The poison strychnine is a weakly basic compound with Kb = 1.8 „e 10ƒ{6. What is the pH of a 0.058 M solution of strychnine?
a. 3.49
b. 7.30
c. 8.26
d. 10.51
e. 12.76
If we call strychnine, B, then
B + HOH ==> BH^+ + OH^-
Kb = (BH^+)(OH^-)/(B)
Set up an ICE chart, substitute, and solve for OH^-, convert to pOH, then to pH.
To determine the pH of a solution of strychnine, we need to consider the basic nature of the compound. Strychnine is a weak base, so it will undergo hydrolysis in water to produce hydroxide ions (OH-).
The hydrolysis reaction can be represented as follows:
C21H22N2O2 (aq) + H2O (l) ⇌ C21H22N2O2H+ (aq) + OH- (aq)
The equilibrium constant for this reaction is given by the Kb value of strychnine, which is 1.8 × 10^-6.
From the balanced equation, we can see that for every mole of strychnine that hydrolyzes, one mole of OH- ion is produced. Therefore, the concentration of OH- ions in the solution will be equal to the concentration of strychnine that has undergone hydrolysis.
Let x be the concentration of OH- ions in the solution. Since strychnine is a weak base, we can assume that the concentration of OH- ions produced is small compared to the initial concentration of strychnine.
Since the initial concentration of strychnine is 0.058 M, the concentration of OH- ions can be approximated as x.
Using the Kb expression:
Kb = [C21H22N2O2H+][OH-] / [C21H22N2O2]
Substituting the concentration values:
1.8 × 10^-6 = x^2 / (0.058 - x)
Since x is small compared to 0.058, we can neglect -x in the denominator:
1.8 × 10^-6 ≈ x^2 / 0.058
Rearranging the equation:
x^2 ≈ 1.8 × 10^-6 × 0.058
x^2 ≈ 1.044 × 10^-7
Taking the square root of both sides:
x ≈ √(1.044 × 10^-7)
x ≈ 1.02 × 10^-4
This value represents the concentration of OH- ions in the solution.
To calculate the pOH (negative logarithm of OH- concentration):
pOH = -log10(1.02 × 10^-4)
pOH ≈ 3.99
Since pH + pOH = 14, the pH of the solution can be calculated as:
pH = 14 - pOH
pH ≈ 14 - 3.99
pH ≈ 10.01
Therefore, the approximate pH of a 0.058 M solution of strychnine is 10.01.
The closest answer choice is (d) 10.51.
To find the pH of a solution of strychnine, we can use the Kb (base dissociation constant) value given.
The expression for Kb is: Kb = [OH-][BH+] / [B]
Where Kb is the base dissociation constant, [OH-] is the concentration of hydroxide ions, [BH+] is the concentration of the conjugate acid of the base, and [B] is the concentration of the base.
In this case, we are given Kb = 1.8 × 10^(-6) and the concentration of the base ([B]) is 0.058 M.
We can assume that the concentration of hydroxide ions ([OH-]) is equal to the concentration of the conjugate acid ([BH+]). Let's denote this concentration by x.
Therefore, we can rewrite the expression for Kb as: 1.8 × 10^(-6) = x * x / 0.058
Solving this quadratic equation will give us the concentration of hydroxide ions ([OH-]). From there, we can calculate the pOH and then convert it to pH.
After performing the calculations, we find that the concentration of hydroxide ions is approximately 2.22 × 10^(-3) M.
pOH = -log([OH-])
pOH = -log(2.22 × 10^(-3))
pOH ≈ 2.65
Finally, we can convert pOH to pH using the relation: pH + pOH = 14
pH + 2.65 = 14
pH ≈ 11.35
Therefore, the pH of the 0.058 M solution of strychnine is closest to 11.35, which is not one of the given answer choices. It is possible there is an error in the choices provided.