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In each of the following gas-phase reactions, determine whether the total pressure at the end of the reaction (carried out in a sealed, rigid vessel) will be greater than, less than, or equal to the total pressure at the beginning. Assume all reactants and products are gases at the same temperature. a. \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) b. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) c. \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\)

Short Answer

Expert verified
Answer: For Reaction (a), the pressure at the end is equal to the beginning. For Reaction (b), the pressure at the end is greater than the beginning. For Reaction (c), the pressure at the end is lesser than the beginning.

Step by step solution

01

Identify the reactants and products

In reaction(a), the reactants are \(\mathrm{H}_{2}(g)\) and \(\mathrm{Cl}_{2}(g)\), and the product is \(2 \mathrm{HCl}(g)\).
02

Analyze the number of gas moles

On the reactants' side, we have 1 mole of \(\mathrm{H}_{2}(g)\) and 1 mole of \(\mathrm{Cl}_{2}(g)\), so the total moles are 1 + 1 = 2. On the products' side, we have 2 moles of \(\mathrm{HCl}(g)\).
03

Compare the number of gas moles before and after the reaction

Since both the reactants and products have the same number of moles (2), the pressure at the end of the reaction is equal to the pressure at the beginning. #Reaction (b)#
04

Identify the reactants and products

In reaction(b), the reactants are \(4 \mathrm{NH}_{3}(g)\) and \(5 \mathrm{O}_{2}(g)\), and the products are \(4 \mathrm{NO}(g)\) and \(6\mathrm{H}_{2} \mathrm{O}(g)\).
05

Analyze the number of gas moles

On the reactants' side, we have 4 moles of \(\mathrm{NH}_{3}(g)\) and 5 moles of \(\mathrm{O}_{2}(g)\), so the total moles are 4 + 5 = 9. On the products' side, we have 4 moles of \(\mathrm{NO}(g)\) and 6 moles of \(\mathrm{H}_{2} \mathrm{O}(g)\), so the total moles are 4+6=10.
06

Compare the number of gas moles before and after the reaction

Since the total number of moles after the reaction (10) is greater than the total number of moles before the reaction (9), the pressure at the end of the reaction is greater than the pressure at the beginning. #Reaction (c)#
07

Identify the reactants and products

In reaction(c), the reactants are \(2 \mathrm{NO}(g)\) and \(\mathrm{O}_{2}(g)\), and the product is \(2 \mathrm{NO}_{2}(g)\).
08

Analyze the number of gas moles

On the reactants' side, we have 2 moles of \(\mathrm{NO}(g)\) and 1 mole of \(\mathrm{O}_{2}(g)\), so the total moles are 2 + 1 = 3. On the products' side, we have 2 moles of \(\mathrm{NO}_{2}(g)\).
09

Compare the number of gas moles before and after the reaction

Since the total number of moles after the reaction (2) is lower than the total number of moles before the reaction (3), the pressure at the end of the reaction is lesser than the pressure at the beginning.

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Key Concepts

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

Gas Moles
In chemical reactions involving gases, the concept of gas moles is critical. Each mole corresponds to a specific number of gas particles, known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles. When examining gas-phase reactions, counting the number of moles of reactants and products can help predict changes in pressure.

Consider the reaction given in the exercise, \(\mathrm{H}_{2}(g) + \mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\). Here, the moles of reactants and the moles of products are equal (2 moles each). This means there is no change in the number of gas particles present, which implies that the total pressure remains constant, assuming the reaction occurs at constant temperature and volume.

To determine how gas moles affect a reaction, remember the following:
  • Count the moles on both sides of the equation.
  • Compare the totals before and after the reaction to predict pressure changes.
Pressure Change
Pressure changes during a chemical reaction can provide valuable insight into the reaction dynamics. In a sealed, rigid vessel, pressure changes are directly related to the number of gas moles present. This relationship arises from the Ideal Gas Law, \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the gas constant, and \(T\) is temperature.

When moles of gas increase, so does the pressure, given constant volume and temperature. For example, in the reaction \(4\mathrm{NH}_{3}(g) + 5\mathrm{O}_{2}(g) \rightarrow 4\mathrm{NO}(g) + 6\mathrm{H}_{2} \mathrm{O}(g)\), the moles increase from 9 to 10. Consequently, the pressure rises as well.

In contrast, if the number of moles decreases, pressure also reduces. This is evident in the reaction \(2\mathrm{NO}(g) + \mathrm{O}_{2}(g) \rightarrow 2\mathrm{NO}_{2}(g)\), where moles drop from 3 to 2. Hence, the pressure is less at the end of the reaction compared to the beginning.

In summary, remember that increases in gas moles often lead to higher pressure, while decreases result in lower pressure, assuming constant temperature and volume.
Chemical Equilibria
Chemical equilibria in gas-phase reactions refer to the state where reactants and products exist in a balanced condition without further net change. When dealing with equilibria, both moles and pressure play significant roles.

During a reversible reaction, the forward and reverse reactions occur at the same rate at equilibrium, resulting in stable concentrations of moles. Given the reactions in the example, once equilibrium is achieved, the moles of gases would remain constant at that state, indicating stabilized pressure.

However, conditions can influence the position of the equilibrium. Factors include:
  • Temperature: Often affects reaction rates and equilibria positioning.
  • Volume changes: May shift equilibria in reactions involving gas moles.
  • Pressure changes: In reactions where gas moles vary, equilibria can shift to favor fewer gas moles under pressure increase, according to Le Chatelier's Principle.
Understanding equilibria helps predict how a reaction will respond to various stresses, such as changes in pressure, which can alter the balance of moles and the direction of the reaction adjustment.

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