Octane (C8 H18) is a component of gasoline. Complete...

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 $2.650 \mathrm{~kg} / \mathrm{gal}$

Key Concepts

Density and Mass Conversion

Density is a physical property that relates mass to volume, and it is crucial for converting between these units in practical problems. In the context of this problem, the density of octane is used to determine its mass from a given volume, which is then essential for performing stoichiometric calculations and evaluating the overall efficiency of the combustion process.

Reaction Efficiency

Reaction efficiency in chemical processes is the measure of how effectively the reactants are converted into the desired product. In the context of combustion, it is defined by the fraction of the fuel that produces carbon dioxide rather than unwanted byproducts. This involves calculating the conversion rates of reactants to desired products using stoichiometric relationships and comparing them to the total amount of reactant consumed.

Stoichiometry

Stoichiometry involves using the balanced chemical equations to relate the amounts, in moles or mass, of reactants and products. It is a fundamental concept that allows you to calculate how much of each product is formed from a given amount of reactant, and it plays a crucial role in determining the efficiency of a chemical process.

Complete vs Incomplete Combustion

Combustion reactions are a key class of reactions where a fuel reacts with an oxidizer, typically oxygen. Complete combustion occurs when the fuel burns fully, producing only carbon dioxide and water, while incomplete combustion happens when oxygen is limited, leading to the production of carbon monoxide along with other products. Understanding the differences between these reactions is essential for analyzing engine efficiency and environmental impacts.

Transcript

00:11 So given information we have complete combustion of octane.

00:24 Combustion of octane.

00:34 So the reaction of complete combustion of octane is 2 mole of octane plus 25 moles of oxygen, 16 mole of co2 plus 18 mole of h2o.

01:11 And incomplete combustion of octane, 2 moles of octane plus 17 moles of oxygen, and 16 more of co2 plus 18 moles of h2o.

02:02 The volume of octane is v is equal to 1 .00 gallon and the density of octane is d is equal to 2 .650 kg per gallon the total mass of co2 co and h2o is is the mass mass of product is equal to 11 .53 kg is equal to 11530 gram and let us calculate calculate the friction of octane converted to co2 first we will find the mass of octane so mass of octane is equal to density into volume is equal to 2 .650 kilogram per gallon into 1 .00 gallon is equal to 2 .650 kilogram kilogram is equal to 2 .650 kilogram is equal to 2 .650.

05:34 Into 10 raise to the power 3 ground.

05:46 Now we will find the number of moles of octane.

06:02 Octane the molar mass of octane is molar mass of octane is equal to 8 into molar mass of carbon plus 18 into molar mass of hydrogen is equal to 8 into molar mass of carbon is 12 .11 gram per mole plus a 18 into molar mass of hydrogen is 1 .008 gram per mole.

06:57 The calculated molar mass of octane is 114 .2 .32 gram per mole.

07:19 The number of moles of octane is number of moles of octane is equal to mass of octane divided by molar mass of octane is equal to mass of octane is equal to mass of octane is 2 .650 into 10 raise to the power 3.

08:18 Gram divided by molar mass of octane is 114 .2 .232 gram per mole is equal to 23 .198 mole.

08:54 Gram -gum cancel and left it left is small.

09:00 So the molar mass, molar number of moles of octane is 23 .198 moles.

09:18 And now we will find the number of moles and mass of water.

09:26 Find the number of moles and mass of water.

09:48 Since 2 moles of octane produces 18 moles of water.

09:57 And 23 .198 moles of octane will produce...

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