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Methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), can be produced in industrial plants by reacting carbon dioxide with hydrogen in the presence of a catalyst. Water is the other product. How many volumes of hydrogen are required for each volume of carbon dioxide when each gas is at the same temperature and pressure?

Short Answer

Expert verified
3 volumes of hydrogen are required for each volume of carbon dioxide.

Step by step solution

01

Identify the Reaction Equation

The chemical reaction between carbon dioxide and hydrogen to form methanol and water can be represented as: \( \text{CO}_2 + 3\text{H}_2 \rightarrow \text{CH}_3\text{OH} + \text{H}_2\text{O} \). This equation shows the reactants and products of the reaction.
02

Balance the Chemical Equation

Let's verify if the chemical equation is balanced. We have:- 1 carbon atom on both sides.- 4 hydrogen atoms on both sides (3 from \( \text{H}_2 \) and 1 from methanol).- 2 oxygen atoms on both sides (2 from \( \text{CO}_2 \), 1 in \( \text{CH}_3\text{OH} \) and 1 in \( \text{H}_2\text{O} \)).Therefore, the equation is balanced: \( \text{CO}_2 + 3\text{H}_2 \rightarrow \text{CH}_3\text{OH} + \text{H}_2\text{O} \).
03

Analyze the Stoichiometry of the Balanced Equation

From the balanced equation, 1 mole of \( \text{CO}_2 \) reacts with 3 moles of \( \text{H}_2 \) to produce 1 mole of \( \text{CH}_3\text{OH} \) and water. The ratio of \( \text{H}_2 \) to \( \text{CO}_2 \) is 3:1.
04

Apply Avogadro's Law

Avogadro's law states that equal volumes of gases, at the same temperature and pressure, contain the same number of moles. Hence, the volume ratio of gases at the same temperature and pressure is equivalent to their mole ratio. Therefore, 3 volumes of \( \text{H}_2 \) are required for every 1 volume of \( \text{CO}_2 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Equation Balancing
Balancing a chemical equation is an essential foundational step in understanding chemical reactions. It ensures the law of conservation of mass is obeyed, meaning the number of atoms for each element remains constant throughout the reaction.
To balance a chemical equation, follow these steps:
  • Write down the unbalanced equation.
  • List the number of atoms for each element on both sides of the equation.
  • Adjust coefficients to balance the atoms for each element.
In the methanol production reaction, we start with the equation: \[\text{CO}_2 + 3\text{H}_2 \rightarrow \text{CH}_3\text{OH} + \text{H}_2\text{O}\]By balancing, we confirm that each side of the reaction has 1 carbon atom, 4 hydrogen atoms, and 2 oxygen atoms, maintaining equal elemental count on both sides. This balanced equation tells us the stoichiometric ratio, which is crucial for further calculations.
Avogadro's Law
Avogadro's Law is a simple yet powerful principle in chemistry. It states that equal volumes of gases, at the same temperature and pressure, have the same number of molecules. This law is incredibly useful in converting volume units to moles in gas reactions.In practical terms, suppose you are dealing with a reaction involving gaseous reactants and products. If two gases are at the same conditions of temperature and pressure, you can directly relate their volumes to the number of moles. For the equation in our methanol example, the stoichiometry shows a ratio of 3 volumes of \(\text{H}_2\) for every 1 volume of \(\text{CO}_2\). This direct volume ratio eliminates the need for additional conversion factors, simplifying the calculations involved in chemical processes.
Industrial Methanol Production
Industrial methanol production is a fascinating application of chemical engineering combining chemistry with efficiency. It involves the catalytic reaction of \(\text{CO}_2\) and \(\text{H}_2\) to form methanol, \(\text{CH}_3\text{OH}\), and water. This reaction is crucial in the chemical industry as methanol serves as a precursor for a wide range of chemicals and fuels.Key points in industrial methanol production include:
  • The reaction uses catalysts, often based on copper, to accelerate the reaction and increase yield.
  • Maintaining optimal temperature and pressure conditions is essential for efficient production.
  • Sustainability and resource efficiency are enhanced by using waste carbon dioxide as a feedstock.
Thus, industrial methanol production not only reflects the importance of balanced chemical reactions and Avogadro's principles but also highlights the link between chemical processes and sustainable industrial practices.

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Most popular questions from this chapter

You fill a balloon with helium gas to a volume of \(2.68 \mathrm{~L}\) at \(23^{\circ} \mathrm{C}\) and \(789 \mathrm{mmHg}\). Now you release the balloon. What would be the volume of helium if its pressure changed to \(632 \mathrm{mmHg}\) but the temperature were unchanged?

A 1-liter container is filled with \(2.0\) mol \(\mathrm{Ar}, 2.0 \mathrm{~mol} \mathrm{H}_{2}\), and \(4.0 \mathrm{~mol} \mathrm{Kr}\). Which of the following statements about these gases is false? a. The \(\mathrm{Kr}\) is the densest of the three gases. b. The mole fraction of Ar in the flask is \(0.25\). C. The total pressure in the flask is four times the pressure of the Ar. d. The Ar atoms hit the walls of the flask with the greatest force of the three gases. e. \(\mathrm{H}_{2}\) has the highest rms velocity of the three gases.

An experiment called for \(4.83\) L of sulfur dioxide, \(\mathrm{SO}_{2}\), at \(0^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm} .\) What would be the volume of this gas at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm} ?\)

You have three identical flasks, each containing equal amounts of \(\mathrm{N}_{2}, \mathrm{O}_{2}\), and He. The volume of the \(\mathrm{N}_{2}\) flask is doubled, the \(\mathrm{O}_{2}\) flask volume is halved, and the He flask volume is reduced to one-third of the original volume. Rank the flasks from highest to lowest pressure both before and after the volume is changed and indicate by what factor the pressure has changed.

In a series of experiments, the U.S. Navy developed an undersea habitat. In one experiment, the mole percent composition of the atmosphere in the undersea habitat was \(79.0 \% \mathrm{He}, 17.0 \%\) \(\mathrm{N}_{2}\), and \(4.0 \% \mathrm{O}_{2}\). What will the partial pressure of each gas be when the habitat is \(58.8 \mathrm{~m}\) below sea level, where the pressure is \(6.91\) atm?

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