Ch.10 - Gases: Their Properties & Behavior

Problem 149d

Chapter 10, Problem 149d

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?

Verified step by step guidance

Step 1: Convert the pressure of gas D from mm Hg to atm using the conversion factor (1 atm = 760 mm Hg).

Step 2: Use the ideal gas law, PV = nRT, to calculate the number of moles of gas D. Remember to use the appropriate values for R (0.0821 L atm/mol K) and convert the temperature from Celsius to Kelvin (K = °C + 273.15).

Step 3: Calculate the total moles of gases C and D initially present using the ideal gas law for the combined volume, temperature, and pressure given for the explosion.

Step 4: Subtract the moles of gas D from the total moles calculated in Step 3 to find the moles of gas C.

Step 5: Identify the likely chemical identities of gases C and D based on their chemical behavior (reaction with copper to form CuO) and typical products of nitroglycerin decomposition.

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Key Concepts

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

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 essential for calculating the number of moles of gases produced in a reaction, as it allows us to determine how many moles correspond to a given volume and pressure at a specific temperature.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. Understanding stoichiometry is crucial for determining the amounts of gases C and D produced from the decomposition of nitroglycerin, as it provides the ratios needed to relate the moles of reactants to the moles of products.

Gas Collection and Analysis

Gas collection and analysis involve measuring the properties of gases, such as mass, volume, and pressure, to identify their composition. In this scenario, the mass and pressure of gas D are given, which can be used alongside the Ideal Gas Law to calculate the number of moles and potentially identify the gas based on its properties.

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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.

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Open 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, 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?

Textbook Question

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.

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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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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. (a) What is the empirical formula of methyl tert-butyl ether?

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