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Chapter 16: Problem 75

Ephedrine, a central nervous system stimulant, is used in nasal sprays as a decongestant. This compound is a weak organic base: \(\mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ON}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ONH}^{+}(a q)+\mathrm{OH}^{-}(a q)\) (a) What A \(0.035 \mathrm{M}\) solution of ephedrine has a pH of 11.33 . are the equilibrium concentrations of \(\mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ON}\), \(\mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ONH}^{+},\) and \(\mathrm{OH}^{-} ?\) (b) Calculate \(K_{b}\) for ephedrine.

Short Answer

Expert verified
The short version of the answer is: 1. Calculate the concentration of OH- ions from the given pH: pOH = 14 - pH and [OH⁻] = $10^{-pOH}$. 2. Set up the ICE table and add the change in concentration term 'x'. 3. Plug equilibrium concentrations into the Kb expression and solve for x. 4. Use the value of x to determine the equilibrium concentrations of C10H15ON, C10H15ONH⁺, and OH⁻ ions. 5. Plug equilibrium concentrations into the Kb expression to calculate Kb for ephedrine.

Step by step solution

01

Calculate the concentration of OH- ions from the given pH

The given pH of the solution is 11.33. We can find the pOH of the solution by subtracting the pH from 14 (since pH + pOH = 14). Then, we can calculate the concentration of OH- ions using the formula for pOH: \[pOH = -\log_{10} [OH^{-}]\]
02

Set up the ICE table

An ICE table represents the initial, change, and equilibrium concentrations for each species in the reaction. We will set up an ICE table for ephedrine, its conjugate acid, and hydroxide ions. Initial concentrations: - [C10H15ON]: 0.035 M - [C10H15ONH+]: 0 - [OH-]: Value calculated in Step 1 Change in concentration: - C10H15ON: -x - C10H15ONH+: +x - OH-: +x Equilibrium concentrations: - [C10H15ON]: 0.035 - x - [C10H15ONH+]: x - [OH-]: Value calculated in Step 1 + x
03

Use the Kb expression and equilibrium concentration values to find x

The Kb expression for this reaction is: \[K_b = \frac{[C_{10}H_{15}ONH^{+}] [OH^{-}]}{[C_{10}H_{15}ON]}\] We will plug in the equilibrium concentrations from the ICE table into the Kb expression and solve for x.
04

Calculate the equilibrium concentrations of the species

Using the value of x, we can now calculate the equilibrium concentrations of C10H15ON, C10H15ONH+, and OH- ions by plugging the value of x into the equilibrium concentrations from the ICE table.
05

Determine the Kb value for ephedrine

Now that we have the equilibrium concentrations of all three species, we can plug these values into the Kb expression and solve for Kb: \[K_b = \frac{[C_{10}H_{15}ONH^{+}] [OH^{-}]}{[C_{10}H_{15}ON]}\]

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Most popular questions from this chapter

Phenylacetic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\right)\) is one of the substances that accumulates in the blood of people with phenylketonuria, an inherited disorder that can cause mental retardation or even death. A \(0.085 \mathrm{M}\) solution of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{COOH}\) has a \(\mathrm{pH}\) of \(2.68 .\) Calculate the \(K_{a}\) value for this acid.

(a) What is a strong acid? (b) A solution is labeled \(0.500 \mathrm{M}\) HCl. What is \(\left[\mathrm{H}^{+}\right]\) for the solution? (c) Which of the following are strong acids: \(\mathrm{HF}, \mathrm{HCl}, \mathrm{HBr}, \mathrm{HI?}\)

Calculate the percent ionization of propionic acid \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right)\) in solutions of each of the following concentrations \(\left(K_{a}\right.\) is given in Appendix \(\left.D\right):\) (a) \(0.250 \mathrm{M}\), (b) \(0.0800 \mathrm{M}\), (c) \(0.0200 \mathrm{M}\).

Identify the Lewis acid and Lewis base in each of the following reactions: (a) \(\mathrm{HNO}_{2}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{NO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) \(\mathrm{FeBr}_{3}(s)+\mathrm{Br}^{-}(a q) \rightleftharpoons \mathrm{FeBr}_{4}^{-}(a q)\) (c) \(\mathrm{Zn}^{2+}(a q)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q)\) (d) \(\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)\)

Calculate the concentration of an aqueous solution of \(\mathrm{NaOH}\) that has a pH of \(11.50 .\)
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