Problem 15 - Chemistry and Chemical Reactivity

Question

The reaction of methane and water is one way to prepare hydrogen for use as a fuel: $$\mathrm{CH}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g})$$ If you begin with 995 g of \(\mathrm{CH}_{4}\) and \(2510 \mathrm{g}\) of water, (a) Which reactant is the limiting reactant? (b) What is the maximum mass of \(\mathrm{H}_{2}\) that can be prepared? (c) What mass of the excess reactant remains when the reaction is completed?

Step-by-Step Solution

Answer

(a) CH₄ is the limiting reactant. (b) Max mass of H₂ is 376.87 g. (c) 1390.08 g of H₂O remains.

Step 1: Calculate the Moles of CH₄ and H₂O

First, calculate the moles of the reactants. The molar mass of methane (CH₄) is 16.04 g/mol, and for water (H₂O), it is 18.02 g/mol.Moles of CH₄: \[ \text{moles of CH}_4 = \frac{995 \text{ g}}{16.04 \text{ g/mol}} \approx 62.06 \text{ moles} \]Moles of H₂O:\[ \text{moles of H}_2\text{O} = \frac{2510 \text{ g}}{18.02 \text{ g/mol}} \approx 139.29 \text{ moles} \]

Step 2: Determine the Limiting Reactant

Now, we need to use the chemical equation to find the limiting reactant. The balanced equation is:\[ \text{CH}_4 + \text{H}_2\text{O} \rightarrow \text{CO} + 3 \text{H}_2 \]According to the equation, 1 mole of CH₄ reacts with 1 mole of H₂O. Compare the moles to find the limiting reactant:Since we have 62.06 moles of CH₄ and 139.29 moles of H₂O, CH₄ is the limiting reactant because we need 1 mole of CH₄ for each mole of H₂O, and we don't have enough CH₄ to react with all the H₂O.

Step 3: Calculate the Maximum Mass of H₂

From the reaction, 1 mole of CH₄ produces 3 moles of H₂. Therefore, 62.06 moles of CH₄ will produce:\[ \text{moles of H}_2 = 3 \times 62.06 = 186.18 \text{ moles} \]The molar mass of H₂ is 2.02 g/mol. Hence, the mass of H₂ produced is:\[ \text{mass of H}_2 = 186.18 \text{ moles} \times 2.02 \text{ g/mol} \approx 376.87 \text{ g} \]

Step 4: Calculate the Remaining Mass of Excess Reactant (H₂O)

Since CH₄ is the limiting reactant, all 62.06 moles are consumed. This will consume 62.06 moles of H₂O. We began with 139.29 moles of water, so the remaining moles of H₂O are:\[ \text{remaining moles of H}_2\text{O} = 139.29 - 62.06 = 77.23 \text{ moles} \]Convert the remaining moles back to mass:\[ \text{mass of remaining H}_2\text{O} = 77.23 \text{ moles} \times 18.02 \text{ g/mol} \approx 1390.08 \text{ g} \]

Key Concepts

Stoichiometry

Stoichiometry is an essential concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's like a recipe in cooking, indicating how much of each ingredient you need to make a certain amount of food. In a chemical equation, stoichiometry involves understanding and using the coefficients to balance the chemical equation. This helps chemists determine the amount of each substance required or produced.

For instance, in the reaction given, \(\text{CH}_4 + \text{H}_2\text{O} \rightarrow \text{CO} + 3 \text{H}_2\), the coefficients tell you that one molecule of methane reacts with one molecule of water to produce one molecule of carbon monoxide and three molecules of hydrogen. When solving problems, stoichiometry involves converting masses to moles using molar masses, which is why we calculate the moles first when determining the limiting reactant.

By understanding stoichiometry, you can predict how much of a product is formed from given reactants, or determine how much of the reactants are needed to form a desired amount of product.

Chemical Reactions

Chemical reactions are processes where substances, the reactants, transform into new substances, known as products. They are all around us and key to countless processes in our daily lives, such as burning fuels, cooking food, and even in our body’s metabolism. The reaction in the exercise between methane and water is an example of a simple but significant reaction known as steam reforming.

In a balanced chemical equation, each side of the reaction obeys the law of conservation of mass, meaning atoms are neither created nor destroyed, just rearranged. For the given equation \(\text{CH}_4 + \text{H}_2\text{O} \rightarrow \text{CO} + 3 \text{H}_2\), this balance ensures that the same number of each type of atom is present on both sides of the equation.

• Energy changes occur during these reactions; they can be either exothermic (release energy) or endothermic (absorb energy).
• The conditions such as temperature, pressure, and presence of a catalyst can affect the rate and outcome of a reaction.

By understanding the principle of chemical reactions, one can effectively predict and control the results of chemical processes.

Hydrogen Production

Hydrogen is an important element used as a clean fuel, as its combustion in air produces water, not carbon emissions. One industrial method of producing hydrogen is through the reaction of hydrocarbons with water in a process called steam reforming. In the exercise, methane reacts with steam to produce hydrogen and carbon monoxide.

This reaction is significant because hydrogen is used in various industries for refining processes, as a fuel in fuel cells, and in the manufacture of fertilizers. The production process requires careful monitoring of conditions to optimize yield and efficiency. Steam reforming of methane not only produces hydrogen efficiently but also leverages natural gas, a relatively abundant resource.

• Hydrogen as a fuel holds potential for clean energy technology, but challenges such as storage and transportation remain.
• The reaction efficiency plays a vital role in determining the scalability of hydrogen as a sustainable energy source.

Understanding this reaction helps in evaluating its role in the future of energy production.