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Chapter 3: Problem 155

Octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is a component of gasoline. Complete combustion of octane yields \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CO}_{2} .\) Incomplete combustion produces \(\mathrm{H}_{2} \mathrm{O}\) and CO, which not only reduces the efficiency of the engine using the fuel but is also toxic. In a certain test run, 1.000 gal of octane is burned in an engine. The total mass of \(\mathrm{CO}, \mathrm{CO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\) produced is \(11.53 \mathrm{~kg} .\) Calculate the efficiency of the process; that is, calculate the fraction of octane converted to \(\mathrm{CO}_{2}\). The density of octane is \(2.650 \mathrm{~kg} / \mathrm{gal}\)

Short Answer

Expert verified
The efficiency of the combustion process can be calculated by finding the mass of CO2 produced, which will give us the mass of octane that should have been burned to obtain this CO2. This is then divided by the total mass of octane consumed and multiplied by 100 to get the percentage efficiency.

Step by step solution

01

Calculate the total mass of octane

Given the volume of octane and its density, calculate the total mass of the octane. The volume of octane given is 1.000 gal and its density is 2.650 kg/gal. The mass is calculated by multiplying the volume by the density: \( mass = volume \times density = 1.000 gal \times 2.65 kg/gal = 2.65 kg \).
02

Calculate the mass of CO2 produced

From the problem, it's known that the total mass of CO, CO2, and H2O produced is 11.53 kg. However, to calculate the efficiency, the mass of only CO2 is needed. In other words, the total mass of CO and H2O must be deduced from 11.53 kg. Considering the molar mass of CO2 is 44 g/mol and the molar mass of CO and H2O are 28 g/mol and 18 g/mol respectively, assume x moles of CO and y moles of H2O and solve for x and y such that massCO + massH2O = 11.53 kg - massCO2 which then gives us the massCO2.
03

Calculate the mass of octane that should be burned to obtain the mass of CO2 produced

From complete combustion of octane, for each mole of octane, suppose one mole of CO2 is produced. Using the molar mass of octane (114 g/mol), and knowing the moles of CO2 calculated in the previous step, one can find the mass of octane that should have reacted completely to produce the measured CO2.
04

Calculate the combustion efficiency

After obtaining the necessary masses, calculate the combustion efficiency. The combustion efficiency of this process is defined as the mass of octane that reacted completely (to produce CO2) divided by the total mass of octane consumed, multiplied by 100%: \((mass_{octane-toCO2} / mass_{totalOctane})*100\%

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Most popular questions from this chapter

A sample of iron weighing \(15.0 \mathrm{~g}\) was heated with potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\) in an evacuated container. The oxygen generated from the decomposition of \(\mathrm{KClO}_{3}\) converted some of the Fe to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). If the combined mass of Fe and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) was \(17.9 \mathrm{~g}\), calculate the mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed and the mass of \(\mathrm{KClO}_{3}\) decomposed.

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