For the unbalanced combustion reaction shown, 1 mol of ethanol, C₂H₅OH, releases 327 kcal (1370 kJ):
C₂H₅OH + O₂ → CO₂ + H₂O
e. If the density of ethanol is 0.789 g/mL, calculate the combustion energy of ethanol in kilocalories/milliliter and kilojoules/milliliter

Question

For the unbalanced combustion reaction shown, 1 mol of ethanol, C₂H₅OH, releases 327 kcal (1370 kJ):

C₂H₅OH + O₂ → CO₂ + H₂O

e. If the density of ethanol is 0.789 g/mL, calculate the combustion energy of ethanol in kilocalories/milliliter and kilojoules/milliliter

Accepted Answer

Welcome back, everyone in the combustion of one mole of cyclone which corresponds to negative 828 kg of energy being released. The unbalanced reaction is as follows where we've got cyclo heen reacting with one mole of oxygen to form carbon dioxide and water as products, we need to determine the combustion energy in kilocalories per milliliter and kilojoules per milliliter. Given that the density of cyclo hexen is 0.948 g per milli. Our first step is to ensure that we have a balanced equation. So we're going to need to compare both the reactant and product side as far as the number of atoms present on each side. So rewriting the reaction, we're going to again compare reactants to products. We've got on the reactant side, carbon hydrogen, oxygen as the atoms listed and the same thing on our product side. Whereas we can list out the numbers. So for the reactant side, we've got six carbons total, we've got a total of 12 hydrogens and we've got a total of three oxygen atoms. And on the product side, we've got one total atom of carbon, two total atoms of hydrogen and three total atoms of oxygen. We're going to begin balancing by placing a coefficient of six in front of carbon on the product side. So six in front of CO2 to now give us a total of six carbons on both sides of our reaction, which will change the number of oxygens to a total of 13. Now, on the product side, but we can then also fix the number of hydrogens that we've got on both sides of the equation by placing a coefficient of six in front of water on the product side, which will give us a total of now 12 moles of hydrogen on both sides of the reaction. And we change our oxygen from 13 to now a total of 18 moles of oxygen. On the product side, we still only have three moles of oxygen on the reactant side. So we're going to then place a coefficient of 17 over two in front of oxygen on the reactant side, which will cancel out to reduce to just 17 moles of oxygen plus the additional oxygen present in the formula of cyclohexane, which would then give us a total of 18 moles of oxygen on both sides of our reaction. And with these coefficients written out, we now have a confirmed balanced reaction. So now that we've got that, that step taken care of, we are then going to calculate the molar mass of our reagent cyclo hexen. So for the molar mass of cycle hexen, we have its chemical formula given as C six H 11 0 H. And beginning with our carbon atoms, we've got six moles of carbon, which is multiplied by the molar mass of carbon on the periodic table, which would be 12 point oh one g per mole. So let's actually just write out six carbon atoms so that we don't have to cancel out any units since we want molar mass and grams per mole, this is then going to be added to the 12 moles or sorry, just the 12 atoms of hydrogen, which is multiplied by the molar mass of hydrogen from the periodic table, which we would observe is a value of 1.8 g per mole. So then added to that is then our one atom of oxygen which is multiplied by oxygen's molar mass from the periodic table of 16 point oh grams per mole. So, simplifying and taking the sum here, we would find a molar mass for cyclo hein equal to about 100.156 g per mole. And this should say grams per mole. So that is our molar mass of cyclo heen. So now we are going to determine the combustion energy first in Kilic calories per milliliter. So, combustion energy in kill cows per mil liter, and we would determine that first by beginning with the given combustion energy where we are told that we've got the release of 828 kg per mole of energy. And because this is the release of energy, we would make this value negative. So we'd got, we'd have negative 8 28 kg cos per mole. And we are going to first multiply to cancel out the unit of moles. So we're going to multiply by the molar mass of cycle hexen where we've got moles in the numerator and grams in the denominator. And so we can plug in for one mole of cyclo hein 100.156 g that will then allow us to make our next conversion factor. After we cancel out moles, we would want to then cancel out grams by making our third conversion factor be the given density of cycle hexen from the prompt as 0.948 g per millilitre. So this allows us to then cancel out our units of grams and that leaves us with Kics per milliliter as our final units. So, simplifying, we would find that we've got the combustion of energy in Kics per milliliter equal to a value of negative 7.84 Kilic cos per mil liter as our first answer being the combustion of energy in kill cos per milli for cyclo hexen. And now we're going to then find the combustion of energy in now kilojoules per millilitre for cycle heal where we would begin with the equivalence of the combustion of energy released in kilojoules, which is told to us in parentheses in the prompt being 3464 kilojoules per mole. And this is going to be negative. Since again, energy is being released, we would multiply again to cancel out the unit of moles. So we've got in the numerator, one mole of cyclo heen, which is out of in our denominator 100.1 g of cycle hexen. So canceling out moles, we've got now kilojoules per gram and we need kilojoules per milliliter. So we would make our second conversion factor that we multiply by allow us to go from the density given again. So we've got 0.948 g per mil liter. So canceling out grams, we are then left with kilojoules per milliliter as the final units. And so simplifying, we would then find the combustion of energy in kilojoules per milliliter equal to a value of negative 32.8 kilojoules per milliliter. And this would be our second final answer to complete this example as the combustion of energy of cyclo hexen in kilos per M liter. So these are our two final answers. I hope that this made sense and let us know if you have any questions.

For the unbalanced combustion reaction shown, 1 mol of ethanol, C₂H₅OH, releases 327 kcal (1370 kJ):
C₂H₅OH + O₂ → CO₂ + H₂O
e. If the density of ethanol is 0.789 g/mL, calculate the combustion energy of ethanol in kilocalories/milliliter and kilojoules/milliliter

Verified video answer for a similar problem:

Key Concepts

Combustion Reaction

Energy Conversion

Density and Volume Calculations

For the unbalanced combustion reaction shown, 1 mol of ethanol, C2H5OH, releases 327 kcal (1370 kJ): C2H5OH + O2 → CO2 + H2O e. If the density of ethanol is 0.789 g/mL, calculate the combustion energy of ethanol in kilocalories/milliliter and kilojoules/milliliter

Verified video answer for a similar problem:

Key Concepts

Combustion Reaction

Energy Conversion

Density and Volume Calculations

For the unbalanced combustion reaction shown, 1 mol of ethanol, C₂H₅OH, releases 327 kcal (1370 kJ):
C₂H₅OH + O₂ → CO₂ + H₂O
e. If the density of ethanol is 0.789 g/mL, calculate the combustion energy of ethanol in kilocalories/milliliter and kilojoules/milliliter