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Kim Pham
Numerade Educator

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Fuel Value

The fuel value of a substance is the amount of heat released when a specified amount (e.g. 1 gram) of the substance is completely combusted in oxygen (O) at a constant pressure (e.g. 1 atm) in a bomb calorimeter. The heat of combustion is the enthalpy change of combustion. The enthalpy change of combustion is the amount of heat released during the combustion of a given substance, and is equivalent to the fuel value of the substance. The amount of heat released is the heat of combustion and the substance is the fuel. The most commonly used fuels are hydrocarbons, particularly methane. The standard state used is 1 atmosphere (atm) pressure. The heat of combustion of a fuel is the enthalpy change (?H) of combustion. The heat of combustion is the enthalpy change of combustion. The enthalpy change of combustion is the amount of heat released during the combustion of a given substance, and is equivalent to the fuel value of the substance. The amount of heat released is the heat of combustion and the substance is the fuel. The most commonly used fuels are hydrocarbons, particularly methane. The standard state used is 1 atmosphere (atm) pressure. The fuel value of a substance is the amount of heat released when a specified amount (e.g. 1 gram) of the substance is completely combusted in oxygen (O) at a constant pressure (e).

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Video Transcript

so in application of the bomb calorie burner is actually finding the fuel value different things. So you can actually use bomb calorie country to find the number of calories in food. And so that is one real world application. Um, for those types of problems. So this is often reported in energy person kind of breast density and have something like calorie program, those rules per mall and so on on DSO. It's also important to note that the fuel value is always positive because when you're reporting, say, the calorie a bag of cereal, you don't report the calories as a negative value but a positive value. But it is important to note that the, um, entropy of combustion, which is often used to figure out the fuel value, is always negative because when you're combusting something that is always an extra thermic reaction. And so the Delta H is negative and services, um, better demonstrated by a few examples. But essentially, this is thought of as kind of the final step. Two different bomb Kalorama tree problems. And so, for our first problem, if we have the delta age of a reaction, we need to figure out the fuel value for propane. So to join the fuel value. You want this in Mass? Um, so let's say you want units of killer jewels. Okay, so do this problem. We just need to figure out the mole arrests of propane on, then using dimensional analysis, we can get the units that we want. And so protein has a chemical formula of C three h eight. And so if you figure out the Mueller Mass, we need to multiply three by the atomic mass of common. And we have eight protons, so that would be one point students or eight times eight. And so the molar mass approving is 44.1 g Permal. And so if we set this up, like so we can divide this by the molar mass. So we get moles on top and grams on the bottom. And so if you do this, you are left with 12 white, one Villa Jewel's program. And because the field value is reported as a positive number, we do not use the negative sign. And so this would be our final answer. So for the second part of the problem were given that if we have a more of table sugar undergoing a commission reaction and given the Delta H, we need to figure out the field value. And so here were given a Delta H with just units of kill jewels. And so we need to first get killed, jewels promote and then convert that to kill jewels program. And so were given that we have one more of sugar, so we can simply divide this by one wall, and we need to determine the field value for sugar. So we need to divide this by the molar mass. Do you get the right units? So the molar mass of table sugar is 300 42.3 has shown in our previous videos. And so if we do out the math, we get a answer. 6.89 kill jewels program. And so as long as you know what units you need, thes problems are relatively straightforward. So for the next problem will be determining the Delta H of combustion for the combustion of butin. Given that it's still value is 8.3 killer Joel's progress. And so, before we, uh, actually start this problem, we need to write out the chemical reaction PT to figure out the moles of butane that are involved on Then, from there we can use the more mass to determine the Delta H, which will be in units of illegal and so few. Team has a chemical formula of C four HTM. And so for a combustion reaction, we need to react this with oxygen guests so we can write C for each time, which is a liquid STP directing thio oxygen gas to yield carbon dioxide and work. So whenever we're running chemical equations, we also need to balance it. And so we see that we have four carbons on the left side. And so we need for carbon dioxide and we also need 1000 arms and we have to on the right side. So we need to go for shit five and for oxygen. We have to on the left side and we have two times four just eight plus five. And so that brings us to a total of 13. And so we need 6.5 molecules off option in gas Onda. While we're running chemical reactions again, we don't want fractions, and so we can actually multiply all the conditions. By do so, we end up with two moles. Beauty mean 13 moles of oxygen 84 coming outside in 10 for water. And so you can see that we need, uh, two moles of beauty for the commotion. And so using this to determine the delta h of combustion. And so now we can use mental analysis to get the right units. And so we know that the fuel value is 8.3 your jewels program. And so now we need thio use the molar s for butane thin. So butane, the C four h done. And so Mueller Mass is four times 12.1 plus 10 times 1.8 And when you calculate this, you should get a more mass of 58 0.12 g per mole. That's how we can use this information to make sure we get units of field jewels. And so we need grams to cancel. And so we can multiply this by the molar mass e don't have enough space. So let's just you're at this part, so I'll be 58 0.12 g for more, so our grants will cancel. But we also need a multi cancel. And so we know that we need tools of beauty mean for the commission of you teen and so weaken multiplies by to cancel the moles. And then you end up with a final answer of 965 your jewels. And we know that the Delta Age for a commission reaction must be negative because it is an extra temic reaction. And so the final answer is negative. 965 killed jewels on DSO. We also needs around the city to significant figures. And so we could write this as negative 970 killer jewels. And now for our last problem, we need to determine the number of moles of fuel consumed if its full value is 9.1 killer jewels program. Given that the Miller Mass is 723 g per mole and the entropy of combustion is 1363 Children. And so for this problem, we can just use mental analysis to get the moles from what we're given. And so we know that we can have bulls using more mass. And so we can write this as one mole over 723 g and now we need to cancel the grams. And to do that we can use the fuel value which also have units of killed jewels. So we know that we have 1 g for a 9.1 killed joules of energy. And finally, we can multiply this value by killer jewels to get units of malt. And so were given that the delta H of combustion is 1363 killed jewels. And so we can multiply this quality by this valley. And so we see that the grams canceled and the key eligibles cancel. And if you put this in your calculator, you end up with 0.27 moles, which, right into two significant figures, is 0.21 moles, which is your final answer.

Kim Pham
Brown University
Chemistry 101

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