Question

Solid \(\mathrm{NH}_{4} \mathrm{SH}\) is introduced into an evacuated flask at \(24^{\circ} \mathrm{C}\). The following reaction takes place: $$\mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g)$$ At equilibrium, the total pressure (for \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{~S}\) taken together) is \(62.21 \mathrm{kPa}\). What is \(K_{p}\) for this equilibrium at \(24^{\circ} \mathrm{C} ?\)

Short answer

The value of Kp for the given equilibrium reaction at 24°C is approximately 967.980 kPa².

Step-by-step solution

We start with an evacuated flask containing only NH4SH solid. There are no gases present initially, so the initial partial pressures of NH3 and H2S are both zero. #Step 2: Determine the change in the partial pressure of gases#

As the reaction proceeds, NH4SH solid decomposes and an equal amount of NH3 and H2S gas are formed. Let the change in partial pressure of NH3 and H2S be 'x'. At equilibrium, the partial pressure of NH3 is x, and the partial pressure of H2S is also x. #Step 3: Write the expression for Kp#

For the given reaction: NH4SH(s) NH3(g) + H2S(g) The expression for Kp at equilibrium is given by: Kp \(= \frac{P_{NH3} \times P_{H2S}}{P_{NH4SH}} \) Since NH4SH is a solid, its partial pressure does not affect the Kp value. Therefore, the expression becomes: Kp \(= P_{NH3} \times P_{H2S} \) #Step 4: Total pressure and partial pressures of gases at equilibrium#

At equilibrium, the total pressure is given as: Total pressure = Partial pressure of NH3 + Partial pressure of H2S We're given that the total pressure at equilibrium is 62.21 kPa. Since we know that at equilibrium both NH3 and H2S have the same partial pressure (x) we can write: 62.21 kPa = x + x #Step 5: Solve for partial pressure 'x'#

Combining the terms for x, we get: 62.21 kPa = 2x Solve for x: x = 31.105 kPa So, the partial pressure of NH3 at equilibrium is 31.105 kPa, and the partial pressure of H2S is also 31.105 kPa. #Step 6: Calculate Kp#

Now, we can use the partial pressures obtained in step 5 to find the Kp value: Kp \(= P_{NH3} \times P_{H2S} \) Kp = (31.105 kPa) × (31.105 kPa) Kp = 967.980 kPa² The value of Kp for the given equilibrium reaction at 24°C is approximately 967.980 kPa².

Key concepts

Equilibrium Constant

In chemical equilibrium, the equilibrium constant (\( K \)) is a critical value that describes the ratio of concentrations or pressures of products to reactants at a given temperature. This constant is crucial because it allows us to predict the direction in which a chemical reaction will proceed under certain conditions. For gaseous reactions, the equilibrium constant can be expressed in terms of partial pressures, known as \( K_{p} \).
For the reaction \(\mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g)\), \( K_{p} \) can be determined using the partial pressures of the products. Importantly, because \( \mathrm{NH}_{4} \mathrm{SH} \) is a solid, its activity is constant and does not appear in the expression for \( K_{p} \).
To calculate \( K_{p} \) for the reaction:

• The partial pressure of \( \mathrm{NH}_{3} \) and \( \mathrm{H}_{2} \mathrm{S} \) at equilibrium must be known.
• At equilibrium, their product gives \( K_{p} \) according to the formula \( K_{p} = P_{NH3} \times P_{H2S} \).

This gives us a way to quantify the balance between reactants and products at equilibrium and predict how shifts in pressure or concentration can affect the system.

Partial Pressure

Partial pressure refers to the pressure exerted by a single gas in a mixture. Each gas in a container contributes to the total pressure according to its mole fraction, which is a reflection of its proportion predominantly seen in gaseous reactions.
In the reaction \( \mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g) \), partial pressures play a fundamental role in determining equilibrium properties. Initially, the partial pressures of \( \mathrm{NH}_{3} \) and \( \mathrm{H}_{2S} \) are zero, as no gases have formed. As \( \mathrm{NH}_{4} \mathrm{SH} \) decomposes, the pressures of these gases increase equally.
The total pressure at equilibrium is the sum of the individual partial pressures. Given that the total pressure is 62.21 kPa and both \( \mathrm{NH}_{3} \) and \( \mathrm{H}_{2} \mathrm{S} \) are present in equal amounts, each has a partial pressure of 31.105 kPa.

• The sum of the partial pressures of all gases equals the total pressure.
• Each substance’s contribution to total pressure is determined by its amount in moles.

Understanding partial pressures is vital in dealing with gaseous equilibria as it affects calculations and predictions of equilibrium constants.

Gaseous Reactions

Gaseous reactions involve substances in the gas phase, and understanding them requires attention to parameters like temperature, pressure, and volume, impacting how reactions reach equilibrium. In a closed system, such as an evacuated flask, gas reactions are particularly sensitive to changes in conditions, and the formation of gases from solids or liquids can drastically change the system dynamics.
Gaseous equilibria are dynamic, meaning molecules of gaseous reactants and products continue to react with each other, even after equilibrium is reached; however, their concentrations remain constant over time.
In the example of \( \mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g) + \mathrm{H}_{2} \mathrm{S}(g) \), gaseous products form from a solid reactant, demonstrating a common theme in chemistry where physical states play a crucial role at equilibrium.

• It is important to note that reactions involving gases can be driven by Le Chatelier’s principle, where changes in pressure will shift the position of equilibrium to counterbalance the change.
• In reactions producing gases, the total pressure is sensitive, as seen in the partial pressures of \( \mathrm{NH}_{3} \) and \( \mathrm{H}_{2} \mathrm{S} \) affecting \( K_{p} \).

Understanding gaseous reactions and their behavior can lead to better predictions and manipulations of chemical systems, offering critical insights into industrial chemical processes.