The complete combustion of octane, C8H18, produces 5470 kJ of heat. Calculate how many grams of octane are required to produce 20,000 kJ of heat.

Verified step by step guidance

Step 1: Write the balanced chemical equation for the complete combustion of octane: \[ 2 \text{C}_8\text{H}_{18} + 25 \text{O}_2 \rightarrow 16 \text{CO}_2 + 18 \text{H}_2\text{O} \].

Step 2: Note that the combustion of 2 moles of octane produces 5470 kJ of heat. Therefore, calculate the heat produced per mole of octane by dividing 5470 kJ by 2.

Step 3: Determine the number of moles of octane needed to produce 20,000 kJ of heat by dividing 20,000 kJ by the heat produced per mole of octane calculated in Step 2.

Step 4: Calculate the molar mass of octane (C8H18) by adding the atomic masses of carbon (C) and hydrogen (H): \[ 8 \times 12.01 \text{ g/mol} + 18 \times 1.01 \text{ g/mol} \].

Step 5: Convert the moles of octane needed (from Step 3) to grams by multiplying the number of moles by the molar mass of octane calculated in Step 4.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate how much of a substance is needed or produced based on the balanced chemical equation. In this case, understanding the stoichiometric coefficients will help determine the amount of octane required to produce a specific amount of heat.

Heat of Combustion

The heat of combustion is the amount of energy released when a substance undergoes complete combustion with oxygen. For octane, the heat of combustion is given as 5470 kJ per mole. This value is crucial for calculating how many grams of octane are needed to achieve a desired energy output, such as 20,000 kJ in this problem.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For octane (C8H18), the molar mass can be calculated by summing the atomic masses of its constituent elements. This concept is essential for converting between moles of octane and grams, allowing us to find the mass needed to produce the specified amount of heat.

Recommended video:

Guided course

02:11

Molar Mass Concept

Related Practice

Textbook Question

The complete combustion of octane, C8H18, a component of gasoline, proceeds as follows: 2 C₈H₁₈(l) + 25 O₂(g) → 16 CO₂(g) + 18 H₂O(g) (b) How many grams of O₂ are needed to burn 10.0 g of C₈H₁₈?

Textbook Question

The complete combustion of octane, C₈H₁₈, a component of gasoline, proceeds as follows: 2 C₈H₁₈ (l) + 25 O₂ (g) → 16 CO₂ (g) + 18 H₂O (g) (c) Octane has a density of 0.692 g/mL at 20 °C. How many grams of O₂ are required to burn 15.0 gal of C₈H₁₈ (the capacity of an average fuel tank)?

views

Textbook Question

Detonation of nitroglycerin proceeds as follows: 4 C3H5N3O91l2¡ 12 CO21g2 + 6 N21g2 + O21g2 + 10 H2O1g2 (a) If a sample containing 2.00 mL of nitroglycerin 1density = 1.592 g>mL2 is detonated, how many moles of gas are produced?

Textbook Question

The combustion of one mole of liquid octane, CH3(CH2)6CH3, produces 5470 kJ of heat. Calculate how much heat is produced if 1.000 gallon of octane is combusted.

Textbook Question

Consider the mixture of ethanol, C2H5OH, and O2 shown in the accompanying diagram. (b) Which reactant is the limiting reactant?

Textbook Question

Consider the mixture of ethanol, C2H5OH, and O2 shown in the accompanying diagram. (c) How many molecules of CO2, H2O, C2H5OH, and O2 will be present if the reaction goes to completion?