/*! 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 70 Detonation of nitroglycerin proc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 70

Detonation of nitroglycerin proceeds as follows: $$ \begin{aligned} 4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}(l) & \longrightarrow \\ & 12 \mathrm{CO}_{2}(g)+6 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) \end{aligned} $$ (a) If a sample containing \(2.00 \mathrm{~mL}\) of nitroglycerin (density \(=\) \(1.592 \mathrm{~g} / \mathrm{mL}\) ) is detonated, how many moles of gas are produced? (b) If each mole of gas occupies \(55 \mathrm{~L}\) under the conditions of the explosion, how many liters of gas are produced? (c) How many grams of \(\mathrm{N}_{2}\) are produced in the detonation?

Short Answer

Expert verified
(a) 0.1015 mol of gas is produced. (b) 5.58 L of gas is produced. (c) 0.588 g of N2 is produced.

Step by step solution

01

Calculate moles of nitroglycerin

First, we need to convert the given volume of nitroglycerin (2.00 mL) to mass using the given density (1.592 g/mL). Mass = Volume 脳 Density Mass = 2.00 mL 脳 1.592 g/mL = 3.184 g Now, we need to find the molar mass of nitroglycerin (C3H5N3O9). Use the atomic masses from the periodic table: C: 12.01 g/mol, H: 1.01 g/mol, N: 14.01 g/mol, O: 16.00 g/mol. Molar mass of nitroglycerin = 3(12.01) + 5(1.01) + 3(14.01) + 9(16.00) = 227.13 g/mol. Now, calculate the moles of nitroglycerin: Moles = Mass/Molar Mass Moles = 3.184 g / 227.13 g/mol = 0.0140 mol
02

Calculate moles of gas produced

From the balanced equation, we know that 4 moles of nitroglycerin (C3H5N3O9) produce: - 12 moles of CO2, - 6 moles of N2, - 1 mole of O2, and - 10 moles of H2O. Total moles of gas produced = 12 + 6 + 1 + 10 = 29 moles. Now we can use the mole ratio to find the moles of gas produced: Moles of gas produced = moles of nitroglycerin 脳 (moles of gas produced/moles of nitroglycerin) Moles of gas produced = 0.0140 mol 脳 (29 mol/4 mol) = 0.1015 mol
03

Calculate the volume of gas produced

We are given that each mole of gas occupies 55 L under the conditions of the explosion. To find the volume of gas produced, multiply the moles of gas produced by 55 L/mol: Volume of gas = Moles of gas 脳 Volume per mole Volume of gas = 0.1015 mol 脳 55 L/mol = 5.58 L
04

Calculate the mass of N2 produced

To find the mass of N2, we need the moles of N2 produced. From the balanced equation, we know that 4 moles of nitroglycerin produce 6 moles of N2. Moles of N2 produced = moles of nitroglycerin 脳 (moles of N2 /moles of nitroglycerin) Mole of N2 produced = 0.0140 mol 脳 (6 mol N2/4 mol nitroglycerin) = 0.0210 mol N2 Now, using the molar mass of N2 (2 脳 14.01 g/mol = 28.02 g/mol), we can find the mass of N2 produced: Mass of N2 produced = moles of N2 脳 molar mass of N2 Mass of N2 produced = 0.0210 mol 脳 28.02 g/mol = 0.588 g Answer: (a) The number of moles of gas produced is 0.1015 mol. (b) The volume of gas produced is 5.58 L. (c) The mass of N2 produced is 0.588 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.

Chemical Reactions
Chemical reactions involve the transformation of reactants into products. When nitroglycerin detonates, as in the given exercise, it breaks down into different products, including gases like carbon dioxide, nitrogen, oxygen, and water vapor. This transformation is represented by a balanced chemical equation, which ensures the conservation of mass and atoms.
  • Each compound on the reactant side must be balanced with the same number of each type of atom on the product side.
  • In detonation reactions, energy release can be significant, showing why nitroglycerin is used as an explosive.
  • Balanced equations allow us to understand the stoichiometry of the reaction, which helps in calculating quantities of reactants and products.
Understanding these principles helps us make predictions about the amounts of substances involved in the reaction and is essential for calculations in stoichiometry.
Molar Mass
Molar mass is crucial for converting between mass and moles of a substance. It's the mass of one mole of a compound, measured in g/mol, and is pivotal for solving stoichiometry problems.
  • To calculate molar mass, sum up the atomic masses of all the atoms in the molecular formula.
  • In the exercise, nitroglycerin's molar mass is calculated by adding the masses of carbon, hydrogen, nitrogen, and oxygen atoms in the formula \( \text{C}_3\text{H}_5\text{N}_3\text{O}_9 \).
  • This gives us a molar mass of 227.13 g/mol.
  • Using this, we can convert the given mass of nitroglycerin into moles by dividing the mass by the molar mass.
Accurate molar mass calculation is vital for determining the correct proportions in chemical equations and understanding the scale of reactions.
Gas Laws
Gas laws explain how gases behave under different conditions. In stoichiometry, understanding these laws helps calculate the volumes of gases produced in reactions. This exercise focuses on the link between moles of gas and the volume they occupy.
  • Each mole of gas typically occupies a certain volume鈥攍ike 55 L in the given conditions鈥攚hich can be used to convert moles to volume.
  • The ideal gas law is a common tool in stoichiometry: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant, and \( T \) is temperature.
  • Understanding these relationships helps us predict how the change in one condition (like temperature or pressure) could affect the gas volume.
These principles are fundamental for practical applications, such as calculating the amount of gas produced during an explosive reaction like nitroglycerin's detonation.

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

The allowable concentration level of vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl},\) in the atmosphere in a chemical plant is \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). How many moles of vinyl chloride in each liter does this represent? How many molecules per liter?

Determine the formula weights of each of the following compounds: (a) Butyric acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH},\) which is responsible for the rotten smell of spoiled food; (b) sodium perborate, \(\mathrm{NaBO}_{3}\), a substance used as bleach; (c) calcium carbonate, \(\mathrm{CaCO}_{3},\) a substance found in marble. (c) \(\mathrm{CF}_{2} \mathrm{Cl}_{2},\) a refrigerant known as Freon; \((\mathbf{d}) \mathrm{NaHCO}_{3},\) known as baking soda and used in bread and pastry baking; \((\mathbf{e})\) iron pyrite, \(\mathrm{FeS}_{2}\) which has a golden appearance and is known as "Fool's Gold."

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally \(\mathrm{N}_{2}(\sim 79 \%)\) and \(\mathrm{O}_{2}(\sim 20 \%) .\) In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "NO \(_{x}\) " gases. In 2009 , the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of \(\mathrm{NO}_{x}\) gases is an unwanted side reaction of the main engine combustion process that turns octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) into \(\mathrm{CO}_{2}\) and water. If \(85 \%\) of the oxygen in an engine is used to combust octane and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of \(500 \mathrm{~g}\) of octane.

Calcium hydride reacts with water to form calcium hydroxide and hydrogen gas. (a) Write a balanced chemical equation for the reaction. (b) How many grams of calcium hydride are needed to form \(4.500 \mathrm{~g}\) of hydrogen?

Consider a sample of calcium carbonate in the form of a cube measuring 2.005 in. on each edge. If the sample has a density of \(2.71 \mathrm{~g} / \mathrm{cm}^{3},\) how many oxygen atoms does it contain?
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

The Earths Atmosphere

Read Explanation

Making Measurements

Read Explanation

Organic Chemistry

Read Explanation

Kinetics

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.