Problem 35 - General Chemistry: Principles and Modern Applications

Question

A 275 mL sample of vapor in equilibrium with 1-propylamine at \(25.0^{\circ} \mathrm{C}\) is removed and dissolved in \(0.500 \mathrm{L} \mathrm{H}_{2} \mathrm{O} .\) For 1 -propylamine, \(\mathrm{p} K_{\mathrm{b}}=3.43\) and v.p. \(=316\) Torr. (a) What should be the pH of the aqueous solution? (b) How many \(\mathrm{mg}\) of \(\mathrm{NaOH}\) dissolved in \(0.500 \mathrm{L}\) of water give the same pH?

Step-by-Step Solution

Answer

(a) The pH of the aqueous solution should be 11.79. (b) 122.6 mg of NaOH dissolved in 0.500 L of water will give the same pH.

Step 1: Calculate the concentration of 1-propylamine

\[n = PV/RT \]\[n = (316 Torr)(275 mL) / (62.364 L Torr /mol K)(298.15 K) = 0.00462 mol\]\[C = n/V = 0.00462 mol/0.500 L = 0.00923 M\]

Step 2: Calculate the hydroxide ion concentration

For base ionization of 1-propylamine: \n\[NH3 + H2O <=> NH4+ + OH-\]Kb = [NH4+][OH-] / [NH3]. Hence, \[OH-] = √(Kb * [NH3])\]First, calculate Kb from pKb: \n\[Kb = 10^-(pKb) = 10^-3.43 = 3.72 \times 10^-4\]Next, calculate [OH-]:\n\[[OH-] = √((3.72 \times 10^-4) * 0.00923) = 6.13 \times 10^-3 M\]

Step 3: Calculate the pH of the solution

First, calculate pOH from [OH-]: \n\[pOH = -log[OH-] = -log(6.13 \times 10^-3) = 2.21\]Then, calculate pH: \n\[pH = 14 - pOH = 14 - 2.21 = 11.79\]

Step 4: Calculate the concentration of NaOH

Since NaOH is a strong base and fully dissociates in water, the [OH-] is the same as the concentration of the NaOH, which is [OH-] = 6.13 \times 10^-3 M.

Step 5: Calculate the mass of NaOH

\[n = C \times V = (6.13 \times 10^-3 M) \times (0.500 L) = 3.065 \times 10^-3 mol\]Then, calculate the mass: \n\[m = n \times MW = 3.065 \times 10^-3 mol \times 40 g/mol = 0.1226 g\],or convert to mg: \n\[m = 0.1226 g \times 1000 mg/g = 122.6 mg\]

Key Concepts

1-propylamine

1-propylamine is an organic compound, specifically an amine. Amines are derived from ammonia and have one or more alkyl groups replacing hydrogen atoms. In terms of structure, 1-propylamine consists of a three-carbon chain (propyl group) attached to an amino group (-NH2). This makes it a primary amine because the nitrogen atom is connected to one carbon chain. Amines like 1-propylamine are often bases, meaning they can accept protons. This chemical reactivity is crucial in various processes, including pH adjustments in solutions.
Being a base, 1-propylamine reacts with water to form hydroxide ions (OH⁻), thereby increasing the pH of the solution it is in. Understanding this behavior is fundamental for calculating pH when working with aqueous solutions that contain amines.

pH calculation

When calculating the pH of a solution, it's important to first consider whether the substance is an acid or a base. In our case, 1-propylamine is a base, so it must be treated differently than acids. The key steps in determining the pH of a base like 1-propylamine involve using the substance's base dissociation constant (Kb) or its corresponding pK_b. This value helps us figure out how much the base will dissociate in solution. First, you convert pK_b to Kb using the formula: \[ Kb = 10^{-pK_b} \]Once you have Kb, you can find the concentration of hydroxide ions ([OH⁻]) through the equation:\[ [OH^-] = √{Kb \times [1-propylamine]} \]After finding [OH⁻], it can be converted to pOH by:\[ pOH = -\log[OH^-] \]Finally, relate pOH to pH with:\[ pH = 14 - pOH \]This series of calculations allows precise determinations of the pH level for a given 1-propylamine solution. Understanding these steps is important for grasping how bases influence solution pH.

aqueous solution chemistry

Aqueous solution chemistry refers to chemical reactions and processes that occur in water. Water is a polar solvent, meaning it can dissolve many substances, including bases like 1-propylamine. When substances dissolve in water, they may dissociate into ions. For instance, when 1-propylamine dissolves, it can form hydroxide ions (OH⁻), influencing the pH. In any aqueous solution:

• Substances that release ions upon dissolving are called electrolytes.
• Solutions have different concentrations depending on the amount of solute dissolved.
• The properties of water, such as its high dielectric constant, help it dissolve many ionic compounds.

For pH calculations, the behavior of dissolved substances in water is critical. For instance, strong bases fully dissociate, whereas weak bases like 1-propylamine partially dissociate. This partial dissociation affects how we calculate hydroxide ion concentration and ultimately the solution's pH. By understanding how substances interact in aqueous solutions, you can predict and calculate changes in pH correctly.