Hydrogen and methanol have both been proposed as alternatives to hydrocarbon fuels. Which fuel contains the most energy in the least mass?

Video transcript

Hi everyone for this problem. We're told that biofuels such as Butin all and ethanol are used as a more environmentally friendly alternative to fossil fuels. We need to identify which of the two contains the greater energy per unit of mass. And so we know our energy is going to be in killing jewels and our unit of mass is in grams. So essentially we're solving for our standard entropy change for our reaction. And we're looking for which one is going to have the higher value and kill a jewels per gram. So let's go ahead and get started. So we know we have Butin all and ethanol. So we're going to calculate two separate things here and then compare for beauty and all are chemical reaction and it's going to be balanced is going to be C four H 10. Oh, that is beautiful. And when it reacts with oxygen, it produces four carbon dioxides Plus five H 20. So this is our chemical, our balanced chemical equation. And we need to solve for our standard and they'll be change for our reaction. And we're going to need the standard heats of formation for each of our reactant and products in order to solve for this. And this is going to be the sum of our products minus the sum of our reactant. And the standard heats of formation is something that we're going to have to look up online. The values for that. And so I'll write them in for what the values are so far our products, we have two products carbon dioxide and water. And so we need to multiply our standard heats of formation for each by the number of moles of each. Okay, and so let's start off with our water H 20. We have five moles of H 20. And when we look up the standard heat of formation for water, it is going to be -285. killer jewels per mole minus. Sorry, this is plus the some of our products plus We have four moles of carbon dioxide. And our standard heats of formation for carbon dioxide is negative 393 0.5 kg jewels per mole. So that's the sum of our products minus the sum of our reactant. And so we have six moles of oxygen. And oxygen is in its elemental state. And anything in its elemental state has a standard heat of formation of zero. So this is going to be time zero killer jewels per mole. Plus We have one mole of beautiful. And the standard heat of formation for butin all is negative 328 0.4. Kill the jewels Permal. So now we've put in all of our values and we just need to solve so we can go ahead and cross our Six moles of out because we know that's going to be zero. And when we saw for our standard entropy change for a reaction, we get for Beauty in all, it is going to equal -260 Sorry negative 2674. killer jewels Permal. But the answer asked us for it. And energy per unit mass. And so were in kill o jewels per mole. And we need it in kila jules per gram. And so that means we're going to need the molar mass of beauty in all in order to do that conversion. And so we know that and one more Of beauty in all. We need to find the molar mass. And when we look that up and calculated the Molar mass is going to be 74.14 g. Okay. And so our our moles cancel and we're left with killer joules per gram which is what we want. And so we get a final answer of negative 36.07. Kill the jewels program of butte and all. Okay so that is our standard entropy change of the reaction for butin also. Now we need to do the same thing for ethanol and then we'll compare to see which has the greater energy per unit of mass. And so our chemical equation for ethanol is C. Two age five O. H. Reacts with three oxygen's to produce two carbon dioxides plus three waters. Okay so we're gonna do the same thing. Our standard entropy change of our reaction is going to equal the sum of our products minus the sum of our reactant. And we need to look up the standard heats of formation for our products and our react ints. And so we see here That for our products we have three moles of water and their standard heat of formation is negative 80 5.8. Kill jules per more. So I'm going to For the sake of space, I'm not going to write the units here. So we have negative 2 85.8 And then we have two moles of c. 0 2. And The standard heat of formation is - 0.5. So that's the sum of our products minus the sum of our reactant. We have three oxygen's and we know that is zero. The standard formation is zero plus one mole of ethanol. In the standard heat of formation of ethanol Is -2 69.3. Okay, So now we get a standard heat of four nation or a standard entropy change for our reaction to be -1375. killer jewels Permal. And we need this and kill a jules program. So that means we're going to need the molar mass of Ethanol. So in one mole of ethanol, the molar mass is .08 g. Our moles cancel. And we're left with killer joules per gram. And so once we do that math we get negative 29.84 killer jewels her gram of ethanol. Okay, so now we've calculated our energy per unit mass and it's asking for which of the two contains the greater one. And so we're looking for that one with the higher standard entropy change and that one is going to be beautiful, negative 36.7 killer jewels per gram is greater than negative 29.84 killer jewels per gram. And so that is the final answer. And that is the end of this problem. I hope this was helpful.