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Ch.10 - Gases: Their Properties & Behavior
Chapter 10, Problem 149

Chemical explosions are characterized by the instantaneous release of large quantities of hot gases, which set up a shock wave of enormous pressure (up to 700,000 atm) and velocity (up to 20,000 mi/h). For example, the explosion of nitroglycerin (C3H5N3O9) releases four gases, A, B, C, and D, represented by the equation C3H5N3O9(l) → a A(g) + b B(g) + c C(g) + d D(g). Assume that the explosion of 1 mol (227 g) of nitroglycerin releases gases with a temperature of 1950 °C and a volume of 1323 L at 1.00 atm pressure. (a) How many moles of hot gas are released by the explosion of 0.00400 mol of nitroglycerin? (b) When the products released by the explosion of 0.00400 mol of nitroglycerin were placed in a 500.0-mL flask and the flask was cooled to -10 °C, product A solidified and the pressure inside the flask was 623 mm Hg. How many moles of A were present, and what is its likely identity? (c) When gases B, C, and D were passed through a tube of powdered Li2O, gas B reacted to form Li2CO3. The remaining gases, C and D, were collected in another 500.0-mL flask and found to have a pressure of 260 mm Hg at 25 °C. How many moles of B were present, and what is its likely identity?

Verified step by step guidance
1
Step 1: To find the total moles of gas released by the explosion of 0.00400 mol of nitroglycerin, use the ideal gas law equation \( PV = nRT \). First, calculate the total moles of gas released by 1 mol of nitroglycerin using the given conditions: \( P = 1.00 \text{ atm} \), \( V = 1323 \text{ L} \), \( T = 1950 + 273.15 \text{ K} \). Solve for \( n \) using \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \). Then, scale this value to 0.00400 mol of nitroglycerin.
Step 2: For part (b), use the ideal gas law to find the moles of gas remaining in the flask after product A solidifies. Convert the pressure from mm Hg to atm (\( 623 \text{ mm Hg} = 0.819 \text{ atm} \)), and use the volume \( V = 0.500 \text{ L} \) and temperature \( T = -10 + 273.15 \text{ K} \). Solve for \( n \) using \( PV = nRT \). The moles of gas calculated will be the moles of gases B, C, and D.
Step 3: To find the moles of A, subtract the moles of gases B, C, and D (calculated in Step 2) from the total moles of gas released by 0.00400 mol of nitroglycerin (calculated in Step 1). The identity of A can be inferred from its solidification at -10 °C, suggesting it is likely a gas with a high boiling point, such as water vapor (H2O).
Step 4: For part (c), determine the moles of gases C and D using the ideal gas law. Convert the pressure from mm Hg to atm (\( 260 \text{ mm Hg} = 0.342 \text{ atm} \)), and use the volume \( V = 0.500 \text{ L} \) and temperature \( T = 25 + 273.15 \text{ K} \). Solve for \( n \) using \( PV = nRT \).
Step 5: The moles of gas B can be found by subtracting the moles of gases C and D (calculated in Step 4) from the moles of gases B, C, and D (calculated in Step 2). The identity of B can be inferred from its reaction with Li2O to form Li2CO3, suggesting it is likely carbon dioxide (CO2).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of substances consumed and produced in a reaction, using mole ratios derived from the coefficients in the balanced equation. In this question, stoichiometry is essential for calculating the moles of gases released from the explosion of nitroglycerin.
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Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is crucial for understanding the behavior of gases under various conditions. In the context of this question, it helps to determine the moles of gas present after the explosion and when the gases are cooled and compressed in a flask.
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Phase Changes and Gas Behavior

Phase changes refer to the transitions between solid, liquid, and gas states of matter, influenced by temperature and pressure. Understanding how gases behave when cooled or compressed is vital for predicting the outcomes of reactions and the states of products. In this question, the solidification of gas A and the pressure changes in the flasks highlight the importance of phase changes in gas behavior.
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Related Practice
Textbook Question

Isooctane, C8H18, is the component of gasoline from which the term octane rating derives. (b) Assuming that gasoline is 100% isooctane, that isooctane burns to produce only CO2 and H2O, and that the density of isooctane is 0.792 g/mL, what mass of CO2 in kilograms is produced each year by the annual U.S. gasoline consumption of 4.6⨉1010 L?

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Textbook Question

Isooctane, C8H18, is the component of gasoline from which the term octane rating derives. (d) How many moles of air are necessary for the combustion of 1 mol of isooctane, assuming that air is 21.0% O2 by volume? What is the volume in liters of this air at STP?

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Textbook Question
The Rankine temperature scale used in engineering is to the Fahrenheit scale as the Kelvin scale is to the Celsius scale. That is, 1 Rankine degree is the same size as 1 Fahrenheit degree, and 0 °R = absolute zero. (b) What is the value of the gas constant R on the Rankine scale in 1L ~ atm2>1°R ~ mol2? (c) Use the van der Waals equation to determine the pressure inside a 400.0-mL vessel that contains 2.50 mol of CH4 at a temperature of 525 °R. For CH4, a = 2.253 1L2 ~ atm2>mol2 and b = 0.04278 L>mol.
597
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Textbook Question

Chemical explosions are characterized by the instantaneous release of large quantities of hot gases, which set up a shock wave of enormous pressure (up to 700,000 atm) and velocity (up to 20,000 mi/h). For example, explosion of nitroglycerin (C3H5N3O9) releases four gases, A, B, C, and D:

n C3H5N3O9(l) a A(g) + b B(g) + c C(g) + d D(g)

Assume that the explosion of 1 mol (227 g) of nitroglycerin releases gases with a temperature of 1950 °C and a volume of 1323 L at 1.00 atm pressure.

(d) When gases C and D were passed through a hot tube of powdered copper, gas C reacted to form CuO. The remaining gas, D, was collected in a third 500.0-mL flask and found to have a mass of 0.168 g and a pressure of 223 mm Hg at 25 °C. How many moles each of C and D were present, and what are their likely identities?

602
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Textbook Question

Chemical explosions are characterized by the instantaneous release of large quantities of hot gases, which set up a shock wave of enormous pressure (up to 700,000 atm) and velocity (up to 20,000 mi/h). For example, explosion of nitroglycerin (C3H5N3O9) releases four gases, A, B, C, and D:

n C3H5N3O9(l) a A(g) + b B(g) + c C(g) + d D(g)

Assume that the explosion of 1 mol (227 g) of nitroglycerin releases gases with a temperature of 1950 °C and a volume of 1323 L at 1.00 atm pressure.

(e) Write a balanced equation for the explosion of nitroglycerin.

916
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Textbook Question
Combustion analysis of 0.1500 g of methyl tert-butyl ether, an octane booster used in gasoline, gave 0.3744 g of CO2 and 0.1838 g of H2O. When a flask having a volume of 1.00 L was evacuated and then filled with methyl tertbutyl ether vapor at a pressure of 100.0 kPa and a temperature of 54.8 °C, the mass of the flask increased by 3.233 g.(b) What is the molecular weight and molecular formula of methyl tert-butyl ether?
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