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Chapter 16: Problem 73

Calculate the molar concentration of \(\mathrm{OH}^{-}\) ions in a \(0.075 \mathrm{M}\) solution of ethylamine \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} ; K_{b}=6.4 \times 10^{-4}\right) .\) Calcu- late the \(\mathrm{pH}\) of this solution.

Short Answer

Expert verified
The molar concentration of OH- ions in the 0.075 M solution of ethylamine is approximately 0.0068 M, and the pH of the solution is approximately 11.83.

Step by step solution

01

Write the balanced chemical equation for the dissociation of the weak base

The ethylamine, C2H5NH2, acts as a weak base and donates a proton to water (H2O) molecules, resulting in the formation of ethylammonium ions (C2H5NH3+) and hydroxide ions (OH-). The balanced chemical equation for this reaction is: C2H5NH2 (aq) + H2O (l) ⇌ C2H5NH3+ (aq) + OH- (aq)
02

Write the expression for the base dissociation constant (Kb)

The base dissociation constant, Kb, relates the equilibrium concentrations of products and reactants for the above reaction. Kb is given as: Kb = \(\frac{[C_{2}H_{5}NH_{3}^{+}][OH^{-}]}{[C_{2}H_{5}NH_{2}]}\)
03

Set up a table for the calculation of equilibrium concentrations

We will call the change in concentration of C2H5NH2, C2H5NH3+, and OH- by x. At equilibrium, we can express their concentrations as: [C2H5NH2] = 0.075 - x [C2H5NH3+] = x [OH-] = x
04

Substitute the expressions and Kb into the equation

Substitute the concentration terms and given Kb value into the equation: \(6.4 \times 10^{-4}\) = \(\frac{x^2}{0.075-x}\)
05

Simplify and solve for x

Since the dissociation of the weak base is minimal, we can assume that x is very small compared to 0.075. So, the equation simplifies to: \(6.4 \times 10^{-4}\) ≈ \(\frac{x^2}{0.075}\) Solving for x, we get: x ≈ \(\sqrt{(6.4 \times 10^{-4})(0.075)}\) x ≈ 0.0068 M
06

Calculate the pOH and pH of the solution

Now that we have the concentration of OH- ions, we can calculate the pOH and then the pH of the solution. The pOH is given by: pOH = -log[OH-] pOH = -log(0.0068) pOH ≈ 2.17 Since pH + pOH = 14, we can find the pH: pH = 14 - pOH pH = 14 - 2.17 pH ≈ 11.83 The molar concentration of OH- ions in the 0.075 M solution of ethylamine is approximately 0.0068 M, and the pH of the solution is approximately 11.83.

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Most popular questions from this chapter

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.

Calculate the \(\mathrm{pH}\) of each of the following strong acid solutions: (a) \(0.0167 \mathrm{M} \mathrm{HNO}_{3},\) (b) \(0.225 \mathrm{~g}\) of \(\mathrm{HClO}_{3}\) in \(2.00 \mathrm{~L}\) of solution, (c) \(15.00 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\) diluted to \(0.500 \mathrm{~L}, (\mathrm{~d})\) a mixture formed by adding \(50.0 \mathrm{~mL}\) of \(0.020 \mathrm{M} \mathrm{HCl}\) to \(125 \mathrm{~mL}\) of \(0.010 \mathrm{M} \mathrm{HI}\)

The odor of fish is due primarily to amines, especially methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\). Fish is often served with a wedge of lemon, which contains citric acid. The amine and the acid react forming a product with no odor, thereby making the lessthan-fresh fish more appetizing. Using data from Appendix \(D\), calculate the equilibrium constant for the reaction of citric acid with methylamine, if only the first proton of the citric acid \(\left(K_{a 1}\right)\) is important in the neutralization reaction.

Label each of the following as being a strong acid, a weak acid, or a species with negligible acidity. In each case write the formula of its conjugate base, and indicate whether the conjugate base is a strong base, a weak base, or a species with negligible basicity: (a) \(\mathrm{HCOOH},\) (b) \(\mathrm{H}_{2},\) (c) \(\mathrm{CH}_{4}\), (d) \(\mathrm{HF}\) (e) \(\mathrm{NH}_{4}^{+}\).

If a substance is a Lewis acid, is it necessarily a Bronsted-Lowry acid? Is it necessarily an Arrhenius acid? Explain.
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