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Chapter 11: Problem 53

How many liters of air \(\left(78\right.\) percent \(\mathrm{N}_{2}, 22\) percent \(\mathrm{O}_{2}\) by volume) at \(20^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) are needed for the complete combustion of \(1.0 \mathrm{~L}\) of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\) a typical gasoline component that has a density of \(0.70 \mathrm{~g} / \mathrm{mL} ?\)

Short Answer

Expert verified
8.33 liters of air are required for the complete combustion of 1.0 liter of octane.

Step by step solution

01

Write the Balanced Chemical Equation

Octane (\(C_8H_{18}\)) is combusted in the presence of oxygen (\(O_2\)), producing carbon dioxide (\(CO_2\)) and water (\(H_2O\)). The balanced chemical equation is: \(2C_8H_{18} + 25O_2 \rightarrow 16CO_2 + 18H_2O\).
02

Calculate the moles of Octane

Given that octane's density is 0.70 g/mL (0.70 kg/L) and its molar mass is \((8*12.01 + 18*1.008) g/mol = 114.224 g/mol\), we can find the moles in 1 L: \((1 L * 0.70 kg/L) / 114.224 g/mol = 0.00613 mol\).
03

Determine the Required Moles of Air

For every 2 moles of octane, 25 moles of \(O_2\) are required. Therefore, for \(0.00613 mol\) of octane, \(0.00613 mol * (25 O_2 / 2 C_8H_{18}) = 0.0766 mol\) of \(O_2\) are needed. Considering that air is 22% \(O_2\) by volume, the total moles of air needed are \(0.0766 / 0.22 = 0.348 mol\).
04

Convert Moles of Air to Liters

The ideal gas law states \(PV = nRT\), where \(P = 1 atm\), \(n = 0.348 mol\), \(R = 0.0821 L*atm/(mol*K)\), and \(T = 20°C = 293.15 K\). Solving for \(V\), we find \(V = nRT/P = (0.348mol * 0.0821 L*atm/(mol*K) * 293.15K) / 1 atm = 8.33 L\).

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Most popular questions from this chapter

A compound having the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\) does not react with sodium metal. In the presence of light, the compound reacts with \(\mathrm{Cl}_{2}\) to form three compounds having the formula \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OCl}\). Draw a structure for the original compound that is consistent with this information.

What is Markovnikov's rule?

Draw one possible structure for molecules with these formulas: (a) \(\mathrm{CH}_{4} \mathrm{O},\) (b) \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O},\) (c) \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2}\), (d) \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\)

The structural isomers of pentane, \(\mathrm{C}_{5} \mathrm{H}_{12}\), have quite different boiling points (see Example 11.1 ). Explain the observed variation in boiling point, in terms of structure.

Give the chemical names of these organic compounds and write their formulas: marsh gas, grain alcohol, wood alcohol, rubbing alcohol, antifreeze, mothballs, chief ingredient of vinegar.
See all solutions

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