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In one of Fritz Haber's experiments to establish the conditions required for the ammonia synthesis reaction, pure \(\mathrm{NH}_{3}(\mathrm{g})\) was passed over an iron catalyst at \(901^{\circ} \mathrm{C}\) and 30.0 atm. The gas leaving the reactor was bubbled through 20.00 mL of a HCl(aq) solution. In this way, the \(\mathrm{NH}_{3}(\mathrm{g})\) present was removed by reaction with HCl. The remaining gas occupied a volume of 1.82 L at STP. The \(20.00 \mathrm{mL}\) of \(\mathrm{HCl}(\mathrm{aq})\) through which the gas had been bubbled required \(15.42 \mathrm{mL}\) of \(0.0523 \mathrm{M} \mathrm{KOH}\) for its titration. Another \(20.00 \mathrm{mL}\) sample of the same HCl(aq) through which no gas had been bubbled required \(18.72 \mathrm{mL}\) of \(0.0523 \mathrm{M} \mathrm{KOH}\) for its titration. Use these data to obtain a value of \(K_{\mathrm{p}}\) at \(901^{\circ} \mathrm{C}\) for the reaction \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{g})\)

Step by step solution

01

Calculate the Amount of Reacted Ammonia

First, determine the difference in titration volumes of HCI solution with and without gas bubbling through it. Subtract the volume of KOH solution needed to titrate the HCI when gas was bubbled through from when no gas was bubbled through (18.72 ml - 15.42 ml = 3.3 ml). This difference is due to the reaction of ammonia with HCI. When converted to liters (0.0033 L) and multiplied by the molarity of the KOH (0.0523 mol/L), this gives the amount of reacted ammonia in moles (0.0033 L * 0.0523 mol/L = 0.00017259 mol).

02

Calculate the Pressure of Gases

Next, calculate the partial pressures of nitrogen, hydrogen, and ammonia. The total pressure of the gaseous reaction mixture after ammonia was removed is given as 30 atm. According to the reaction stoichiometry, the molar ratio of nitrogen to hydrogen to ammonia is 1:3:2. So for every mole of nitrogen, there is 3 moles of hydrogen while ammonia is produced as 2 moles. The moles of each gas can be calculated from the measured volume of gas, which is 1.82 L at STP. Using the ideal gas law, at STP 1 mole of any gas has a volume of 22.4 L, hence the quantity of gas left after removal of the ammonia can be calculated (1.82 L / 22.4 L = 0.08125 mol). The pressures of nitrogen, hydrogen, and ammonia can be calculated by multiplying the mole fraction of each (1/4, 3/4, and 0) in the equilibrium reaction mixture times the total pressure (30 atm).

03

Calculate the value of Kp

The final step is to calculate the equilibrium constant, Kp, using the calculated pressures. The expression for the equilibrium constant for the reaction is: Kp = [NH3]^2 / ([N2] * [H2]^3). Given the mole fractions, the pressure of each should be inserted into the equation (Kp = (2 * 0.00017259 * 30)^2 / ((1/4 * 30) * (3/4 * 30)^3). Proceding with these calculation, the value of Kp at 901 degrees Celsius will be found.

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Key Concepts

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

Ammonia Synthesis

Ammonia synthesis is a critical process in chemistry, essential for producing ammonia (NH₃), a compound widely used in fertilizers and various industrial applications. The synthesis process involves combining nitrogen (N₂) and hydrogen (H₂) gases to produce ammonia. The reaction is represented by the balanced equation: \[ \mathrm{N}_2(\mathrm{g}) + 3 \mathrm{H}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{g}) \]This reaction is exothermic, releasing heat and favoring the formation of ammonia under high-pressure and moderate-temperature conditions. However, achieving significant yields of ammonia requires careful manipulation of temperature and pressure alongside catalysts.

In practical terms, ammonia synthesis is vital for sustaining agricultural productivity through enhanced soil fertilization and for creating various other chemical products.

Haber Process

The Haber Process revolutionized the production of ammonia through a method that maximizes efficiency and output. Developed by Fritz Haber in the early 20th century, this process involves reacting nitrogen and hydrogen gases under high pressures (typically 150-200 atm) and temperatures (400-500°C). An iron catalyst is crucial in this setup to increase the rate of reaction, making the process economically viable.

Key components of the Haber Process include:

• High Pressure: The pressure favors the forward reaction, helping to increase ammonia yield, as predicted by Le Chatelier's principle.
• Moderate Temperature: While lower temperatures favor ammonia formation, the reaction rate drops significantly. Therefore, a compromise temperature is chosen.
• Recycling: Unused nitrogen and hydrogen are cycled back into the system to maximize resource efficiency.

Through these methods, the Haber Process became a cornerstone in the mass production of ammonia, fundamentally transforming agriculture and industry.

Iron Catalyst

An iron catalyst plays a pivotal role in the Haber Process, driving the reaction between nitrogen and hydrogen to form ammonia at a feasible rate. It acts to lower the activation energy required for the reaction, increasing the rate at which ammonia is formed without being consumed in the reaction itself.

The choice of iron as a catalyst is primarily due to its effectiveness and abundance, which makes it a cost-effective option. In the setup:

• Iron is often mixed with promoters such as potassium and calcium oxides to enhance its catalytic properties.
• The catalyst surface facilitates the adsorption of nitrogen and hydrogen, allowing them to interact more readily and form ammonia.
• Over time, the catalyst can degrade, necessitating care in maintaining its activity and periodic replacement or regeneration.

Thus, the use of an iron catalyst is integral to the efficiency and success of ammonia synthesis in the Haber Process.