Ethanol, C2H5OH, is mixed with gasoline and sold as gasohol. Use the following to calculate the grams of ethanol needed to provide 367 kJ of heat.
C2H5OH(l) + 3 O2(g) �¨ 2 CO2(g) + 3 H2O(g)
ƒ¢H = −1235 kJ
I suppose that funny symbolism is delta H.
So 1235 kJ heat are released when 1 mol(46 grams) C2H5OH are combusted. YOu want 367 kJ; therefore,
46 grams x (367 kJ/1235 kJ) = ? grams.
To calculate the grams of ethanol needed to provide 367 kJ of heat, we need to use the given enthalpy change (ΔH) and the stoichiometry of the balanced chemical equation.
Given:
ΔH = -1235 kJ
Desired heat = 367 kJ
To determine the moles of ethanol required, we can use the following equation:
ΔH = n × ΔH_rxn
Where:
n = moles of ethanol
ΔH_rxn = enthalpy change of the reaction
Rearranging the equation to solve for moles of ethanol:
n = ΔH / ΔH_rxn
Plugging in the values:
n = 367 kJ / (-1235 kJ)
n = -0.297
Since we cannot have a negative number of moles, this result indicates that we need 0.297 moles (or approximately 0.3 moles) of ethanol.
Now, we can use the molar mass of ethanol to convert moles to grams. The molar mass of ethanol (C2H5OH) is 46.07 g/mol.
Mass of ethanol = moles of ethanol × molar mass of ethanol
Mass of ethanol = 0.3 moles × 46.07 g/mol
Mass of ethanol ≈ 13.82 g
Therefore, approximately 13.82 grams of ethanol are needed to provide 367 kJ of heat.
To calculate the grams of ethanol needed to provide 367 kJ of heat, we can use the following steps:
Step 1: Determine the molar mass of ethanol (C2H5OH)
The molar mass of ethanol (C2H5OH) can be calculated by summing up the atomic masses of its constituent elements.
C: 2 atoms x atomic mass of carbon (12.01 g/mol) = 24.02 g/mol
H: 6 atoms x atomic mass of hydrogen (1.01 g/mol) = 6.06 g/mol
O: 1 atom x atomic mass of oxygen (16.00 g/mol) = 16.00 g/mol
Total molar mass of ethanol (C2H5OH) = 24.02 g/mol + 6.06 g/mol + 16.00 g/mol = 46.08 g/mol
Step 2: Calculate the moles of ethanol required
We know that the enthalpy change (ΔH) for the reaction is -1235 kJ. We can use this information to convert the given energy value in kJ to moles of ethanol.
ΔH = -1235 kJ
Energy in J = 367 kJ x 1000 J/kJ = 367,000 J
Now we can use the equation ΔH = Energy / (moles of ethanol x molar mass) to solve for the moles of ethanol.
ΔH = 367,000 J
ΔH = moles of ethanol x molar mass of ethanol
Rearranging the equation, we can solve for moles of ethanol:
moles of ethanol = ΔH / molar mass of ethanol
moles of ethanol = 367,000 J / 46.08 g/mol = 7958.6 mol
Step 3: Convert moles to grams of ethanol
Finally, to convert moles of ethanol to grams, we use the molar mass of ethanol.
grams of ethanol = moles of ethanol x molar mass of ethanol
grams of ethanol = 7958.6 mol x 46.08 g/mol = 366,606.288 g
Therefore, approximately 366,606 grams (or 366.6 kg) of ethanol would be needed to provide 367 kJ of heat.