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Chapter 16: Problem 56

The pH of a \(0.30 M\) solution of a weak base is 10.66 . What is the \(K_{\mathrm{b}}\) of the base?

Short Answer

Expert verified
The \(K_{\mathrm{b}}\) of the base is \(6.97 脳 10^-9\).

Step by step solution

01

Convert pH to pOH

The pOH of a solution can be found by subtracting the pH from 14: pOH = 14 - pH. Using the given pH of 10.66 will give a pOH of 14 - 10.66 = 3.34
02

Convert pOH to OH鈭� concentration

The concentration of OH鈭� ions (also known as hydroxide ions) can be calculated from the pOH value. As the pOH is the negative logarithm of the OH鈭� concentration, use this formula to find the OH鈭� concentration: [OH鈭抅 = 10^(-pOH). So, [OH鈭抅 = 10^(-3.34) = 4.57 脳 10^-4 M.
03

Find the ion concentration [BH+]

Because the solution is a weak base, the concentration of the corresponding acid [BH+] is the same as the hydroxide concentration. Therefore, [BH+] = [OH鈭抅 = 4.57 脳 10^-4 M.
04

Calculate the Kb value using the formula

The equilibrium constant Kb can be calculated using the formula for weak base reactions (Kb = [BH+][OH-]/[B]). Now plug in the calculated values: Kb = (4.57 脳 10^-4 M) * (4.57 脳 10^-4 M) / (0.30 M - 4.57 脳 10^-4 M). The term involving the subtraction can be approximated as 0.30 M, as M is much larger than 4.57 脳 10^-4 M. Therefore, Kb = (4.57 脳 10^-4 M)^2 / 0.30 M = 6.97 脳 10^-9.

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Most popular questions from this chapter

Without referring to the text, write the formulas of four strong acids and four weak acids.

Hydrocyanic acid (HCN) is a weak acid and a deadly poisonous compound that, in the gaseous form (hydrogen cyanide), is used in gas chambers. Why is it dangerous to treat sodium cyanide with acids (such as HCl) without proper ventilation?

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