/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 122 Ammonia and hydrogen chloride re... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 122

Ammonia and hydrogen chloride react to form solid ammonium chloride: $$\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$$ Two 2.00 -L flasks at \(25^{\circ} \mathrm{C}\) are connected by a valve, as shown in the drawing. One flask contains 5.00 \(\mathrm{g}\) of \(\mathrm{NH}_{3}(g),\) and the other contains 5.00 \(\mathrm{g}\) of \(\mathrm{HCl}(g) .\) When the valve is opened, the gases react until one is completely consumed. (a) Which gas will remain in the system after the reaction is complete? (b) What will be the final pressure of the system after the reaction is complete? (Neglect the volume of the ammonium chloride formed.) (c) What mass of ammonium chloride will be formed?

Short Answer

Expert verified
a) Ammonia (\(NH_3\)) will remain in the system after the reaction is complete. b) The final pressure of the system after the reaction is complete is 0.968 atm. c) The mass of ammonium chloride formed is 7.34 g.

Step by step solution

01

Identify the limiting reactant

First, we need to determine which gas is the limiting reactant. We are given the mass of both gases and can use their molar mass to convert to moles. Moles of \(NH_3\): \(\frac{5.00 \mathrm{g}}{17.03 \mathrm{g/mol}}=0.2937 \mathrm{mol}\) Moles of \(HCl\): \(\frac{5.00 \mathrm{g}}{36.46 \mathrm{g/mol}}=0.1372 \mathrm{mol}\) The stoichiometry of the balanced equation is 1:1. Since there are more moles of \(NH_3\) than \(HCl\), \(HCl\) is the limiting reactant.
02

Calculate the moles of reactants after the reaction

Now, we need to determine the amount of each reactant left after the reaction is complete. Since \(HCl\) will be completely consumed, there will be no moles of \(HCl\) left. The moles of \(NH_3\) left can be calculated. Moles of \(NH_3\) left: \(0.2937 - 0.1372 = 0.1565 \mathrm{mol}\)
03

Calculate the final pressure of the system

The initial pressure of the system can be calculated using the ideal gas law, \(PV=nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin. The temperature is given as \(25^{\circ} \mathrm{C}\), which is equal to \(298.15 \mathrm{K}\). The ideal gas constant, \(R\), is \(0.0821 \mathrm{L \cdot atm/mol \cdot K}\). Initially, only \(NH_3\) is in the first flask, so: Initial pressure (both flasks): \(P_1=\frac{n_1 \cdot R \cdot T_1}{V_1}\) \(P_1=\frac{0.2937 \mathrm{mol} \cdot 0.0821 \mathrm{L \cdot atm/mol \cdot K} \cdot 298.15 \mathrm{K}}{2.00 \mathrm{L}}\) \(P_1=3.63 \mathrm{atm}\) After the reaction, the final pressure can be calculated using the moles of \(NH_3\) left: Final pressure (both flasks): \(P_2=\frac{n_2 \cdot R \cdot T_2}{V_2}\) \(P_2=\frac{0.1565 \mathrm{mol} \cdot 0.0821 \mathrm{L \cdot atm/mol \cdot K} \cdot 298.15 \mathrm{K}}{4.00 \mathrm{L}}\) \(P_2=0.968 \mathrm{atm}\)
04

Calculate the mass of ammonium chloride formed

Finally, we need to determine the mass of ammonium chloride formed from the reaction. Since \(HCl\) is the limiting reactant, the mass of ammonium chloride produced can be calculated using the stoichiometry of the balanced equation. Moles of \(NH_4Cl\) produced: \(0.1372 \mathrm{mol}\) Mass of \(NH_4Cl\) produced: \(0.1372 \mathrm{mol} \times 53.49 \mathrm{g/mol} = 7.34 \mathrm{g}\) In summary: a) The gas that will remain in the system after the reaction is complete is ammonia (\(NH_3\)). b) The final pressure of the system after the reaction is complete is 0.968 atm. c) The mass of ammonium chloride formed is 7.34 g.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stoichiometry
Understanding stoichiometry is key to solving problems involving chemical reactions and their outcomes. It involves the quantitative relationships between reactants and products in a chemical reaction. To determine this, we need a balanced chemical equation. For the reaction between ammonia and hydrogen chloride to form ammonium chloride, the balanced equation is: \[ \mathrm{NH}_{3}(g) + \mathrm{HCl}(g) \rightarrow \mathrm{NH}_{4}\mathrm{Cl}(s) \] This equation shows a 1:1 molar ratio between ammonia and hydrogen chloride, meaning 1 mole of \( \mathrm{NH}_{3} \) reacts with 1 mole of \( \mathrm{HCl} \) to produce 1 mole of \( \mathrm{NH}_{4}\mathrm{Cl} \).
Using stoichiometry allows us to identify the limiting reactant鈥攖he substance that will be completely consumed first, limiting the amount of product formed. Here, hydrogen chloride is the limiting reactant because there are fewer moles of \( \mathrm{HCl} \) compared to \( \mathrm{NH}_{3} \). This concept helps us predict the amounts of remaining reactants and the mass of products formed as we saw with the mass of ammonium chloride calculated at 7.34 g.
Ideal Gas Law
The ideal gas law, expressed as \( PV = nRT \), is a fundamental equation that relates the pressure, volume, moles of gas, and temperature. In this formula:
  • \( P \) is the pressure
  • \( V \) is the volume
  • \( n \) is the number of moles
  • \( R \) is the ideal gas constant (0.0821 \( \mathrm{L \cdot atm/mol \cdot K} \))
  • \( T \) is the temperature in Kelvin

