Problem 88 - Chemistry: Principles and Reactions

Question

A tube \(5.0 \mathrm{ft}\) long is evacuated. Samples of \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\), at the same temperature and pressure, are introduced simultaneously through tiny openings at opposite ends of the tube. When the two gases meet, a white ring of \(\mathrm{NH}_{4} \mathrm{Cl}(s)\) forms. How far from the end at which ammonia was introduced will the ring form?

Step-by-Step Solution

Answer

Based on the given problem and solution, the short answer is: The white ring of NH4Cl(s) will form 2.5 ft from the end at which NH3 was introduced.

Step 1: Identify the chemical equations

In this exercise, NH3 and HCl react when they meet to form NH4Cl(s) as per the following balanced chemical equation: NH3(g) + HCl(g) → NH4Cl(s)

Step 2: Calculate the moles of NH3 and HCl

Since both NH3 and HCl gases have the same temperature and pressure and are meeting within the 5.0 ft tube, we can use the molar volumes to determine the moles of NH3 and HCl. At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 L (liters) or roughly 22.7 ft³. Therefore, we can assume that the NH3 and HCl are at STP conditions. The moles of NH3 and HCl can be calculated as follows: moles = volume (ft³) / molar volume (ft³/mol) Since both NH3 and HCl gases occupy the entire 5.0 ft tube, the moles of NH3 and HCl will be: moles_NH3 = moles_HCl = 5.0 ft / 22.7 ft³/mol

Step 3: Compare the stoichiometry of the chemical reaction

For the reaction NH3(g) + HCl(g) → NH4Cl(s) The stoichiometry of NH3 and HCl is 1:1. If the number of moles of NH3 and HCl is equal, the reaction will be complete, and the white ring of NH4Cl(s) will form exactly in the middle of the tube. If there are more moles of NH3, the reaction will be complete more towards the HCl end, and vice versa. In this case, moles_NH3 = moles_HCl. Hence, the reaction will be complete in the middle of the tube.

Step 4: Determine the position of the white ring of NH4Cl(s)

As the moles of NH3 and HCl are equal and the stoichiometry of the reaction is 1:1, the white ring of NH4Cl(s) will form exactly in the middle of the tube. Since the total length of the tube is 5.0 ft, the white ring will form at a distance of: distance (NH3 end) = total length / 2 distance (NH3 end) = 5.0 ft / 2 = 2.5 ft So, the white ring of NH4Cl(s) will form 2.5 ft from the end where NH3 was introduced.

Key Concepts

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between the elements and compounds as they undergo chemical reactions. In the context of gas reactions, stoichiometry allows us to calculate the amounts of reactants and products involved. In the given problem, the stoichiometry is crucial for determining where the white ring of ammonium chloride (NH4Cl) will form in the tube.

For the reaction between ammonia (\(\text{NH}_3\)) and hydrogen chloride (\(\text{HCl}\)), the balanced chemical equation is:

• \(\text{NH}_3(g) + \text{HCl}(g) \to \text{NH}_4\text{Cl}(s)\)

This equation indicates a 1:1 molar ratio between the reactants and the products. This means one mole of ammonia reacts with one mole of hydrogen chloride to produce one mole of ammonium chloride.

Understanding this molar equivalence is key to finding out that the NH4Cl will form at the exact point where both gases meet in equal moles, which happens given they start at equal pressure and temperature conditions within the tube.

Molar Volume

The concept of molar volume is essential in understanding how gases behave under specified conditions. The molar volume at standard temperature and pressure (STP) is 22.4 liters, which represents the volume occupied by one mole of an ideal gas at STP.

• Standard Temperature and Pressure (STP) is defined as 0 degrees Celsius and 1 atm pressure.
• The molar volume at STP can also be approximated as 22.7 ft³ when considering volumes in foot cubes, crucial for setups like the tube in the problem.

In the exercise, knowing that the molar volume of a gas at STP lets us determine how many moles are present in a given volume of gas. This is done by dividing the gas's overall volume by the molar volume. Therefore, with a 5.0 ft long tube filled with gases at STP, we calculate the moles of each gas as:\[moles = \frac{\text{volume (ft³)}}{\text{molar volume (ft³/mol)}}\]Because both gases fill the tube equally, we can understand that their mole numbers are similar, leading to a balanced point of reaction midway.

Chemical Equation

Chemical equations are representations of chemical reactions, with the compounds involved being expressed in terms of their chemical formulas. They not only tell us the substances involved but also give us a clear depiction of the reactants and products through their balanced formats.

The balanced chemical equation for the reaction between ammonia and hydrogen chloride is:

• \(\text{NH}_3(g) + \text{HCl}(g) \to \text{NH}_4\text{Cl}(s)\)

This clearly indicates that one mole of ammonia gas reacts with one mole of hydrochloric gas to give one mole of solid ammonium chloride. It is essential to remember that balancing is guided by the principle of conservation of mass, where the number of each type of atom should be the same on both sides of the equation.

Understanding the balanced chemical equation helps students determine the proportions of reactants needed to achieve a complete reaction, such as in this problem where the equal moles result in the formation of the white NH4Cl ring precisely where they meet inside the tube.

NH4Cl Formation

The formation of ammonium chloride (\(\text{NH}_4\text{Cl}\)) in this context results from a gas reaction between ammonia (\(\text{NH}_3\)) and hydrochloric acid (\(\text{HCl}\)), forming a white ring of solid at the point where these gases meet.

This reaction is a perfect demonstration of a simple substance mixing and producing a new compound. At the instant molecular collision, the reaction can be evidenced by the visible formation of a solid product from gaseous reactants.

• This occurs due to the strong affinity ammonium ions (\(\text{NH}_4^+\)) and chloride ions (\(\text{Cl}^-\)) have for forming an ionic bond.
• The white ring is indicative of the solid nature of ammonium chloride as opposed to the gaseous nature of its reactants.

In the exercise, this monument of a reaction provides a vivid visual cue of where the gases have mixed. This observation is grounded in both molecular interactions and stoichiometric principles that govern the reaction's occurrence and magnitude, establishing a clear midpoint given equal initial conditions of the gases involved.