Problem 20 - Chemistry and Chemical Reactivity

Question

Compare the mass of \(\mathrm{H}_{2}\) expected from the reaction of steam (H \(_{2} \mathrm{O}\) ) per mole of methane, petroleum, and coal. (Assume complete reaction in each case. Use \(\mathrm{CH}_{2}\) and \(\mathrm{CH}\) as representative formulas for petroleum and coal, respectively.)

Step-by-Step Solution

Answer

Methane: 8 g/mol, Petroleum: 4 g/mol, Coal: 2 g/mol of H₂.

Step 1: Write Balanced Chemical Equations

For methane: \[ \text{CH}_4 + 2\text{H}_2\text{O} \rightarrow \text{CO}_2 + 4\text{H}_2 \] For petroleum (using \(\text{CH}_2\) as a representative): \[ \text{CH}_2 + \text{H}_2\text{O} \rightarrow \text{CO} + 2\text{H}_2 \] For coal (using \(\text{CH}\) as a representative): \[ \text{CH} + \text{H}_2\text{O} \rightarrow \text{CO} + \text{H}_2 \]

Step 2: Determine Molar Masses

Calculate the molar masses of the reactants and products involved. \[ \text{Molar mass of CH}_4 = 16 \text{ g/mol} \] \[ \text{Molar mass of CH}_2 = 14 \text{ g/mol} \] \[ \text{Molar mass of CH} = 13 \text{ g/mol} \] \[ \text{Molar mass of H}_2 = 2 \text{ g/mol} \]

Step 3: Calculate Mass of Hydrogen for Methane

From the reaction, \( 1 \text{ mol of CH}_4 \) produces \( 4 \text{ mol of H}_2 \).\[ 4 \text{ mol of H}_2 \times 2 \text{ g/mol} = 8 \text{ g of H}_2 \] from methane.

Step 4: Calculate Mass of Hydrogen for Petroleum

From the reaction, \( 1 \text{ mol of CH}_2 \) produces \( 2 \text{ mol of H}_2 \).\[ 2 \text{ mol of H}_2 \times 2 \text{ g/mol} = 4 \text{ g of H}_2 \] from petroleum.

Step 5: Calculate Mass of Hydrogen for Coal

From the reaction, \( 1 \text{ mol of CH} \) produces \( 1 \text{ mol of H}_2 \).\[ 1 \text{ mol of H}_2 \times 2 \text{ g/mol} = 2 \text{ g of H}_2 \] from coal.

Key Concepts

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They provide valuable information about the reactants and products involved in the reaction, as well as their stoichiometric proportions. When you write a chemical equation, it is crucial to balance it, meaning that the number of atoms of each element on the reactant side must equal the number on the product side. Balancing ensures conservation of mass and adheres to the law of conservation of matter.
In the original exercise, we have equations representing the conversion of methane, petroleum, and coal into hydrogen gas (H_2). For instance, the equation for the reaction of methane and water is: \[ ext{CH}_4 + 2 ext{H}_2 ext{O} ightarrow ext{CO}_2 + 4 ext{H}_2 \] which is balanced, showing that one molecule of methane reacts with two molecules of water to produce one molecule of carbon dioxide and four molecules of hydrogen.

Molar Mass Calculation

Molar mass is the weight of one mole of a substance, measured in grams per mole ( ext{g/mol}). It is the mass of all the atoms in a given formula unit of that substance. To determine the molar mass, simply add the atomic masses of all atoms present in the molecular formula.
For example, let's consider methane ( ext{CH}_4). Methane consists of one carbon atom and four hydrogen atoms. The atomic mass of carbon is approximately 12 ext{g/mol} and that of hydrogen is about 1 ext{g/mol}. Thus, the molar mass of methane is \[ 12 + 4(1) = 16 ext{ g/mol} \].
In the exercise, understanding molar masses like those of methane (16 ext{g/mol}), petroleum (14 ext{g/mol} for ext{CH}_2), and coal (13 ext{g/mol} for ext{CH}) is necessary to perform stoichiometric calculations.

Hydrogen Production

Hydrogen production from various chemical reactions is an essential process in many industrial applications, including the generation of clean energy through hydrogen fuel cells and as an important component in chemical manufacturing.
In the context of the exercise, the hydrogen is produced by reacting steam ( ext{H}_2 ext{O} ) with different carbon-based fuels such as methane, petroleum, and coal. The efficiency of hydrogen production can be compared by calculating the amount of hydrogen each reaction yields per mole of fuel. For example, methane yields 8 grams of hydrogen per mole, while petroleum and coal yield 4 and 2 grams respectively. This information is critical for assessing the viability of each fuel source in hydrogen production.

Methane Reaction

Methane ( ext{CH}_4) is a simple hydrocarbon and a major component of natural gas. It reacts readily with steam in a process known as steam methane reforming (SMR) to produce hydrogen.
The chemical reaction is:\[ ext{CH}_4 + 2 ext{H}_2 ext{O} ightarrow ext{CO}_2 + 4 ext{H}_2 \]
Methane's reaction is highly efficient in producing hydrogen, yielding 4 moles of hydrogen for every mole of methane. This high yield, 8 grams of hydrogen per mole of methane, makes methane an attractive candidate for hydrogen production in industrial applications.

Petroleum Reaction

Petroleum is a complex mixture of hydrocarbons. For stoichiometry, ext{CH}_2 is often used as a simplified representative formula. In the steam reforming of petroleum, hydrogen is produced, albeit less efficiently compared to methane.
The simplified reaction is:\[ ext{CH}_2 + ext{H}_2 ext{O} ightarrow ext{CO} + 2 ext{H}_2 \]
This equation indicates that each mole of ext{CH}_2 reacts with one mole of water to produce 2 moles of hydrogen, equating to 4 grams of hydrogen per mole of petroleum. Understanding this process is crucial for assessing petroleum's role in hydrogen production environments where petroleum is available as a byproduct.

Coal Reaction

Coal, often represented by the formula ext{CH}, is another carbon-based fuel that can react with steam to produce hydrogen. However, its efficiency is lower compared to methane and petroleum.
The relevant chemical equation is:\[ ext{CH} + ext{H}_2 ext{O} ightarrow ext{CO} + ext{H}_2 \]
Here, each mole of coal produces only 1 mole of hydrogen, resulting in a yield of 2 grams of hydrogen per mole of coal. This reflects coal's lesser efficiency in hydrogen production, which is a consideration when opting for cleaner fuel technologies that rely on hydrogen.