Strychnine 1C21H22N2O22, a deadly poison used for killing rodents, is a weak base having Kb = 1.8 * 10-6. Calculate the pH of a saturated solution of strychnine (16 mg/100 mL).

검증된 단계별 안내

Convert the mass of strychnine to moles using its molar mass. First, find the molar mass of strychnine (C_{21}H_{22}N_{2}O_{2}) by adding the atomic masses of all the atoms in the formula.

Calculate the molarity of the strychnine solution by dividing the number of moles by the volume of the solution in liters.

Set up the equilibrium expression for the weak base dissociation of strychnine: \[ \text{C}_{21}\text{H}_{22}\text{N}_{2}\text{O}_{2} + \text{H}_2\text{O} \rightleftharpoons \text{C}_{21}\text{H}_{22}\text{N}_{2}\text{O}_{2}\text{H}^+ + \text{OH}^- \]

Use the K_b expression: \[ K_b = \frac{[\text{C}_{21}\text{H}_{22}\text{N}_{2}\text{O}_{2}\text{H}^+][\text{OH}^-]}{[\text{C}_{21}\text{H}_{22}\text{N}_{2}\text{O}_{2}]} \] to find the concentration of OH^- ions at equilibrium.

Calculate the pOH from the concentration of OH^- ions, and then use the relationship \( \text{pH} + \text{pOH} = 14 \) to find the pH of the solution.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Weak Bases and Kb

A weak base is a substance that partially ionizes in solution, establishing an equilibrium between the un-ionized base and its ions. The base dissociation constant (Kb) quantifies the strength of a weak base, indicating the extent to which it can accept protons from water. In this case, strychnine's Kb value of 1.8 x 10^-6 suggests it is a weak base, meaning it will not fully dissociate in solution.

pH Calculation

pH is a measure of the acidity or basicity of a solution, calculated as the negative logarithm of the hydrogen ion concentration. For basic solutions, the pH can be determined using the relationship between Kb and the concentration of hydroxide ions produced. In this scenario, the pH of the saturated strychnine solution can be calculated by first determining the concentration of hydroxide ions and then converting that to pH.

Saturation and Concentration

Saturation refers to the maximum concentration of a solute that can dissolve in a solvent at a given temperature. In this problem, the concentration of strychnine is given as 16 mg in 100 mL, which must be converted to molarity to relate it to the Kb value. Understanding how to calculate molarity from mass and volume is essential for determining the pH of the solution.