Problem 64 - Chemistry Matter and Change

Question

Greenhouse Gas Carbon dioxide is a greenhouse gas that is linked to global warming. It is released into the atmosphere through the combustion of octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) in gasoline. Write the balanced chemical equation for the combustion of octane and calculate the mass of octane needed to release 5.00 \(\mathrm{mol}\) of \(\mathrm{CO}_{2}\)

Step-by-Step Solution

Answer

The balanced chemical equation for the combustion of octane is \(C_8H_{18} + 12.5O_2 \rightarrow 8CO_2 + 9H_2O\). To release 5.00 moles of CO2, 0.625 moles of octane are needed, which is equivalent to 71.41 g of octane.

Step 1: Unbalanced Chemical Equation

To write the unbalanced combustion reaction, we will add oxygen (O2) to the reactants and carbon dioxide (CO2), and water (H2O) to the products: \(C_8H_{18} + O_2 \rightarrow CO_2 + H_2O\) Step 2: Balance the chemical equation

Step 2: Balance the Chemical Equation

To balance the combustion reaction, we start by balancing the carbon atoms, then hydrogen atoms, and finally oxygen atoms: \( C_8H_{18} + O_2 \rightarrow 8CO_2 + H_2O \) (8 carbon atoms balanced) \( C_8H_{18} + O_2 \rightarrow 8CO_2 + 9H_2O \) (18 hydrogen atoms balanced) Now, count the oxygen atoms on each side: There are 2 oxygen atoms on the left and 25 oxygen atoms on the right (16 from CO2 and 9 from H2O). To balance the oxygen atoms, we put a coefficient of 25/2 (12.5) in front of O2: \( C_8H_{18} + 25/2O_2 \rightarrow 8CO_2 + 9H_2O \) (Oxygen atoms balanced) Now, the balanced chemical equation is: \( C_8H_{18} + 12.5O_2 \rightarrow 8CO_2 + 9H_2O \) Step 3: Calculate the mass of octane needed to release 5.00 moles of CO2

Step 3: Calculating Mass of Octane

To calculate the mass of octane, we first need to find the molar mass of octane, which is given by the sum of the atomic masses of its constituent elements: Molar mass of octane = 8 × (mass of C) + 18 × (mass of H) = 8 × 12.01 g/mol + 18 × 1.01 g/mol = 96.08 g/mol + 18.18 g/mol = 114.26 g/mol From the balanced equation, we see that 1 mole of octane reacts to produce 8 moles of CO2. Dividing the amount of CO2 by the stoichiometric ratio gives us the moles of octane: Moles of octane = moles of CO2 ÷ 8 = 5.00 mol ÷ 8 = 0.625 mol Now, we will find the mass of octane. Use the following formula: Mass of octane = Moles of octane × Molar mass of octane = 0.625 mol × 114.26 g/mol = 71.4125 g Therefore, the mass of octane needed to release 5.00 moles of CO2 is 71.41 g (rounded to two decimal places).

Key Concepts

Explaining Greenhouse Gases

Carbon dioxide (CO2) is a prevalent greenhouse gas, which is a type of gas that traps heat in the Earth's atmosphere. This heat-trapping effect contributes to global warming and climate change. When carbon fuels like gasoline are burned, they release CO2 as a byproduct. This process adds more greenhouse gases to the atmosphere, thereby intensifying the earth's heat retention.

• Greenhouse gases include not only CO2 but also methane (CH4), nitrous oxide (N2O), and water vapor (H2O).
• Plants, when breathing, take in CO2 and release oxygen. However, human activities have increased CO2 levels drastically.
• Combustion of fossil fuels is a significant source of CO2 emissions worldwide.

Understanding the role of CO2 in the atmosphere is crucial for developing strategies to combat global warming. Making more environmentally friendly choices, like reducing the use of fossil fuels, can help mitigate these effects.

Balancing Chemical Equations

A balanced chemical equation is vital as it ensures the conservation of mass and reflects the reality of chemical reactions. Each side of the equation must have the same number of each type of atom, thus obeying the Law of Conservation of Mass, which dictates that matter cannot be created or destroyed in a chemical reaction.

• Start by writing the unbalanced equation.
• Balance one type of atom at a time, usually starting with the most complex molecule.
• Adjust coefficients to ensure the same number of each atom on both sides of the equation.

In the combustion of octane, as seen in the exercise, the equation is initially unbalanced. By balancing carbons first, then hydrogens, and finally oxygens, we obtain a clear picture of how much each element is needed in the reaction. This step is critical to accurately perform further calculations, such as determining the amount of reactant needed.

Calculating Molar Mass

Molar mass is the mass of one mole of a substance, often expressed in grams per mole (g/mol). It's a crucial factor when converting between moles and grams in chemical reactions. To find the molar mass, add up the atomic masses of all atoms present in the chemical formula.

For instance, to calculate the molar mass of octane (C8H18):

• Carbon (C) has an atomic mass of 12.01 g/mol, and there are 8 carbon atoms: 8 x 12.01 g/mol = 96.08 g/mol.
• Hydrogen (H) has an atomic mass of 1.01 g/mol, and there are 18 hydrogen atoms: 18 x 1.01 g/mol = 18.18 g/mol.

By adding these masses together, we find that octane's molar mass is 114.26 g/mol.

Understanding molar mass allows chemists to convert moles into grams and vice versa, facilitating the practical use of substances in laboratory settings and industrial applications. It forms the basis of calculating how much of a substance is necessary for a given chemical reaction.