- Identify the number of moles of gas on the reactant side: \(2 + 1 = 3\) moles.
- Identify the number of moles of gas on the product side: 2 moles.
- Apply Le Chatelier's Principle: increasing pressure favors the side with fewer moles of gas.
- Since 2 moles < 3 moles, increasing the pressure shifts the equilibrium towards the product side, favoring the forward reaction. The correct choice is (a). \(\boxed{a}\)
Explanation
- Analyzing the Equilibrium System
We consider the chemical equation for the synthesis of water:
\[2 H_2(g) + O_2(g) \rightleftharpoons 2 H_2 O(g)\]
The system is in a state of chemical equilibrium. We need to determine the effect of an increase in the system's pressure on this equilibrium. Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions (such as pressure, temperature, or concentration), the system will shift its equilibrium position to counteract the effect of the disturbance.
- Applying Le Chatelier's Principle
To apply Le Chatelier's Principle regarding pressure, we count the total number of moles of gas on each side of the balanced chemical equation.
- On the reactant side (left side), there are 2 moles of \(H_2(g)\) and 1 mole of \(O_2(g)\), giving a total of \(2 + 1 = 3\) moles of gas.
- On the product side (right side), there are 2 moles of \(H_2 O(g)\), giving a total of 2 moles of gas.
When the pressure of a system at equilibrium is increased, the system will shift to favor the reaction that produces fewer moles of gas in order to decrease the pressure back towards its original state. Conversely, if the pressure is decreased, the system will shift to favor the direction that produces more moles of gas.
- Determining the Effect of Pressure Increase
Comparing the two sides:
- Reactants: 3 moles of gas.
- Products: 2 moles of gas.
Since the product side has fewer moles of gas (2 moles) than the reactant side (3 moles), increasing the pressure will favor the forward reaction, which converts 3 moles of reactants into 2 moles of products, thereby reducing the total pressure within the system. Therefore, increasing the pressure favors the formation of water. This corresponds to option (a).
Examples
In industrial chemical engineering, Le Chatelier's Principle is vital for optimizing production. For instance, in the Haber process for ammonia synthesis, \(\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)\), the system starts with 4 moles of gas on the reactant side and results in 2 moles on the product side. By increasing the pressure, engineers shift the equilibrium forward, effectively increasing the yield of ammonia. Understanding this principle allows for the design of systems that maximize the efficiency of chemical reactions by manipulating physical conditions like pressure and temperature.