2 / [C17H21O4N]
--------------
Find the molarity of C17H21O4N and substitute it into the formula for Kb along with the value of [OH-].

If the solubility is 0.17 g/100 mL, that is equivalent to 1.7 g/1000 mL. And moles = grams/molar mass will give you the molarity.

Use the equation given.
You know pH, convert that to pOH, then to OH^-.
Kb = (C17H21O4NHH^+)(OH^-)/(C17H21O4N).
You know OH^- now, that is the same as C17H21O4NH^+, and the C17H21O4N is 1.7/molar mass - (OH^-). You may be able to neglect OH^- in the denominator if it is small in comparison to the cocaine molarity. Post your work if you get stuck.

Is 3.3*10^-9

To find the concentration in moles per liter (M) from the given data of solubility in grams per 100 mL, we need to follow a few steps.

Step 1: Convert the mass of solute to moles.
The molar mass of cocaine (C17H21O4N) can be calculated by adding up the atomic masses of its constituent elements:
C (12.01 g/mol) x 17 + H (1.01 g/mol) x 21 + O (16.00 g/mol) x 4 + N (14.01 g/mol) x 1 = 303.36 g/mol.

Using the given solubility data of 0.17 g/100 mL, we can set up a proportion to find the moles of cocaine:
0.17 g cocaine / 100 mL solution = x moles cocaine / (1000 mL/1 L) solution.

Simplifying this:
0.17 g cocaine = x moles cocaine * (100 mL/1000 mL)
0.17 g cocaine = x moles cocaine * 0.1

Solving for x, we have:
x = 0.17 g cocaine / 0.1

Step 2: Calculate the concentration (M) in moles per liter.
The volume of the solution is 1000 mL, which is equivalent to 1 liter.
Therefore, the concentration (M) can be calculated as follows:
M = x moles cocaine / 1 L solution = x moles cocaine / 1L.

By substituting the value of x obtained in Step 1 into this equation, we can find the concentration (M) of cocaine.

Now that we have the concentration (M), we can move on to finding the value of Kb for cocaine.

Given the equation of the dissociation of cocaine in water:
C17H21O4N + H2O ↔ C17H21O4NH+ + OH-

The dissociation constant Kb can be calculated by using the expression:
Kb = [C17H21O4NH+][OH-] / [C17H21O4N]
However, at equilibrium, the concentration of OH- will be equal to the concentration of C17H21O4NH+.

Thus, we can write the expression:
Kb = [C17H21O4NH+]^2 / [C17H21O4N]

Given the pH of the saturated solution (pOH = 14 - pH = 14 - 10.08 = 3.92), we can calculate the concentration of OH- as follows:
[OH-] = 10^(-pOH) mol/L

Using this concentration, we rearrange the expression and solve for Kb:
Kb = ([OH-])^2 / [C17H21O4N]

By substituting the known values into the equation, you will find the value of Kb for cocaine.

Remember to check your units during the calculations to ensure consistency.

No