The initial pressure was calculated before the reaction by applying this formula to both flasks considered as one system. Initially, 5 g of \( \mathrm{NH}_{3} \), equivalent to 0.2937 mol, gave an initial pressure of 3.63 atm in a single 2 L flask. After the valve opening, the systems combine into 4 L, and as \( \mathrm{HCl} \) fully reacts, the pressure decreases.
With ammonia left unreacted, a final pressure of 0.968 atm was computed, illustrating how the idea of gases interacting in a closed system predicts pressure changes linked to chemical reactions.
Ammonium Chloride Formation
The formation of ammonium chloride from ammonia and hydrogen chloride is a classic example of a chemical reaction between two gases to form a solid. In the given problem, after mixing, \( \mathrm{NH}_{3} \) and \( \mathrm{HCl} \) gases react to produce a white, solid \( \mathrm{NH}_{4}\mathrm{Cl} \). This reaction is straightforward due to its 1:1 stoichiometry, resulting in complete utilization of hydrogen chloride since it is the limiting reactant.
The process ceases once \( \mathrm{HCl} \) is depleted, leaving some amount of \( \mathrm{NH}_{3} \) since it started in excess. The calculation of the mass of \( \mathrm{NH}_{4}\mathrm{Cl} \) formed uses the previous stoichiometric ratio, resulting in 7.34 g of product. This transformation illustrates the principle of mass conservation in chemical reactions, where the mass of reactants equals the mass of products once the reaction reaches completion.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A 6.53 -g sample of a mixture of magnesium carbonate and calcium carbonate is treated with excess hydrochloric acid. The resulting reaction produces 1.72 \(\mathrm{L}\) of carbon dioxide gas at \(28^{\circ} \mathrm{C}\) and 743 torr pressure. (a) Write balanced chemical equations for the reactions that occur between hydrochloric acid and each component of the mixture. (b) Calculate the total number of moles of carbon dioxide that forms from these reactions. (c) Assuming that the reactions are complete, calculate the percentage by mass of magnesium carbonate in the mixture.

(a) How high in meters must a column of glycerol be to exert a pressure equal to that of a \(760-\mathrm{mm}\) column of mercury? The density of glycerol is 1.26 \(\mathrm{g} / \mathrm{mL}\) , whereas that of mercury is 13.6 \(\mathrm{g} / \mathrm{mL}\) . (b) What pressure, in atmospheres, is exerted on the body of a diver if she is 15 ft below the surface of the water when the atmospheric pressure is 750 torr? Assume that the density of the water is \(1.00 \mathrm{g} / \mathrm{cm}^{3}=1.00 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .\) The gravitational constant is \(9.81 \mathrm{m} / \mathrm{s}^{2},\) and \(1 \mathrm{Pa}=1 \mathrm{kg} / \mathrm{m}-\mathrm{s}^{2} .\)

A 35.1 g sample of solid \(\mathrm{CO}_{2}(\) dry ice \()\) is added to a container at a temperature of 100 \(\mathrm{K}\) with a volume of 4.0 \(\mathrm{L} .\) If the container is evacuated (all of the gas removed), sealed and then allowed to warm to room temperature \((T=298 \mathrm{K})\) so that all of the solid \(\mathrm{CO}_{2}\) is converted to a gas, what is the pressure inside the container?

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains \(\mathrm{O}_{2}\) gas at a pressure of \(16,500 \mathrm{kPa}\) at \(23^{\circ} \mathrm{C}\) . (a) What mass of \(\mathrm{O}_{2}\) does the tank contain? (b) What volume would the gas occupy at STP? (c) At what temperature would the pressure in the tank equal 150.0 atm? (d) What would be the pressure of the gas, in kPa, if it were transferred to a container at \(24^{\circ} \mathrm{C}\) whose volume is 55.0 \(\mathrm{L}\) ?

In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. Hg. \((\mathbf{a})\) Convert this pressure to torr. \((\mathbf{b})\) Convert this pressure to atm.
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Organic Chemistry

Read Explanation

Making Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.