Question

When ethanol (grain alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) ) is burned in oxygen, approximately \(1360 \mathrm{~kJ}\) of heat energy is released per mole of ethanol.$$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)$$ a. What quantity of heat is released for each gram of ethanol burned? b. What is \(\Delta H\) for the reaction as written? c. How much heat is released when sufficient ethanol is burned so as to produce 1 mole of water vapor?

Short answer

a. The heat released for each gram of ethanol burned is 29.51 kJ/g. b. The ΔH value for the reaction as written is -1360 kJ/mol. c. The heat released when enough ethanol is burned to produce 1 mole of water vapor is 453.33 kJ.

Step-by-step solution

a. Calculate the heat released for each gram of ethanol burned.

To find the heat released for each gram of ethanol burned, we need to divide the heat released per mole by the molecular weight of ethanol. First, we will calculate the molecular weight of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). Ethanol contains 2 carbon atoms, 6 hydrogen atoms, and an oxygen atom. Using Atomic weights from the periodic table: Carbon (C) - 12.01 g/mol Hydrogen (H) - 1.01 g/mol Oxygen (O) - 16.00 g/mol Molar Mass of Ethanol = (2 x 12.01) + (6 x 1.01) + (1 x 16.00) Molar Mass of Ethanol = 46.07 g/mol Now we can calculate the heat released for each gram of ethanol burned: Heat released per gram = (Heat released per mole) / (Molar mass of ethanol) Heat released per gram = (1360 kJ/mol) / (46.07 g/mol) Heat released per gram = 29.51 kJ/g

b. Calculate the ΔH value for the reaction as written.

In the given reaction, 1 mole of ethanol reacts with 3 moles of oxygen to produce 2 moles of carbon dioxide and 3 moles of water vapor. The heat released for 1 mole of ethanol is 1360 kJ. Therefore, the enthalpy change ΔH for the reaction as written is: ΔH = -1360 kJ/mol (the negative sign indicates that heat is released, exothermic reaction)

c. Calculate the heat released when enough ethanol is burned to produce 1 mole of water vapor.

In the given reaction, 1 mole of ethanol produces 3 moles of water. Now we need to calculate the heat released when enough ethanol is burned to produce 1 mole of water. From the stoichiometry of the reaction, burning 1 mole of ethanol produces 3 moles of water. Therefore, to produce 1 mole of water, we need to burn 1/3 mole of ethanol. Now, as the heat released per mole of ethanol is 1360 kJ, we need to find the heat released for 1/3 mole of ethanol. Heat released = (1360 kJ/mol) x (1/3) Heat released = 453.33 kJ So, the heat released when enough ethanol is burned to produce 1 mole of water vapor is 453.33 kJ.

Key concepts

Heat Released Per Gram

When calculating the heat released per gram of a substance, we must take into consideration the substance's molecular weight, known as its molar mass. This allows us to determine how much energy is produced when a tiny, measurable portion of that substance is used. For instance, ethanol, a commonly used fuel, releases a certain amount of heat when burned.

To find the heat released per gram, we first need the heat released per mole, a unit that measures the bulk amount of molecules. Given the reaction for ethanol with oxygen, we know that it releases 1360 kJ per mole. By dividing the heat per mole by the substance's molar mass, we find the energy released per gram:

• Heat released per gram = (Heat released per mole) / (Molar Mass of Ethanol)
• With the molar mass of ethanol calculated as 46.07 g/mol, we proceed:

This gives us a value of 29.51 kJ/g, which tells us how much energy is released for every single gram of ethanol when it combusts.

Molar Mass Calculation

Calculating the molar mass of a substance is a fundamental step in many chemical calculations. It starts with understanding the composition of the molecule in terms of its constituent elements. For ethanol, (\( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \)), the composition includes carbon, hydrogen, and oxygen.

To calculate its molar mass, we sum up the atomic masses of all atoms contained in one molecule of ethanol:

• Carbon (C) has an atomic mass of 12.01 g/mol. Since there are 2 carbon atoms, they contribute 24.02 g/mol.
• Hydrogen (H) has an atomic mass of 1.01 g/mol. With 6 hydrogen atoms, we get an additional 6.06 g/mol.
• Oxygen (O), with 1 atom, contributes 16.00 g/mol.

Adding up all these contributions gives the total molar mass of ethanol as 46.07 g/mol. Knowing the molar mass is crucial, as it lets us convert between the quantity of substance in moles and its mass, an essential step in calculating the energy release per gram.

Stoichiometry of Reactions

Stoichiometry is the part of chemistry that calculates the relationships between the reactants and products in a chemical reaction. It is essentially a ratio-based problem-solving method that lets us predict the amount of products formed from given reactants or vice versa. In the combustion of ethanol, stoichiometry helps us understand how moles of oxygen react with moles of ethanol to form carbon dioxide and water.

The balanced equation: \[ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) + 3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g) + 3 \mathrm{H}_{2} \mathrm{O}(g) \] tells us that one mole of ethanol reacts with three moles of oxygen to create two moles of carbon dioxide and three moles of water.

This relationship comes into play when calculating the heat released for producing specific amounts of products. For example, to find the heat released when generating one mole of water, we utilize the mole ratio between ethanol and water (1 mole of ethanol produces 3 moles of water). By determining how much heat corresponds to a specific output of moles, we can easily convert this to energy values useful in practical applications like predicting fuel efficiency.