Problem 90 - Chemistry: An Atoms-Focused Approach

Question

Jupiter's Atmosphere Ammonium hydrogen sulfide \(\left(\mathrm{NH}_{4} \mathrm{SH}\right)\) has been detected in the atmosphere of Jupiter, where it probably exists in equilibrium with ammonia and hydrogen sulfide: $$ \mathrm{NH}_{1} \mathrm{SH}(j) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g) $$ The value of \(K_{p}\) for the reaction at \(24^{\circ} \mathrm{C}\) is \(0.126 .\) Suppose a sealed flask contains an equilibrium mixture of \(\mathrm{NH}_{4} \mathrm{SH}\), \(\mathrm{NH}_{3},\) and \(\mathrm{H}_{2} \mathrm{S}\). At equilibrium, the partial pressure of \(\mathrm{H}_{2} \mathrm{S}\) is 0.355 atm. What is the partial pressure of \(\mathrm{NH}_{3} ?\)

Step-by-Step Solution

Answer

Answer: The partial pressure of ammonia (NH3) at equilibrium is approximately 0.355 atm.

Step 1: Write the reaction and the expression for Kp

We have the reaction: $$ \mathrm{NH}_{4} \mathrm{SH}(j) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g) $$ And the expression for Kp is: $$ K_p = \frac{P_{NH_3} \times P_{H_2S}}{P_{NH_4SH}} $$

Step 2: Find the pressure of NH3 at equilibrium

We are given the equilibrium constant, Kp, value as \(0.126\) and the partial pressure of \(\mathrm{H}_{2} \mathrm{S}\) at equilibrium as \(0.355\ \mathrm{atm}\). Now, let the partial pressure of \(\mathrm{NH}_{3}\) be \(P_{NH_3}\). Since \(\mathrm{NH}_{4} \mathrm{SH}\) does not contribute to the pressure, we can assume its partial pressure as 1. Then, the expression for Kp becomes: $$ 0.126 = \frac{P_{NH_3} \times 0.355}{1} $$

Step 3: Calculate the partial pressure of NH3

To find the partial pressure of NH3, we solve for \(P_{NH_3}\): $$ P_{NH_3} = \frac{0.126}{0.355} $$

Step 4: Determine the partial pressure of NH3

Now, calculate the partial pressure: $$ P_{NH_3} = \frac{0.126}{0.355} \approx 0.355 \mathrm{atm} $$ At equilibrium, the partial pressure of ammonia (NH3) is approximately \(0.355\ \mathrm{atm}\).

Key Concepts

Ammonium Hydrogen Sulfide

Ammonium hydrogen sulfide, often written as \( \text{NH}_4\text{SH} \), is a compound that plays an interesting role in chemistry, and specifically in the context of Jupiter's atmosphere. It is a combination of ammonia (\( \text{NH}_3 \)) and hydrogen sulfide (\( \text{H}_2\text{S} \)). This compound is significant for several reasons:

• It can decompose into ammonia and hydrogen sulfide, which are both gases at certain conditions.
• This decomposition reaction is central to the equilibrium process discussed in Jupiter’s atmosphere.
• The study of \( \text{NH}_4\text{SH} \) and its reactions help researchers understand atmospheric processes and conditions.

Understanding how it interacts within an atmosphere, especially one as complex as Jupiter’s, helps scientists learn about pressure and temperature conditions present on the planet. This compound thus acts as a component in modeling the planet's chemical dynamics.

Partial Pressure

The concept of partial pressure is crucial in understanding gas mixtures. Each gas in a mixture contributes to the total pressure exerted by the gases. In our context, it refers to:

• The pressure that ammonia (\( \text{NH}_3 \)) exerts alone in the mixture with other gases.
• The pressure that hydrogen sulfide (\( \text{H}_2\text{S} \)) exerts alone in the mixture.

Partial pressure can be thought of as the pressure a single gas would exert if it occupied the total volume by itself. This idea is used heavily in chemical equilibrium calculations. The pressures of ammonia and hydrogen sulfide are part of the equilibrium reaction, where their partial pressures together determine the conditions in the sealed flask example.The equilibrium constant \( K_p \) relates these partial pressures, making partial pressure calculations fundamental for solving equilibrium problems.

Jupiter's Atmosphere

Exploring Jupiter's atmosphere reveals a fascinating mixture of gases, different from Earth's. The atmosphere contains compounds such as ammonium hydrogen sulfide, ammonia, and hydrogen sulfide.

• This atmosphere is mainly composed of hydrogen and helium, but these additional compounds add complexity to its composition.
• The behavior of ammonium hydrogen sulfide and its decomposition involving ammonia and hydrogen sulfide provides insight into the atmospheric chemistry.

Studying these reactions helps scientists to understand the temperature and pressure conditions of Jupiter’s atmosphere. These factors are responsible for phenomena such as cloud formations and potentially, the presence of certain weather patterns on Jupiter. The equilibrium involving \( \text{NH}_4\text{SH} \) is just one of many reactions that occur in this dynamic environment, showcasing the richly diverse chemical interactions present.

Equilibrium Constant

The equilibrium constant, symbolized as \( K_p \) when dealing with gases, is a fundamental aspect of chemical reactions at equilibrium. It provides a numerical value that helps predict the proportions of reactants and products at equilibrium:

• For the decomposition of ammonium hydrogen sulfide in the atmosphere, \( K_p \) represents the ratio of the partial pressures of ammonia and hydrogen sulfide.
• The given \( K_p \) value of 0.126 is used to determine the equilibrium state under the specific conditions provided.

The significance of \( K_p \) lies in its ability to indicate the favorability of the reaction in terms of products or reactants. A small value (like 0.126) suggests that, under equilibrium conditions, there are more reactants than products. Understanding \( K_p \) thus provides insights into reaction behavior and helps in predicting the outcome of a chemical process, such as those taking place in celestial atmospheres like that of Jupiter.