Question

Which of the following reaction will be favoured at low pressure: (a) \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3}\) (b) \(\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\) (c) \(\mathrm{PCl}_{5} \rightleftharpoons \mathrm{PCl}_{3}+\mathrm{Cl}_{2}\) (d) \(\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}\)

Short answer

Reaction (c) is favored at low pressure.

Step-by-step solution

Analyzing the Change in Moles

For each reaction, calculate the change in the number of moles of gas. This can be determined from the coefficients in the balanced equation. For reaction (a), reactants contain 1 mole of \( ext{N}_2\) and 3 moles of \( ext{H}_2\) giving a total of 4 moles, and the product contains 2 moles of \( ext{NH}_3 \), resulting in a decrease of 2 moles. For reaction (b), both reactants and products have 2 moles, so the change is 0. For reaction (c), \( ext{PCl}_5 \) has 1 mole and the products have 2 moles, so there is an increase of 1 mole. For reaction (d), both sides of the equation have 2 moles, resulting in no change in moles.

Applying Le Chatelier's Principle

Le Chatelier's Principle states that a system at equilibrium will adjust to counteract any changes in conditions. A decrease in pressure will favor the reaction that produces more moles of gas, as the system will shift to increase pressure. Thus, reactions that result in an increase in moles of gas will be favored at low pressure.

Identifying the Reaction Favored at Low Pressure

Among the reactions given, only reaction (c), \( ext{PCl}_5 ightarrow ext{PCl}_3 + ext{Cl}_2 \), shows an increase in the number of moles of gas from reactants to products (from 1 to 2 moles). This increase makes it the reaction that will be favored when there is a decrease in pressure as it helps in increasing the pressure by producing more gas moles.

Key concepts

Mole Change Calculation

To understand which reaction will be favored under specific conditions, you first need to analyze the change in the number of moles. The number of moles in a balanced chemical equation can greatly influence the reaction's behavior under varying conditions such as pressure. To calculate the change in moles, examine the coefficients of the reactants and products in the chemical equation:

• For reaction (a): There are 4 total moles of reactants (2 for \(\mathrm{N}_2\) and 3 for \(\mathrm{H}_2\)) and 2 moles of product (\(\mathrm{NH}_3\)), resulting in a decrease of 2 moles.
• In reaction (b): Both the reactants and products have 2 moles, so there is no change in the moles (0 mole change).
• For reaction (c): You start with 1 mole of \(\mathrm{PCl}_5\) and end with 2 moles in total for \(\mathrm{PCl}_3\) and \(\mathrm{Cl}_2\), which means an increase of 1 mole.
• Reaction (d): Similarly shows no change in moles, initially having and ending with 2 moles.

Recognizing whether there is an increase or decrease in moles can help predict the direction a reaction might shift when external conditions are altered.

Reaction Equilibrium

Reaction equilibrium occurs when the forward and reverse reactions proceed at the same rate. At this point, the concentrations of reactants and products remain constant. But, dynamic changes in concentration can occur if the system's conditions are altered. This is where Le Chatelier's Principle comes into play. Le Chatelier's Principle suggests how a reaction will change to counteract changes in concentration, temperature, or pressure. Understanding equilibrium helps in predicting how a change in conditions, like pressure, affects the direction of the reaction. For instance, if pressure is decreased, the system will move in a direction that increases pressure, usually by forming more gas molecules if the number of moles allows for such a shift. In the exercise provided, reaction (c) shows an increase in the number of moles of products, indicating that it would be favored when the pressure is decreased. This ability to predict changes is essential for controlling reactions in industrial processes and laboratory settings.

Pressure Effect on Equilibrium

Pressure changes have a specific impact on reactions involving gases. According to Le Chatelier’s Principle, if the pressure is decreased, the equilibrium will shift towards the side of the reaction that produces more moles of gas. This is because increasing the number of gas molecules can help raise the pressure back to its original state. Consider the following:

• For reaction (a), a decrease in moles suggests it will not be favored at low pressure.
• Reaction (b) and (d) exhibit no mole change, implying they remain unaffected by pressure changes.
• Reaction (c), however, results in an increase from 1 mole to 2 moles, indicating it will be most favored under reduced pressure conditions, as more gas is produced.

Recognizing the effects of pressure on equilibrium is instrumental for strategic manipulation of chemical reactions, essential in both research and industrial chemical processes.