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Ch.10 - Gases: Their Properties & Behavior
McMurry - Chemistry 8th Edition
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All textbooksMcMurry 8th EditionCh.10 - Gases: Their Properties & BehaviorProblem 147d
Chapter 10, Problem 147d

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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1
Write the balanced chemical equation for the combustion of isooctane (C8H18). The general form of a combustion reaction is: \( \text{Fuel} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \). For isooctane, the balanced equation is: \( C_8H_{18} + \frac{25}{2} O_2 \rightarrow 8 CO_2 + 9 H_2O \).
Calculate the moles of oxygen (O2) needed for the combustion of 1 mole of isooctane. From the balanced equation, 12.5 moles of O2 are required for 1 mole of isooctane.
Determine the total moles of air needed. Since air is 21.0% O2 by volume, you can set up a proportion to find the total moles of air that would contain 12.5 moles of O2: \( \frac{12.5 \text{ moles O}_2}{0.21} \).
Calculate the volume of air at STP. Use the ideal gas law under STP conditions where 1 mole of any gas occupies 22.4 liters. Multiply the total moles of air by 22.4 L/mole to find the volume in liters.
Summarize the findings: The total moles of air required for the combustion of 1 mole of isooctane and the corresponding volume of this air at STP.

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Key Concepts

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

Stoichiometry of Combustion Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions. In the combustion of isooctane, the balanced chemical equation shows how many moles of oxygen are required to completely combust one mole of isooctane. Understanding this relationship is crucial for determining the amount of air needed, as air is composed of approximately 21% oxygen.
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Composition of Air

Air is primarily composed of nitrogen (approximately 78%) and oxygen (about 21%). When calculating the amount of air needed for combustion, it is essential to account for the percentage of oxygen in air. This allows for the conversion of moles of oxygen required for combustion into moles of air, facilitating the determination of the total volume of air needed.
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Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is defined as 0 degrees Celsius (273.15 K) and 1 atmosphere of pressure. At STP, one mole of an ideal gas occupies 22.4 liters. This concept is important for converting the number of moles of air calculated from the combustion reaction into a volume measurement, allowing for practical applications in real-world scenarios.
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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?

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.
Textbook Question

Isooctane, C8H18, is the component of gasoline from which the term octane rating derives. (a) Write a balanced equation for the combustion of isooctane to yield CO2 and H2O.

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?