Problem 152 - General Chemistry

Question

The \(\mathrm{pH}\) of a household cleaning solution is \(11.50 .\) This cleanser is an aqueous solution of ammonia with a density of \(1.00 \mathrm{~g} / \mathrm{mL}\). What is the mass percentage of ammonia in the solution?

Step-by-Step Solution

Answer

The mass percentage of ammonia in the solution is approximately 0.00538%.

Step 1: Understand the Concept of pH and Ammonia

The pH of a solution indicates its acidity or basicity. A pH of 11.50 denotes a basic solution. Ammonia (\(\text{NH}_3\)) is a weak base that partially dissociates in water. The pH is related to the concentration of hydroxide ions (OH\(-\)) in the solution.

Step 2: Calculate Hydroxide Ion Concentration

To determine the hydroxide ion concentration in the solution, use the formula for pH and pOH: \[\text{pOH} = 14 - \text{pH} = 14 - 11.50 = 2.50\]Then calculate \([\text{OH}^-]\) using the formula \([\text{OH}^-] = 10^{-\text{pOH}}\): \[\text{[OH]}^- = 10^{-2.50} \approx 3.16 \times 10^{-3} \text{ M}\]

Step 3: Use Ammonia Equilibrium to Find NH₃ Concentration

Since it's given that ammonia is a weak base and only partially dissociates, we can use the equilibrium expression for ammonia:\[\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-\]To simplify, assume the initial concentration of NH\(\text{\(_3 ext{\)}\) is approximately equal to \([\text{OH}^-]\) because ammonia is primarily responsible for the hydroxide ions.

Step 4: Calculate Mass of Ammonia in 1 Liter Solution

The concentration of NH\(\text{\(_3\)}\) is about 3.16 \(\times 10^{-3}\) M. Calculate the number of moles of NH\(\text{\(_3\)}\) in 1 L of solution:\[\text{moles of NH}_3 = 3.16 \times 10^{-3} \text{ mol/L} \times 1 \text{ L} = 3.16 \times 10^{-3} \text{ mol}\]Using the molar mass of NH\(\text{\(_3\)}\) (17.03 g/mol), find the mass:\[\text{mass of NH}_3 = 3.16 \times 10^{-3} \text{ mol} \times 17.03 \text{ g/mol} \approx 0.0538 \text{ g}\]

Step 5: Calculate Mass Percentage of Ammonia

The density of the solution is given as 1.00 g/mL, so the mass of 1 L (1000 mL) of the solution is 1000 g. The mass percentage is calculated using:\[\text{mass percentage} = \left(\frac{\text{mass of NH}_3}{\text{total mass of solution}}\right) \times 100\]Substitute the values:\[\text{mass percentage} = \left(\frac{0.0538 \text{ g}}{1000 \text{ g}}\right) \times 100 \approx 0.00538\%\]

Key Concepts

Mass Percentage Calculation

When calculating the mass percentage, it's important to understand what it represents. Mass percentage is used to denote the concentration of a particular component (in this case, ammonia) within a mixture. It tells us how much of that component is present, as a percentage of the total mass of the solution.

To calculate this, you use the formula:

• Mass percentage = \( \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100 \)

In this exercise, the mass of the ammonia was determined to be approximately 0.0538 grams in a total solution mass of 1000 grams. Substituting these values into the formula gives the mass percentage of ammonia in the solution as about 0.00538%.

This is a measure of how dilute the solution is, and it tells us how much of the solution's mass is made up by ammonia. Having a lower mass percentage means that ammonia is present in smaller quantities compared to the entire solution.

Ammonia Solution

Ammonia solution is a combination of ammonia gas dissolved in water. Often found in household cleaning products, it’s a colorless, strong-smelling liquid. It’s important to note that ammonia is a weak base.

• Ammonia formula: \( \text{NH}_3 \)
• Characteristics: Weak base, volatile, irritating smell.

In a weak base solution like ammonia, not all ammonia molecules dissociate completely into ions. It’s this partial ionization that results in the solution exhibiting basic characteristics, such as a high pH level. In our case, with the pH given as 11.50, it shows a relatively strong basicity for a household cleaner.

Its significance lies in its cleaning action and acting as a precursor to nitrogen-containing compounds. Understanding its properties helps in explaining why ammonia is effective in cleaning and stain removal.

Weak Base Equilibrium

Weak base equilibrium involves a balance of ammonia and its dissociated ions in water. For ammonia, the equilibrium can be represented as follows:\[ \text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^- \]In this expression, ammonia (\(\text{NH}_3\)) reacts with water (\(\text{H}_2\text{O}\)) to form ammonium ions (\(\text{NH}_4^+\)) and hydroxide ions (\(\text{OH}^-\)).

• The extent of this reaction is limited, meaning it doesn’t go to completion.
• This partial dissociation is why ammonia is classified as a weak base.

Understanding this equilibrium is crucial for calculating the concentration of hydroxide ions, which in turn helps in determining the pH and overall characteristics of the solution. With pH being influenced by the presence of \(\text{OH}^-\) ions, it demonstrates how the weak base partially contributes to the overall basicity of the solution.

Grasping weak base equilibrium is important for interpreting how small changes in concentration can impact the solution's properties significantly.