Methylamine, CH3 NH2, is a gas at room temperature and very...

Methylamine, $\mathrm{CH}_{3} \mathrm{NH}_{2},$ is a gas at room temperature and very soluble in water. An aqueous solution of methylamine has $K_{\mathrm{b}}=4.2 \times 10^{-4}$. How many liters of methylamine at $27^{\circ} \mathrm{C}$ and a pressure of 1.2 atm should be bubbled into $0.750 \mathrm{~L}$ of a solution that is $0.588 \mathrm{M}$ in the methylammonium ion, $\mathrm{CH}_{3} \mathrm{NH}_{3}^{+},$ so that a buffer of $\mathrm{pH} 9.80$ is obtained? Assume no volume changes after methylamine is bubbled into the solution and ignore the vapor pressure of water.

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. This relationship is used to calculate how many moles of a gaseous reactant are added to a solution when the gas is bubbled into it under specified conditions. Such calculations are essential when determining the amount of gas required to achieve the desired concentration in a solution.

Equilibrium Constant Relationships

Equilibrium constants such as Kb for bases and Ka for acids describe the extent of the dissociation of weak bases or acids in solution. A relationship exists between Ka and Kb for a conjugate acid-base pair through the ion product of water (Kw). Understanding and utilizing these constants allows chemists to predict the behavior of acid-base systems and to calculate the concentrations necessary for buffering.

Buffer Solutions

A buffer solution is a system composed of a weak acid and its conjugate base, or a weak base and its conjugate acid, that resists changes in pH upon the addition of small amounts of acid or base. In this context, the solution is buffering pH by having both the conjugate acid (methylammonium ion) and the weak base (methylamine) present, allowing it to maintain a nearly constant pH even when additional acid or base is introduced.

Conjugate Acid-Base Pairs

Conjugate acid-base pairs consist of two species that differ by the gain or loss of a proton. In acid-base equilibria, the strength of a weak acid is related to the strength of its conjugate base. For example, the methylammonium ion is the conjugate acid of methylamine, and their interconversion is central to the buffering action in solution.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a relationship between the pH of a buffer solution, the pKa (or pKb) of its acid (or base), and the ratio of concentrations of the conjugate base and acid. This equation is instrumental for calculating the necessary proportions of acid and base components required to achieve a desired pH in a buffer solution.

Transcript

Please give Ace some feedback