Problem 115 - Chemistry: The Central Science in SI Units, Global Edition

Question

Federal regulations set an upper limit of 50 parts per million (ppm) of \(\mathrm{NH}_{3}\) in the air in a work environment [that is, 50 molecules of \(\mathrm{NH}_{3}(g)\) for every million molecules in the air]. Air from a manufacturing operation was drawn through a solution containing \(1.00 \times 10^{2} \mathrm{~mL}\) of \(0.0105 \mathrm{MHCl} .\) The \(\mathrm{NH}_{3}\) reacts with HCl according to: $$ \mathrm{NH}_{3}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(a q) $$ After drawing air through the acid solution for \(10.0 \mathrm{~min}\) at a rate of \(10.0 \mathrm{~L} / \mathrm{min},\) the acid was titrated. The remaining acid needed \(13.1 \mathrm{~mL}\) of \(0.0588 \mathrm{M} \mathrm{NaOH}\) to reach the equivalence point. (a) How many grams of \(\mathrm{NH}_{3}\) were drawn into the acid solution? (b) How many ppm of \(\mathrm{NH}_{3}\) were in the air? (Air has a density of \(1.20 \mathrm{~g} / \mathrm{L}\) and an average molar mass of \(29.0 \mathrm{~g} / \mathrm{mol}\) under the conditions of the experiment.) (c) Is this manufacturer in compliance with regulations?

Step-by-Step Solution

Answer

(a) 0.00475524 g of NH3 were drawn into the acid solution. (b) The air contained 39.627 ppm of NH3. (c) Yes, the manufacturer is in compliance with the regulations.

Step 1: Initial moles of HCl

First, let's find the initial moles of HCl in the given solution. We know the volume of the solution and its molarity. The formula to calculate moles is: Moles = Molarity × Volume Where the volume is in liters. So, we have: Initial moles of HCl = 0.0105 M × (1.00 × 10^2 mL × (1 L / 1000 mL)) = 0.0105 × 0.100 L = 0.00105 mol

Step 2: Moles of HCl reacted with NaOH

The remaining HCl in the solution is titrated with NaOH. The volume and molarity of NaOH are given, we can now find out how many moles of HCl have reacted with NaOH. Moles = Molarity × Volume Moles of HCl reacted with NaOH = 0.0588 M × (13.1 mL × (1 L / 1000 mL)) = 0.0588 × 0.0131 L = 0.00077028 mol

Step 3: Moles of HCl reacted with NH3

Now, we will find out the moles of HCl that reacted with NH3. We will subtract the moles of HCl reacted with NaOH from the initial moles of HCl. Moles of HCl reacted with NH3 = Initial moles of HCl - Moles of HCl reacted with NaOH = 0.00105 mol - 0.00077028 mol = 0.00027972 mol

Step 4: Moles and mass of NH3

The moles of HCl reacted with NH3 is equal to the moles of NH3. From the balanced chemical equation, we know that the molar ratio between NH3 and HCl is 1:1. Therefore, the moles of NH3 can be found as: Moles of NH3 = 0.00027972 mol Now, we can find the mass of NH3 by using the molar mass of NH3 = 17 g/mol: Mass of NH3 = Moles × Molar mass = 0.00027972 mol × 17 g/mol = 0.00475524 g

Step 5: PPM of NH3

To find the ppm of NH3, we need to calculate the mass of air in grams. We know that the total volume of air is 10.0 L/min × 10.0 min = 100 L. We are given the density of air and its average molar mass. Mass of air = Volume × Density = 100 L × 1.20 g/L = 120 g Now, we can calculate the ppm of NH3: ppm of NH3 = (Mass of NH3 / Mass of air) × 10^6 = (0.00475524 g / 120 g) × 10^6 = 39.627 ppm

Step 6: Compliance with regulations

The manufacturer is in compliance with regulations if the ppm of NH3 is less than or equal to 50 ppm. Since the calculated ppm of NH3 is 39.627, the manufacturer is in compliance with the federal regulations. (a) Mass of NH3 = 0.00475524 g (b) ppm of NH3 = 39.627 ppm (c) Yes, the manufacturer is in compliance with the regulations.

Key Concepts

Ammonia Detection

In a work environment, monitoring ammonia (\(\text{NH}_3 \)) levels is critical for health and safety. Ammonia is a gas that can be harmful when inhaled, leading to irritation of the eyes, nose, throat, and respiratory tract. Detecting ammonia in the air helps ensure environments like industrial sites adhere to safety standards.
To measure \(\text{NH}_3 \), air samples can be passed through a solution where a chemical reaction will occur. In the original exercise, this was done using hydrochloric acid (\(\text{HCl} \)). The \(\text{NH}_3 \) reacts with \(\text{HCl} \) to form ammonium chloride (\(\text{NH}_4\text{Cl} \)). This reaction can be used to quantify how much ammonia was present in the air, by measuring how much \(\text{HCl} \) is left unreacted after the sample has been processed.
This method is effective for detecting and measuring small concentrations of gaseous ammonia, ensuring compliance with safety regulations.

Titration Calculations

Titration is a key analytical technique used to determine the concentration of a solute in a solution. In this exercise, titration was used to calculate how much \(\text{NH}_3 \) was in the original gas sample. The titration process involved using \(\text{NaOH} \) to find the remaining \(\text{HCl} \) in the solution.

• Initial Moles of \(\text{HCl} \): Known volume and molarity of \(\text{HCl} \) allows calculation of initial moles.
• Remaining Moles of \(\text{HCl} \): By titrating with \(\text{NaOH} \), the amount of \(\text{HCl} \) that did not react with \(\text{NH}_3 \) is determined.
• Moles of \(\text{NH}_3 \): The difference between initial and remaining moles of \(\text{HCl} \) gives moles of \(\text{NH}_3 \)

This systematic approach provides an accurate measurement of \(\text{NH}_3 \) levels.

Chemical Compliance Standards

Compliance with chemical safety standards is of utmost importance to ensure a safe working environment. These standards often specify maximum allowable concentrations of hazardous substances like \(\text{NH}_3 \) in the air. In this exercise, regulations stipulate that ammonia levels must not exceed 50 parts per million (ppm).
The calculation of ppm is achieved by comparing the mass of \(\text{NH}_3 \) to the total mass of the air sample tested. If the concentration is less than the specified limit, then the environment is deemed compliant. The original calculation showed an \(\text{NH}_3 \) concentration of 39.627 ppm, demonstrating compliance with federal safety regulations.

• PPM Measure: A metric used to express the concentration of one substance mixed with another.
• Regular Testing: Uses such precise measurements ensure safety over time and across different operational contexts.

Meeting such standards helps protect workers and minimize environmental impact by maintaining safe air quality levels.