Problem 110 - Chemistry The Science in Context

Question

The following reactions were carried out in a cylinder with a piston. If the external pressure is constant, in which reactions will the volume of the cylinder increase? Assume all reactants and products are gases at the same temperature. a. \(\mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{HCN}(g)+3 \mathrm{H}_{2}(g)\) b. \(\mathrm{H}_{2} \mathrm{S}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{3}(g)\) c. \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) d. \(2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

a) CH₄(g) + NH₃(g) → HCN(g) + 3H₂(g) b) H₂S(g) + 2O₂(g) → H₂O(g) + SO₃(g) c) H₂(g) + Cl₂(g) → 2HCl(g) d) 2NO₂(g) → 2NO(g) + O₂(g) Answer: The volume of the cylinder will increase in reactions a and d.

Step 1: Reaction a: \(\mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{HCN}(g)+3\mathrm{H}_{2}(g)\)

On the reactant side, we have 1 molecule of CH\(_4\) and 1 molecule of NH\(_3\) which sum up to 2 gas molecules. On the product side, we have 1 molecule of HCN and 3 molecules of H\(_2\), which sum up to 4 gas molecules. Since the number of gas molecules increases (2 to 4), the volume of the cylinder will increase.

Step 2: Reaction b: $\mathrm{H}_{2} \mathrm{S}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{3}(g)\(

On the reactant side, we have 1 molecule of H\)_2\(S and 2 molecules of O\)_2\(, which sum up to 3 gas molecules. On the product side, we have 1 molecule of H\)_2\(O and 1 molecule of SO\)_3$, which sum up to 2 gas molecules. Since the number of gas molecules decreases (3 to 2), the volume of the cylinder will not increase.

Step 3: Reaction c: \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\)

On the reactant side, we have 1 molecule of H\(_2\) and 1 molecule of Cl\(_2\), which sum up to 2 gas molecules. On the product side, we have 2 molecules of HCl, which is also a total of 2 gas molecules. Since the number of gas molecules remains the same (2 to 2), the volume of the cylinder will not increase.

Step 4: Reaction d: \(2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

On the reactant side, we have 2 molecules of NO\(_2\), which sum up to 2 gas molecules. On the product side, we have 2 molecules of NO and 1 molecule of O\(_2\), which sum up to 3 gas molecules. Since the number of gas molecules increases (2 to 3), the volume of the cylinder will increase. In conclusion, the volume of the cylinder will increase in reactions a and d.

Key Concepts

Cylinder Volume Change

Imagine a cylinder with a movable piston. The volume inside changes with the number of gas molecules involved in a reaction. If you have more gas molecules on the product side compared to the reactant side, the piston moves up and the volume increases. This is simply because gases expand to fill their container.

Let's look at how this works in some chemical reactions:

• Reaction a: The number of gas molecules increases from 2 to 4, causing the cylinder's volume to increase.
• Reaction b: The number of gas molecules decreases from 3 to 2, leading to no increase in volume.
• Reaction c: The number of gas molecules stays the same, so the volume remains constant.
• Reaction d: The number of gas molecules increases from 2 to 3, resulting in an increased volume.

Reaction Stoichiometry

Stoichiometry helps us understand and predict how much products or reactants in a chemical reaction are needed or produced. It relies on balancing equations, which ensures that the number of each type of atom is the same on both sides of the equation.

In our exercise, stoichiometry allows us to determine the number of gas molecules in reactions. By comparing the amount of gas on each side of the reactions, we can predict changes to cylinder volume.

In some cases:

• In Reaction a, we predict the cylinder volume expands because a greater number of gas molecules form.
• In Reaction b, fewer gas molecules are produced, so the volume decreases or stays the same.

Gas Laws

Gas laws help us understand how gases behave under different conditions, including changes in pressure, volume, and temperature. The Ideal Gas Law, for instance, is a key tool:\[ PV = nRT \]Where:

• P is pressure
• V is volume
• n is the number of moles of gas
• R is the gas constant
• T is temperature

When the number of gas moles changes, volume changes too, given constant pressure and temperature. This occurs in reactions like a and d from our exercise, where the volume of the cylinder changes while maintaining constant external conditions.

Chemical Reactions Analysis

Analyzing chemical reactions involves assessing many factors, such as energy changes, reaction rates, and equilibrium, in addition to volume changes.

For gas reactions within a cylinder:

• Look at the total number of reactants and products as gas molecules. More gas molecules in products compared to reactants indicate volume expansion.
• Understanding the type of reaction (combination, decomposition) can also offer insights into the molecule count shifts.

In the exercise's reactions:

• In Reaction a, a mix of molecules leads to more gaseous products and increased volume.
• In Reaction d, decompose and combine processes yield more gas molecules, causing volume expansion.

Such analysis provides a clear understanding of how reaction dynamics influence practical changes in systems.