Problem 103 - Chemistry: An Atoms-Focused Approach

Question

The following reactions are carried out in sealed containers. Will the total pressure after each reaction is complete be greater than, less than, or equal to the total pressure before the reaction? Assume all reactants and products are gases at the same temperature. a. \(\mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{NO}_{2}(g) \rightarrow 3 \mathrm{NO}(g)+2 \mathrm{O}_{2}(g)\) b. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) c. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

Answer: For Reaction a, the total pressure after the reaction will be greater than before the reaction due to an increase in the number of gas moles. For Reaction b, the total pressure after the reaction will be less than before the reaction due to a decrease in the number of gas moles. For Reaction c, the total pressure after the reaction will be greater than before the reaction due to an increase in the number of gas moles.

Step 1: Reaction a: Counting gas moles before and after the reaction.

Before the reaction, there is 1 mole of N₂O₅(g) and 1 mole of NO₂(g), giving a total of 2 moles of gas. After the reaction, there are 3 moles of NO(g) and 2 moles of O₂(g), giving a total of 5 moles of gas.

Step 2: Reaction a: Comparing gas moles before and after the reaction.

Since the number of gas moles increases from 2 to 5, the total pressure after the reaction will be greater than before the reaction.

Step 3: Reaction b: Counting gas moles before and after the reaction.

Before the reaction, there are 2 moles of SO₂(g) and 1 mole of O₂(g), giving a total of 3 moles of gas. After the reaction, there are 2 moles of SO₃(g), which is the only gas present.

Step 4: Reaction b: Comparing gas moles before and after the reaction.

Since the number of gas moles decreases from 3 to 2, the total pressure after the reaction will be less than before the reaction.

Step 5: Reaction c: Counting gas moles before and after the reaction.

Before the reaction, there is 1 mole of C₃H₈(g) and 5 moles of O₂(g), giving a total of 6 moles of gas. After the reaction, there are 3 moles of CO₂(g) and 4 moles of H₂O(g), giving a total of 7 moles of gas.

Step 6: Reaction c: Comparing gas moles before and after the reaction.

Since the number of gas moles increases from 6 to 7, the total pressure after the reaction will be greater than before the reaction.

Key Concepts

Reaction Stoichiometry

In chemical reactions, stoichiometry allows us to predict how much reactant or product will be present. It’s like a recipe in cooking where you know exactly how much of each ingredient is needed. For the exercise provided, stoichiometry helps us determine how the number of gas molecules changes during a reaction.
Stoichiometry relies on balanced chemical equations. A balanced equation ensures that the same number of each atom is on both sides of the reaction. To use stoichiometry:

• Identify the reactants and products in the chemical reaction.
• Balance the chemical equation to conform to the Law of Conservation of Mass.
• Determine the molar ratio of reactants and products, as demonstrated in the balanced equation.

This molar ratio is key when determining the total number of gas moles before and after reaction, which can then help predict changes in parameters like total pressure.

Mole Concept

The mole concept is a vital tool in chemistry that links the mass of substances to the number of atoms or molecules. A mole is simply a big number (Avogadro's number, around 6.022 x 10^{23}) to express amounts of a chemical substance. Moles are used because:

• They provide a way to count particles by weighing them.
• They allow us to use straightforward calculations rather than dealing with unmanageably large numbers.

For the reactions in the exercise, counting moles of gases before and after will help evaluate changes in total pressure. Using the mole concept, chemists can break down reactions into understandable segments, predicting the amount of reactants required or products produced.

Pressure and Volume

The relationship between pressure, volume, temperature, and the number of moles of gas is explained by the ideal gas law, given by the equation: \[ PV = nRT, \]where \( P \) stands for pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.An important principle seen in this exercise is how the number of gas moles affects pressure.

• More gas moles generally mean higher pressure, assuming constant volume and temperature.
• Conversely, fewer gas moles typically result in lower pressure.

This is because more molecules create more impacts against the container walls, increasing pressure. In the chemical reactions discussed, observing the change in mole count before and after reaction helps predict whether pressure will increase or decrease, assuming volume and temperature are consistent.