Problem 118 - Chemistry Matter and Change

Question

Explain how the percent yield of ammonia is affected by pressure and temperature.

Step-by-Step Solution

Answer

The percent yield of ammonia in the Haber process is affected by pressure and temperature according to Le Chatelier's principle. An increase in pressure favors the formation of ammonia, as the reaction shifts towards the side with fewer moles of gas, resulting in an increased percent yield. On the other hand, since the reaction is exothermic, an increase in temperature causes the equilibrium to shift towards the reactants, leading to a decreased percent yield of ammonia. Conversely, a decrease in temperature favors the formation of ammonia, thus increasing its percent yield.

Step 1: Understand the Haber process

The Haber process is the synthesis of ammonia from nitrogen and hydrogen gases. The balanced equation for the reaction is: \[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \] This reaction is exothermic, meaning it releases heat, and has a decrease in the number of moles when moving from reactants to products.

Step 2: Le Chatelier's principle

To analyze how the yield of ammonia is affected by pressure and temperature, we can use Le Chatelier's principle. This principle states that when a chemical system at equilibrium is disturbed by a change in pressure, temperature, or concentration, the system will shift its position in a direction to counteract the change.

Step 3: Effect of pressure on percent yield

In the Haber process, the total number of moles of reactants is 4 (1 mole of N2 and 3 moles of H2), whereas the total number of moles of the product is 2 (2 moles of NH3). According to Le Chatelier's principle, the system will respond to an increase in pressure by shifting the equilibrium position to the side with fewer moles, which is the product side (ammonia). Therefore, an increase in pressure will result in an increased percent yield of ammonia.

Step 4: Effect of temperature on percent yield

As mentioned earlier, the Haber process is exothermic, meaning it releases heat energy. According to Le Chatelier's principle, an increase in temperature will cause the system to shift its equilibrium position to the endothermic side (the side that absorbs heat) to counteract the effect of increased temperature. In this case, the endothermic side is the side with the reactants (nitrogen and hydrogen). Therefore, an increase in temperature will cause the equilibrium position to shift towards the reactants, resulting in a decreased percent yield of ammonia. Conversely, a decrease in temperature favors the exothermic side (the side that releases heat), resulting in an increased percent yield of ammonia. In summary:

Step 5: Pressure effect on ammonia yield

An increase in pressure leads to an increased percent yield of ammonia, while a decrease in pressure leads to a decreased percent yield.

Step 6: Temperature effect on ammonia yield

An increase in temperature leads to a decreased percent yield of ammonia, while a decrease in temperature leads to an increased percent yield.

Key Concepts

Percent Yield

In chemistry, the percent yield is an important measure of the efficiency of a chemical reaction. It tells us what percentage of the theoretical yield (the maximum amount of product that could be formed from the given reactants) was actually produced in practice. The formula for percent yield is:\[\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%\]In the Haber process, the percent yield of ammonia is critical. It gives chemists an idea of how well the reaction is progressing under specific conditions, like pressure and temperature. Knowing and optimizing the percent yield helps increase the efficiency of industrial processes, which is vital for producing large quantities of chemicals economically.

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept in chemical equilibrium. It explains how a system at equilibrium responds to external changes, such as pressure, temperature, or concentration shifts. When a change is applied to a system at equilibrium, the system adjusts in a way that counteracts the change. This helps the system restore a new equilibrium. For instance, in the Haber process:

• If pressure is increased, the system shifts toward fewer moles of gas, therefore favoring ammonia formation.
• If the temperature rises, the system shifts to absorb heat, favoring the reactants.

Le Chatelier's principle is vital for engineers and chemists. It guides them in adjusting conditions to maximize product yields and optimize industrial reactions.

Pressure and Temperature Effects

Pressure and temperature are crucial factors influencing chemical reactions, especially in gas-producing reactions like the Haber process.

• Pressure Effects: In the Haber process, increasing pressure shifts equilibrium towards forming ammonia. This occurs because the reaction decreases the total number of gas molecules, reducing volume and favoring the side with fewer molecules, which is ammonia.

Reducing pressure has the opposite effect, shifting equilibrium towards the reactants and decreasing ammonia yield.

• Temperature Effects: The reaction is exothermic, so increasing temperature makes the system favor the side that absorbs heat — the reactants. Thus, higher temperatures reduce ammonia yield.

Low temperature, conversely, enhances the yield by favoring the exothermic reaction, but too low a temperature can slow the reaction rate down, making it inefficient. Both pressure and temperature need careful balancing to achieve optimal ammonia production. Adjustments ensure the process remains economically viable while ensuring maximum yield.