A 4.50e-2 M solution of unknown monoprotic weak base has a pH of 10.200 what is the value of kb for the base
BOH ==> B^+ + OH^-
Kb = (B^+)(OH^-)/(BOH)
pH = 10.2; therefore, pOH = 3.8
pOH = -log(OH^-). Solve for OH^- and substitute into Kb expression. For (BOH) substitute 0.045-(OH^-).
Post your work if you get stuck.
For pOH=-log(OH-) I solved to get OH=1.58e-4
then I did kb=(4.50e-2)(1.58e-4)/.045-1.58e-4 to get 1.59e-4 but that's not the right answer
To determine the value of the base dissociation constant (Kb) for an unknown monoprotic weak base, we can use the pH and concentration of the base solution.
First, let's understand the relationship between pH and pOH in an aqueous solution. The pH and pOH are complementary values related by the equation:
pH + pOH = 14
Given that the pH of the solution is 10.200, we can calculate the pOH as follows:
pOH = 14 - 10.200
pOH = 3.800
Next, let's calculate the concentration of hydroxide ions ([OH-]) using the pOH value.
pOH is defined as the negative logarithm of the hydroxide ion concentration:
pOH = -log[OH-]
Rearranging the equation, we get:
[OH-] = 10^(-pOH)
[OH-] = 10^(-3.800)
[OH-] = 1.58 x 10^(-4) M
Since the base is monoprotic, we know that the concentration of hydroxide ions ([OH-]) is equal to the concentration of the weak base ([B]). Therefore, the concentration of the weak base is also 1.58 x 10^(-4) M.
Finally, we can use the concentration of the base and the pH to calculate the base dissociation constant (Kb). The Kb is defined as the ratio of the concentration of the conjugate acid ([BH+]) to the concentration of the weak base ([B]):
Kb = [BH+][OH-] / [B]
Since [BH+] represents the concentration of the conjugate acid and [B] represents the concentration of the weak base, we can set up the equation as:
Kb = [BH+][OH-] / [B] = x(x) / (0.0158 - x)
where x is the concentration of the conjugate acid formed. Since the weak base is very weak, we can assume that the amount ionized is small compared to the initial concentration of the base. Therefore, the concentration of the conjugate acid formed can be approximated as x.
Kb = x * x / (0.0158 - x)
However, since [OH-] = x = 1.58 x 10^(-4) M, the equation simplifies to:
Kb = (1.58 x 10^(-4))^2 / (0.0158 - 1.58 x 10^(-4))
Now, we can calculate Kb using this equation:
Kb = (1.58 x 10^(-4))^2 / (0.0158 - 1.58 x 10^(-4))
After performing the calculations, the value of Kb for the unknown monoprotic weak base can be determined.