Problem 61 - Chemistry: The Central Science

Question

Natural gas consists primarily of methane, \(\mathrm{CH}_{4}(\mathrm{~g})\). (a) Write a balanced chemical equation for the complete combustion of methane to produce \(\mathrm{CO}_{2}(g)\) as the only carbon-containing product. (b) Write a balanced chemical equation for the incomplete combustion of methane to produce \(\mathrm{CO}(g)\) as the only carbon-containing product. (c) At \(25^{\circ} \mathrm{C}\) and \(1.0\) atm pressure, what is the minimum quantity of dry air needed to combust \(1.0 \mathrm{~L}\) of \(\mathrm{CH}_{4}(\mathrm{~g})\) completely to \(\mathrm{CO}_{2}(\mathrm{~g})\) ?

Step-by-Step Solution

Answer

(a) The balanced chemical equation for the complete combustion of methane is: \(CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O\). (b) The balanced chemical equation for the incomplete combustion of methane is: \(CH_4 + 1.5O_2 \rightarrow CO + 2H_2O\). (c) The minimum quantity of dry air needed to combust 1.0 L of \(CH_4(\mathrm{g})\) completely to \(CO_2(\mathrm{g})\) at \(25^{\circ} \mathrm{C}\) and 1.0 atm pressure is \(1.95 \mathrm{~L}\).

Step 1: (a) Complete Combustion of Methane

To balance the chemical equation for the complete combustion of methane, we need to make sure the number of atoms of each element is the same on both sides of the equation. The complete combustion of methane produces carbon dioxide (CO2) and water (H2O). The unbalanced equation looks like this: CH4 + O2 -> CO2 + H2O Now, we balance the equation: CH4 + 2O2 -> CO2 + 2H2O This is the balanced chemical equation for the complete combustion of methane.

Step 2: (b) Incomplete Combustion of Methane

For the incomplete combustion of methane, carbon monoxide (CO) is produced instead of carbon dioxide. The unbalanced equation looks like this: CH4 + O2 -> CO + H2O To balance the equation, we will adjust the number of oxygen atoms: CH4 + 1.5O2 -> CO + 2H2O This is the balanced chemical equation for the incomplete combustion of methane.

Step 3: (c) Minimum Quantity of Dry Air

To find the minimum quantity of dry air required to combust 1.0 L of CH4(g) completely to CO2(g) at 25°C and 1.0 atm pressure, we need to use the Ideal Gas Law equation, which states that: PV = nRT Where P is pressure, V is volume, n is moles, R is the ideal gas constant (0.0821 L atm / K mol), and T is temperature in Kelvin. First, convert the temperature to Kelvin: T = 25°C + 273.15 = 298.15 K Now, use the Ideal Gas Law to find the moles of CH4: (1.0 atm)(1.0 L) = nCH4(0.0821 L atm / K mol)(298.15 K) nCH4 = 0.0409 mol From the balanced equation for complete combustion, 2 moles of O2 are required for every mole of CH4, so: nO2 = 2 × nCH4 = 2 × 0.0409 mol = 0.0818 mol Air is approximately 21% O2 by volume, so the volume of air required can be calculated as: Volume of air = Volume of O2 / 0.21 = 0.0818 mol / 0.21 Now, use the Ideal Gas Law to find the volume of air: PV = nRT (1.0 atm)(Vair) = (0.0818 mol / 0.21)(0.0821 L atm / K mol)(298.15 K) Vair = 1.0 atm × 0.390 L = 1.95 L Therefore, the minimum quantity of dry air needed to combust 1.0 L of CH4(g) completely to CO2(g) at 25°C and 1.0 atm pressure is 1.95 L.

Key Concepts

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance reacts with oxygen, releasing energy in the form of heat and light. This is often seen when fuels like methane are burned. A combustion reaction involves the conversion of the reactants into products typically through the formation of carbon dioxide and water, especially when hydrocarbons like methane are involved.

Key characteristics of these reactions include:

• Involve oxygen as one of the reactants.
• Release a significant amount of energy.
• Produce carbon dioxide and water in complete combustion.

Combustion is a crucial process in various applications, from powering engines to heating homes.

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry that describes the behavior of gases under ideal conditions. It is represented by the formula \(PV = nRT\), where:

• \(P\) is the pressure of the gas.
• \(V\) is the volume of the gas.
• \(n\) is the number of moles of the gas.
• \(R\) is the ideal gas constant, typically 0.0821 L atm / K mol.
• \(T\) is the temperature in Kelvin.

By using the Ideal Gas Law, we can calculate various properties of a gas, such as its pressure, volume, or number of moles, under specific conditions of temperature and pressure. It’s especially useful in determining how much oxygen is needed in reactions like the combustion of methane.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses balanced chemical equations to measure the quantities—usually in moles—of each compound involved.

This concept is vital because it allows chemists to predict the amount and products formed in a reaction, as well as determine the proportions needed to completely consume the reactants. In the context of methane combustion, stoichiometry helps establish the ratio of methane to oxygen needed for complete combustion, ensuring there is no leftover reactant.

Methane Combustion

Methane combustion is a common example of a combustion reaction, where methane reacts with oxygen. It occurs in two primary forms: complete and incomplete combustion.

In complete combustion, methane burns with oxygen to produce carbon dioxide and water: \[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]This type of combustion releases energy efficiently.

Incomplete combustion, however, occurs with insufficient oxygen, producing carbon monoxide and water: \[ \text{CH}_4 + 1.5\text{O}_2 \rightarrow \text{CO} + 2\text{H}_2\text{O} \]This process is less efficient and can be hazardous due to carbon monoxide production.

Chemical Equation Balancing

Chemical equation balancing is essential for ensuring the law of conservation of mass is upheld in a reaction. Every atom that appears on the reactant side should also appear on the product side, in the same quantity.

When balancing equations, it’s important to follow these steps:

• Identify the number of each type of atom present in the reactants and products.
• Adjust coefficients to balance each type of atom across both sides of the equation.
• Re-check the balance of all atoms after adjustments.

This process guarantees that the reaction accurately represents conservation laws, as seen in the chemical equations for methane's combustion.