Question

Federal regulations set an upper limit of 50 parts per million ( \(\mathrm{ppm}\) ) of \(\mathrm{NH}_{3}\) in the air in a work environment [that is, 50 molecules of \(\mathrm{NH}_{3}(\mathrm{~g})\) 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 \(0.0105 \mathrm{M}\) HCl. The \(\mathrm{NH}_{3}\) reacts with \(\mathrm{HCl}\) as follows: $$ \mathrm{NH}_{3}(a q)+\mathrm{HCl}(a q) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(a q) $$ 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) ls this manufacturer in compliance with regulations?

Short answer

\( \text{moles of NaOH} = 7.7058 \times 10^{-4} \mathrm{mol} \) Since moles of NaOH equal moles of unreacted HCl, \(7.7058 \times 10^{-4} \mathrm{mol}\) of HCl remains unreacted. #tag_title#Step 2: Calculate the moles of NH3#tag_content#To determine the moles of NH3, subtract the moles of unreacted HCl from the initial moles of HCl in the solution. $$ \text{moles of NH3} = (\text{initial moles of HCl}) - (\text{moles of unreacted HCl}) $$ The initial moles of HCl can be calculated using the initial volume and concentration of the HCl solution. $$ \text{initial moles of HCl} = (1.00 \times 10^2 \times 10^{-3} \mathrm{L}) \times (0.0105 \mathrm{M}) $$ $$ \text{moles of NH3} = [(1.05 \times 10^{-3} \mathrm{mol}) - (7.7058 \times 10^{-4} \mathrm{mol})] $$ \( \text{moles of NH3} = 2.7942 \times 10^{-4} \mathrm{mol} \) #tag_title#Step 3: Calculate the mass of NH3#tag_content#To calculate the mass of NH3, multiply the moles of NH3 by its molar mass. $$ \text{mass of NH3} = (\text{moles of NH3}) \times (\text{molar mass of NH3}) $$ $$ \text{mass of NH3} = (2.7942 \times 10^{-4} \mathrm{mol}) \times (17.03 \mathrm{g/mol}) $$ \( \text{mass of NH3} = 4.76 \times 10^{-3} \mathrm{g} \) #tag_title#Step 4: Calculate the ppm of NH3#tag_content#To calculate the ppm concentration of NH3 in the air, we use the mass of NH3, the total volume of air, the density of air, and the average molar mass of air. $$ \text{ppm concentration} = \frac{\text{mass of NH3}}{(\text{total volume of air}) \times (\text{density of air}) \times (\text{average molar mass of air})} \times 10^6 $$ $$ \text{ppm concentration} = \frac{4.76 \times 10^{-3} \mathrm{g}}{(10.0 \mathrm{L}) \times (1.20 \mathrm{g/L}) \times (29.0 \mathrm{g/mol})} \times 10^6 $$ \( \text{ppm concentration} = 13.70 \mathrm{ppm} \) #tag_title#Step 5: Check compliance with regulations#tag_content#The calculated ppm concentration of NH3 is 13.70 ppm, which is below the regulatory limit of 50 ppm. Therefore, the manufacturer is in compliance with the federal regulations. In conclusion, (a) 4.76 x 10^-3 g of NH3 was drawn into the acid solution, (b) the air contained 13.70 ppm of NH3, and (c) the manufacturer is in compliance with the federal regulations.

Step-by-step solution

Calculate the moles of HCl and NaOH at the equivalence point

At the equivalence point, moles of NaOH are equal to moles of unreacted HCl in the solution. We use the volume and concentration of the NaOH solution to determine the moles of NaOH. $$ \text{moles of NaOH} = \text{volume} \times \text{concentration} $$ $$ \text{moles of NaOH} = (13.1 \times 10^{-3}\mathrm{L}) \times (0.0588\mathrm{M}) $$

Key concepts

Ammonia Concentration

Ammonia concentration in the air is critical for ensuring safety in the workplace. Regulations stipulate that the air should contain no more than 50 parts per million (ppm) of ammonia (\(\mathrm{NH}_3\)). This means that for every one million molecules of air, there should be a maximum of 50 molecules of ammonia.

Understanding how to calculate ammonia concentration is essential when testing air quality. This involves determining the number of ammonia molecules present in the air during a specific period and comparing it against regulatory limits.

To calculate ammonia concentration in ppm, you need to know:

• The total volume of air tested.
• The reaction of ammonia with a known quantity of another chemical, in this case, hydrochloric acid (HCl).
• The outcome of any further reactions or titrations—used here to determine how much of the original acid remains unreacted.

Titration Calculations

Titration is a laboratory method used to determine the concentration of a specific component in a solution. In this example, it's used to find out how much hydrochloric acid (HCl) remains, helping to calculate the amount of ammonia that reacted with HCl.

Firstly, you'll measure the amount of titrant needed to neutralize the acid that hasn't reacted with ammonia. This step involves:

• Measuring the volume of sodium hydroxide (\(\mathrm{NaOH}\)) used in the titration process.
• Knowing the molarity of the \(\mathrm{NaOH}\) solution.
• Utilizing the equation: \(\text{moles of } \mathrm{NaOH} = \text{volume} \times \text{concentration}\) to find out how many moles of \(\mathrm{NaOH}\) were added.

By calculating the moles of \(\mathrm{NaOH}\), you can determine the moles of unreacted HCl. Since the reaction between \(\mathrm{NH}_3\) and \(\mathrm{HCl}\) is a simple neutralization, this information can help backtrack to discover how much ammonia originally reacted, giving insight into the total ppm of \(\mathrm{NH}_3\) in the air.

Chemical Reactions in Air Quality Testing

Chemical reactions play an integral role in air quality testing. In the given scenario, the reaction of ammonia (\(\mathrm{NH}_3\)) with hydrochloric acid (HCl) is pivotal. The equation representing this reaction is:\[\mathrm{NH}_3(aq) + \mathrm{HCl}(aq) \rightarrow \mathrm{NH}_4Cl(aq)\]This neutralization reaction is essential for capturing and quantifying ammonia in the air. When air containing \(\mathrm{NH}_3\) is passed through the \(\mathrm{HCl}\) solution, \(\mathrm{NH}_3\) reacts to form ammonium chloride (\(\mathrm{NH}_4Cl\)).

The efficiency of this chemical process directly impacts the accuracy of ammonia concentration measurements. The method ensures that all the ammonia introduced reacts with the acid, providing a precise measurement of ammonia concentration.

Effective monitoring through calibrated chemical reactions helps organizations ensure they comply with safety regulations, maintaining a safe work environment and avoiding potential legal pitfalls.